Combined Transcripts: Course

V0.0_Intro [BRIAN] Hello and welcome to the ANU edX course on exoplanets. My name is Brian Schmidt, and I'm an astronomer here at the Australian National University.

I'm normally thought of someone who studies cosmology, the universe on its largest scales, but I also work in the field of exoplanets through a program known as the HAT South telescope network, where we're out searching for going around nearby stars.

[PAUL] And I'm Paul Francis, I'm the other lecturer in this course. My interest in exoplanets comes from the study of comets, which occur both in our and in other solar systems. but I also do work on giant black holes and the origin of the universe.

[ BRIAN] So exoplanets and the study of the exoplanets is arguably one of the exciting topics in today, it has come from nowhere to being a science that is literally lighting up humanity and discovery.

[PAUL] 15 years ago we did not know about any planets around stars other than our own. Now there are over a thousand, and not a week goes by without some new and wierd discovery being in the papers about some strange or something else going on out there.

[BRIAN] and in this course we're going to try to bring you up to date with everything that's happening but it's going to be a challenge because things are changing so quickly.

[PAUL] This is the second of four courses that together make up the Australian National University's first year astronomy unit.

The first course, introduction, is on the greatest unsolved mysteries of the universe, you can do that course online through edX as well.

If you haven't done that course, don't worry, we will repeat the important bits of it here.

[BRIAN] Now this course is at a level which is a little bit more than your average documentary. We really need you to have some understanding of math and science and physics at the high-school level.

If you are unsure, have a look at the first homework set for, problem set for this course and you'll get a sense because that's the level that's throughout the course.

[PAUL] If you can do that, you'll be fine to do the whole course, it doesn't get any harder.

Let me show you how the course works.

Most of the course material can be found here in the coursework tab. each week a new section will be released in each section the two crucial parts are the lesson and the homework you should do the lesson first this is our equivalent of a lecture and it consists of a whole bunch of videos interspersed with questions Down here at the bottom of the video are the controls. They will differ depending on your browser. But you can go full screen, change the speed you play things at, turn the captions on and off and generally play around with them. also each week you will need to do the homework if you want to get a certificate for this course and this will consist of a bunch of numerical or formula type questions and maybe the occasional multiple choice question.

In addition there are a number of things to help you.

There are reference notes. This gives you the key facts from the videos so that when you're coming back to look up something you don't have to go to go through all the videos again There are links to papers, papers referred to in the talks, there are practice questions which will give you practice at solving the same sort of questions you are going to need for the homework.

The practice questions are not worth marks, they are just for practice, and in some cases there will also be web-cast worked examples.

And there is a mystery. Week by week this will build up. And then at the end of the course, in the exam wee will test you on it. also crucial is the discussion here you can pose questions to us and answer questions and generally interact with the other members of the class [BRIAN] So I think that's all you need to know to start this course.

[PAUL] If there's anything still unclear to you, check the reference notes out in this section, or put a post on the bulletin board, the discussion board, and we will let you, answer your question.

[BRIAN] So let's start with, looking at one place where we really expected not to find a planet.

V1.1 Welcome to our first lesson on 'exoplanets', one of the most exciting and active areas of astronomy today.

What is an ''? An exoplanet is a planet that orbits a different star, not our own sun.

We know about the planets orbiting around our sun like Jupiter, Saturn, Earth and so on.

What about planets orbiting others stars? There are billions upon trillions upon trillions of other stars out there.

Do they have planets orbiting them? Are they like like our own? These are the sort of questions we are going to address through this course.

Now, why is this hard? Well, the basic problem is that our own solar system seems pretty big to us, when the furthest a human being has ever been is to the moon and not any of the planets, but in the scheme of the galaxy, our own solar system is very small and exoplanets are very far away.

Let's try an analogy of that.

To get a sense of how big the solar system is and how much empty space there is in it, let's have a scale model. As our scale, imagine the Earth is the size of this ball.

To that scale the moon would be the size of a tennis ball, about 10 metres away.

Jupiter would be the size of a car on that hill.

Pluto would be about twice as far away as this mountain. That's the solar system.

To get to the nearest other solar system, Alpha Centauri, you have to go 25 times around the world.

So, on this scale, the fastest spacecraft that the human race have ever come up with are travelling at about the speed of a garden snail.

So, it's going to take a long time to get anywhere. 25 times around the world.

So, we're not going, in any foreseeable future, to be actually sending space probes, to let alone visiting, to any other solar system.

So, if we can't go there, what can we do? I suppose we could try looking.

We'll point our telescopes there, to light coming from us at the speed of light, and actually see what's going on.

So, we can take the biggest telescopes in the world and point them at a nearby star and just look for them, right? Well, it sounds simple and if you do the calculation, it turns out that, in principle, you can actually see a planet that's actually bright enough that it can be picked up with even a medium- sized telescope, let alone one of the biggest in the world.

The problem is not that the planets are too faint, the problem is that they're very near the star that they're orbiting, as viewed from here, and that star they're orbiting is much, much, much brighter.

So, let's say, if you consider, you're in a dark alleyway at night, and someone is standing there with a candle about 10 to 20 metres away.

Would you be able to see that? Probably, yes.

But let's say that person is sitting in front of a car and they suddenly turn the full-beam headlights on. Can you now see it? Well, let's find out. What have you done to her? The difference in brightness between a candle and full-beam headlights is about a factor of a thousand if you do the figures.

The difference in brightness between a planet and a star is about a billion, so it's actually a lot like someone is standing with a candle with an atom bomb going off behind them. That's actually about the right ratio.

That sounds hopeless. So, we're kind of stuck. We can't go there and we can't see them.

So, there's some other ideas that we can maybe get out of how to find these things.

One idea is the idea of 'Reflex Motion', because as a planet orbits a sun, the sun, of course, orbits the centre of mass.

Both objects orbit the centre of mass and so the star doesn't make a big motion, but it does make a motion that is potentially measurable.

Well, this simulation is grossly exaggerated, the wobble of a star is nothing like this big, but the basic idea is that this star is leaning back a little bit against the gravity of the planet and so we'll be doing a very small circle. So, in principle, if you see a star doing loopty-loops, even though you can't see the planet, you might be able to deduce that it's there.

Yes, sounds like a good idea. So, that's one technique.

The next idea is the transit.

The idea is that if you're lucky, the planet might actually go in front of a disc of a star as seen from here, in which case, once every orbit, you will, well you won't actually be able to see the actual disc of a star, even the nearer stars are just a dot or are far smaller than a pixel, but what might happen is that as it goes in front, the brightness would decrease very slightly, it might be blocking a mere one percent or ten percent of a stars surface.

Here we go, so a very small fraction of the light from the star is not reaching us, and so you might see periodic dips in brightness that tells you that a planet is there.

We know that this happens because just in 2012 we had venus go in front of the sun and it blocked out one part in 10 thousand of the suns' light which isn't going to be easy to measure but maybe it's not impossible.

The third approach is gravitational lensing.

Now, this one's kind of tricky.

So, we know that gravity can bend light and so imagine that you have an object between us and another star.

If that planet gets exactly lined up with the star behind it, it will act as a lens, a gravitational lens, and magnify the background star a little bit.

This is a little confusing because planets, maybe they're on their own, but they're normally around other stars and so you are going to have to figure out whether or not we can use this if a planet if going around, for example, another star.

But, in principle, this can work for objects that are a long, long way away and we really don't care how bright they are, we only care that they have gravity.

The final approach is the brute-force of direct imaging.

We've said that it's really hard to see these things because the star here is a billion times brighter than the planet, but that's sort of the challenge that astronomers and engineers relish.

Maybe there is some way to have such a really good telescope that, despite this overwhelming dazzling light from the star, you can pick out the billion times fainter light from the planet.

It's going to be hard, but maybe it's possible.

There's some tricks of quantum mechanics we might be able to play to get light and the waves to line up and get rid of them.

So, those are the four techniques we're going to talk about.

Now, I should warn you, if we were talking about our own solar system, then we could be very descriptive, of course, because we know that Jupiter's like this, it's got these properties, Mars is like that, it's hot and dry and so on. With the exoplanets, we can't do that. Basically because our data is so bad.

What we are going to have to do is combine understanding of the techniques we use to study these things with the results we get.

At the moment we only have a few clues.

It's like being in a darkened warehouse, we've shone the two narrow beams of the light and we've only got a very small fraction of knowing what's really going on without knowing exactly which direction you've shone the light in, you can't extrapolate from what little we know to what's really out there.

But this is one of the things that makes astronomy so exciting, is that it really is frontier where you are trying to piece together what's happening at a fundamental level from just the beginnings of the information.

But it's a great place to learn new things.

V1.2 So, let's start the story of how planets from others stars were discovered, and it started in the most unlikely way imaginable. Let's take our minds back to 1990.

Back then, no planets had been found around other stars and, basically, no one thought it was possible.

For all the reasons we've just gone through, it seemed to be really, really hard.

People might have thought that maybe 50 years from now it would be something you'd solve, but it wasn't on anyone's near-term horizons.

I remember, it was my first year of graduate school and yes, I said well, someday we'll be able to do it, but certainly not during my lifetime.

But then everything changed, and it changed in a really unlikely place.

So, Brian, we've got all the different sorts of stars in our galaxy. We've got a dwarf like our sun, red giants, blue super giants.

Of all these stars, which one would you say is the least likely type to have planets? The one place that you can guarantee would not be planets.

Well, I studied these massive stars that explode as supernovae, and so I would think that the remnant of a supernova, a neutron star, this incredibly dense thing that the centre of a massive star collapses down to, so that's a star about 10 kilometres across that weighs one and a half times the sun, that would be a place I would struggle to imagine how you might possibly get a planet there.

So, these neutron stars are spinning balls of neutrons 10 kilometres across, we can see them because, for some reason, it's not really well understood, often they omit beams of radio waves.

As the radio waves spin around like a lighthouse, every time they pass towards us we see a flash.

So, you see something go "blip blip blip", flashing at radio waves, that's a pulsar, which is another name for a neutron star that's pulsing. But why were you so sure that these things would not have planets? Well, I think that there's a couple of things that, first of all, the stars that create these things only last for about 5-10 millions years, not even clear if that's long enough to form planets in the first place around the first stars.

But when the stars die, they explode as a giant supernova, so they have 10 solar masses of stuff that are shooting out at a high range, and whatever planet is there is going to be obliterated and if it's not obliterated it's probably going to no longer be bound to the star and go out into interstellar space.

So, there's so many reasons why they shouldn't be there, I can't really count them all.

Okay, so we all agree that the one place where you should absolutely not find planets, one sort of star you should not see planets around, is pulsars or other neutron stars.

Of course, that is the very first place where planets were seen around other stars.

So, let's tell you this rather unlikely story. It all starts with this telescope, the Green Bank 300 foot telescope in the United States.

So, that's one of the largest radio telescopes in the world.

It was, but then one morning, the astronomers found that it had turned to this.

That would have been a bad day.

It was, indeed, a bad day, and you can imagine what effect this news had on the rest of the astronomers around the world.

Yes, so we always like to be safety conscious, so when I would have seen that, if I was running and observatory, I would have said "I think we'd better check the joints and everything in our radio telescope to make sure it doesn't end up in a heap of rubble." This, indeed, is exactly what happened for this, the worlds biggest radio telescope, the one in Arecibo on Puerto Rico.

It's an amazing telescope, what they've done here is actually find a limestone valley and completely carpet it with a telescope.

It only looks straight up, but by moving this focus cabin around a little bit you can look a little bit left and right.

Right, and so instead of being steerable, like the Green Bank telescope is, this one is literally stuck to the ground, but it allows it to be much, much bigger by putting this mesh of metal which goes through and, essentially, fills this perfectly-looking spheric parabolic shape, and so that will then focus the radios' antennas, depending on exactly where the radio waves are coming down, the antenna focuses the radio waves on a part of the sky where you can move this giant collector of, essentially, a little radio antenna itself that you can move around the top of the dish and so you can point to parts of the sky, but this dish doesn't move by moving this around because the radios will go into the different part of the sky depending on where the light waves are coming from.

So, normally, people competed fiercely to get time on this telescope, and they'd say "oh, look at this object" and so this dish would be slid over to the relevant place so you can see a particular object.

But, the managers here were paranoid, could this collapse happen to us? So, they decided to take the telescope offline for a few months while they went over and double-checked every beam, girder, cable and make sure that nothing horrible was going to happen here. But, this provided an opportunity.

In some sense, the telescope still works while they're checking all of the girders.

The trouble is it can only point straight up, and this guy, Aleksander Wolszczan, if that's how it's pronounced, thought "hmm, well this can be kind of useful.

So, if I don't care where I look, I can get an awful lot of time on the worlds biggest radio telescope, I'll just look as the Earth rotates straight overhead, so there'll be a ring around the sky, we can look over and over again at this, and we can use this to look for pulsars." So, that's what he did.

He had a huge amount of time he would have never otherwise have got, had there not been this maintenance, and found a fair number of pulsars, including a millisecond pulsar.

These millisecond pulsars are kind of interesting because they flash, instead of every tenth of a second or something, they're flashing at literally hundreds of times per second, and that's a funny thing to figure out how you can get one in nature.

So, here's a simulation put together by Australia Telescope National Facility, that is you start with a .

You have a supernova, which creates a pulsar.

The second star in the binary later turns into a and it feeds gas into the first one.

As the gas spirals in, it gives it angular momentum and makes it spin faster and faster, you see it going around faster.

That's the classic conservation of angular momentum.

Eventually, the second star will come to the end of its life, as in this simulation, it might end up as a pulsar itself, but a slow-moving one, but it might also just end its life as a .

So, this is the normal idea about how you form a second pulsar.

You have a normal pulsar in a binary system and it forms a normal, slow-moving pulsar after this explosion and then the second star swells up at some later stage, it must be the less-massive star or otherwise it would have exploded first, and dumps gas onto the surface and spins it all up.

So, what you're left with here really depends on how much stuff there's left in a star.

If it was a little star that spun this up, then obviously it's not going to supernova, you have to be greater than eight solar masses to explode into a supernova.

But depending on how much stuff gets dumped up, you can end up with anything here from a white dwarf to a pulsar.

So, a normal theory is that whenever you see a millisecond pulsar, it should be a binary, with something near it, there's something that's spun it up to these enormous speeds.

You've got to imagine something spinning at a thousand times a second, it needs a lot of spinning to make it happen.

The trouble is that when people studied millisecond pulsars, it turns out that some of them do indeed, like this one, have a second pulsar or white dwarf near it, but a lot of them don't. They seem to be by themselves. This is a puzzle that was well known in the early 90's, it's a real puzzle.

How do you get these things spun up to the enormous speeds without something nearby to feed them? Well, we're almost positive that there's no way in a supernova explosion to get them going that fast on their own.

Even if you did, they would slow down, it turns out, due to the magnetic field slowing things down.

So, Aleksander decided to try and see if there was another binary companion, a white dwarf or another neutron star near this one.

Now, how do you do that? Well, here is a pulse from this pulsar. It was pulsing every 6.2 milliseconds, and they can measure the time of a pulse to an accuracy of about 12 microseconds.

So, this pulse is how many radio waves, how much energy in radio energy you're getting arriving here on Earth is a function of time.

So not much, not much, WOAH RADIO, down a bit, up even more then drop down, nothing, nothing, nothing.

The thing to bear in mind is you can measure when this pulse is coming at an accuracy of microseconds, and this is just one pulse.

If you have a pulse every six milliseconds, you get thousands of millions of pulses.

What this means is that you can measure with exquisite precision the timing of these things and that gives you a clue as to what's going on.

Let's say it is in a binary system, so now you've got a pulsar with, let's say, a white dwarf around it, because of the reflex motion we've already talked about, the neutron star, which may be more massive than the white dwarf, is still going to be moving backwards and forwards.

When it's further from us, these pulses have a longer distance to reach us than when they're nearer, which means that they arrive a bit later.

So, instead of all arriving at regular, when it's further away they'll arrive late, when it's nearer they'll arrive early and given when we can measure when these pulsars are arriving to a microsecond accuracy, light only travels 300 metres in a microsecond, so that means that we can tell the changes of distance to accuracies of hundreds of metres, or even less.

Because you can take so many of these measurements, you can actually average and so a single pulse might do 300 metres, but I'm going to have a million pulses because this is doing a thousand seconds, you get a million pulses.

That means that I can average down and probably measure things to better than a metre.

Yes, in fact, some of these things they can measure relative changes to actually a centimetre accuracies, better than you can do surveying on Earth and this is a neutron star they're at the other end of our galaxy.

So, here's how Aleksander thought "we're going to find out if this thing has, as predicted, something like a white dwarf from another neutron star in it, we'll look for it to move towards us and away from us." So, we expect a giant sine wave being many hundreds of metres per second, would be my sense of the scale. Yes, because whatever it is that's near it, it's got to be very close because it's transferred matter over to it, so we're looking for something very close to it, orbiting quite fast, maybe on timescales of days, so you're expecting oscillating days and very large because it's the massive things that's going to cause it to move quite a lot.

That's what was predicted, here's what was actually seen.

Geez, Paul, that doesn't look like a sine wave, it looks like a bit of a dog's breakfast, as we'd say.

Yes, so the first problem is that it's not a clear sine wave, it's all over the place.

Second problem is, we're talking about your 2000 microseconds, about two milliseconds, so we're talking again your kilometres.

So, it's a kilometres variation, that's not very much over a year because this is almost a couple of years worth of data.

That's too slow, so we're talking about timescales of months, not timescales of days, and we're talking about movement of your kilometres, not kilometres per second.

So, it is moving, but it's not moving at a sine wave and it's moving too little and on too slow a time scale.

So, what's the way? What's the solution in here? Well, if you look hard at that, maybe you can see a bit of a pattern. Well, there is a bit of order in the chaos there.

So, Aleksander was playing around with a model fitting software and playing with it, and it clearly doesn't fit a single sine wave, but it turns out that if you added two sine waves together...

Oh, so they beat in and out.

Yes, sometimes they'll line up together and give you a big pulse, sometimes they'll go against and give a small one, but it seems that this thing is doing two oscillations.

One slow oscillation back and forth and a faster oscillation back and forth superimposed.

I don't know if I can do that sort of dance, try and do two dances back and forth at the same time, I thought it'll be too embarrassing to try, but that's what we're talking about here.

So, what's going on here? Okay, so if you have a little planet and a big planet going around different orbits, it's sort of a spirograph that I used to play for, you'll get interesting little patterns like that.

It needs to be a planet, not a binary star because if it was another star, the oscillations are going to be much bigger than this, so you need something that's further out, which means that the oscillations happen on timescales of months rather than days, and it needs to be much smaller than a star, like a planet or two planets.

So, not only do we have one planet where we shouldn't have one, we have two planets.

Okay, so let's go and see if we can actually work out what the properties of these planets are.

V1.3 So, let’s investigate the physics of Reflex Motion. We have a star and we have a planet and we'll make the assumption that the planet is much smaller than the star, which is virtually always a very good assumption.

So, the star will have a mass M star and the planet will have a mass M planet.

Now, they're both going to move around their common centre of mass.

So, that's the common centre of mass.

The star will move in a circle of radius r star and the planet in a larger circle of radius r planet.

Notice the r planet and r star are not the size of the star and the planet, it's how far they are from the centre mass of the whole system.

And they'll both be moving with some velocity.

Let's say v star here and v planet there and they both go in a circle.

So, that's our situation.

What can we actually derive about this? Well, there are 3 constraints we can put.

The first is that they must be moving around their common centre of mass.

The definition of the centre of mass tells you that m star times r star equals m planet times r planet.

That's just a definition of centre of mass.

So, what this is telling you is, as the star weighs much more than the planet, the planet must be much further away from the star to balance out.

If the two were equal mass, it's like a binary star, two stars, then they both orbit around a point midway between themselves.

As the planet gets smaller and smaller, the centre of mass moves closer and closer to the star.

So, that all makes sense.

But, that's not enough by itself.

A second equation we can get comes from the nature of motion in a circle.

For anything to move in a circle, there must be a force, centripetal force, towards the centre which, is enough to keep it going in a circle.

And the equation for centripetal force is that it's equal to the mass, in this case with a star, times the velocity of the star squared over the radius of the circle that it's moving in. m v squared over r.

And that's the general equation for centripetal force. Whether it's a car speeding round a circle. Or a planet in orbit around a star.

So, there must be a force towards the centre of the size acting on the star to make it go in a circle. Otherwise, it would keep going in a straight line or fly off in an ellipse or some other path.

And that must be supplied by gravity. So, gravity, gravitational force given by Newton's law of gravity, G m star m planet over the total distance between them, which is r star plus r p all squared.

And that's also equal to the centripetal force of the planet.

Because the gravity works both ways. It's the gravitational pull of the planet on the star and the gravitational pull of the star on the planet.

So, that's also got to be what keeps the planet at its motion.

So, it also equals m p v p squared over r p.

So, that's our second equation which we get from saying that gravity is supplying enough force to keep things moving in a circle.

And there is one more equation we can use, which is often we won't measure the velocity or measure the period.

So, you might want to relate velocity to period.

Now, if something's moving in a circle, the distance it has to move is the circumference, which is 2 pi r, and if it's going in V, the time it will take is just equal to 2 pi r over v.

The time taken to go in a complete circle is just the period.

So, we have that the period is equal to 2 pi, say r of the star, over the velocity of the star or equivalently 2 pi radius of the planet over the velocity of the planet.

Okay. So, those are our 3 equations.

Now let’s use them to derive something in a system like this.

V1.4 Okay. So, those are our 3 equations.

Now let's use them to derive something in a system like this.

Now, we're going to make some approximations here to make the maths easier.

You can do this calculation without making these approximations, and indeed that's what professionals will do in this field, but it's much messier. So, for the purposes of this course we're going to make the approximations which give us very close to the right answer.

And the main approximation we're going to make is that the mass of the star is very much more than the mass of the planet.

Which is pretty well always true.

So, it's a good approximation to make.

What that means is that the sum of the mass of the star plus the mass of the planet is approximately equal to just the mass of the star.

Adding the planet on makes almost no difference. What it also means it that the distance between the two objects, r star plus r p, is going to about equal to r p.

That's because cause the planet is much less massive than the star, r p has to much more than r star.

So, we can approximate the sum of these two as just r p.

Not quite right, but typically a planet is a thousand times less massive than a star.

So, it's only going to be out by one part in a thousand, or nought point one percent.

So, these are pretty useful approximations that'll get us a nice answer.

So, given these approximate estimations, what can we do? Well, we can look at this equation and make the approximations here on the second half of the sequel to that.

So, what we get here is that G m planet m star over r planet squared, because it's actually r star plus r planet but we're using this approximation up here, is pretty equal to the centripetal force on the planet, which is m p v p squared over r p.

So, we can cancel a bunch of stuff.

The mass of the planet cancels.

We can bring r p up to this side of the equation and we end up with r p equals G m star over v planet squared.

We don't know what v planet is because we don't measure the movement of the planet.

What you measure is the reflex motion of the star itself. So, what we'd know is not the planet, but maybe either the radius of motion of the star or the velocity of the star.

But we do know that v planet equals 2 pi r planet over the period.

That's just from working out how long it takes to go round a circle.

So, if we substitute that into here we end up with r planet equals G m star p squared all over 4 pi squared r planet squared.

So, we should bring the r planet up to this side. We end up with r planet cubed equals G mass of the star period squared over 4 pi squared.

So, if we take the cube root of both sides we get an equation for r p, which is roughly speaking, how far the planet is from the star.

And that's going to be equal to the cube root of all this.

Neat. So, that means if you work out the period of which the star is oscillating backwards and forwards, and you know the mass of the star, that's all you need to work out how far away the planet is from it. r p being approximately equal to some of r star plus r p.

So, that's given us how far out the planet is, what orbit it's in.

How about the mass? Well, for that, remember that r star m star equals r p m p.

We also know that the velocity of the star is equal to 2 pi r star over the period. So, from this let's say we knew the radius of the star's orbit.

That tells us the mass of the planet is just equal to the mass of the star times the orbit of the stars radius over the orbit of the planet's radius, which is about the distance we worked out up here, r p.

So, if we've got how far away the planet is and we know how fast the star is moving, we can estimate the mass of the planet.

Or, if we knew the velocity of the star, say from doppler effect movement, we'll be talking about that next time, we can factor into here v star equals, we've got the r of the star, it's going to be equal to 2 pi over the period, and we've got r star here, which is r planet m p over m star, so it's, m planet over m star times the r.

So, if you know the period we can work out how far out the planet is.

Once we know that, if we know either the velocity of the star or the radius of its motion, we can work out the mass of the planet.

V1.5 So this sounds great! If we know the period of the motion of a neutron star we can work out how far away the planet is, and if you know the amplitude, how much its distance changes we can work out the mass. But there is a problem.

What is this problem? Well, let’s say we’re over here, that’s our eye and we’re looking at a pulsar. And let us say the pulsar is going round in a circle like this.

In that case, what we measure is the change in distance along the line of sight, so when it is nearest point to the Earth - it’s here, at the furthest point it is over there. and so we will measure a radius of its motion which is that, so that’s the R we observe, which in this case is equal to the radius of the motion of the star But - what happens if instead of being edge-on like that the neutron star is moving something like this - inclined to our line of sight, so once again, we’ve got the Earth over here In this case, the closest point to the Earth is over there and the furthest point is over here This is r* but that’s not what we observe - what we see is the difference between the distance here, the closest point to the distance there, the furthest point, so the r we measure is actually this distance here, the r observed so r observed equals r star if the orbit is edge on, but in general they are not going to be equal to each other Hmm - so how are we going to compare them? well, we can look at this with a bit of trigonometry So let’s assume we have our orbit here and once again our line of sight over here to the Earth we normally measure how tilted an orbit is with what’s called an inclination angle Let’s draw a line to the Earth and this here is the axis of rotation, which is perpendicular (at right angles) to the actual orbital plane, and this is the inclination angle as normally used by astronomers Now we know that this r star, the radius of the star’s orbital motion, but, what we actually observe is this r obs So how are r obs and r star related? well, we know that this is the inclination angle here, we know that is 90 degrees that’s ninety degrees so this angle in here must be ninety minus i. As that’s ninety, this angle here must be, remember that the angles in a triangle add up to one hundred and eighty, so you’ve got one hundred and eighty minus that i. now from trigonometry, you remember that the definition of the sine of an angle is opposite over hypotenuse so if that’s i, the opposite is the opposite side of the triangle here which is r obs and the hypotenuse is r star. So, we know that sine i equals opposite r observed over r star so that gives us a relationship between what we observe and what we really care about.

How does that help us? Well, not very much in practice, because actually, we don’t generally know what i is. If you remember, our equation to work out the mass of the planet was m star over m planet equals r planet over r star.

We don’t know r star: what we know is r obs so if we substitute this into here, we get, let’s rearrange it to make the mass of the planet, we get m planet equals m star, we’re taking m planet up this side m star, r star over r planet but if you rearrange this, we find that r star is r obs over sine i. so that means we know that m star r obs over r planet sine i And we don’t know what the inclination angle there is no way to tell it from the pulsar data typically.

This equation is normally rearranged to give us that m planet sine i equals m star r observed over r planet. And if you look at many tables of exoplanets, you can find on the web, you will find that they don’t actually tell you what the mass of the planet is - what they tell you is mass of the planet times the sine of the inclination angle, because that’s normally all you can measure. You don’t know this value. What does it mean? Well let’s take this equation over here. What it means is if the inclination angle is zero, the mass of the planet could be infinity! If the inclination angle gets larger, up to ninety degrees, then the mass of the planet is just m star r obs over r planet. So all we can really tells is a lower limit on the mass of the planet. We can tell that it could be bigger than that value, but all we really know is a limit on it.

Bummer!

V1.6 OK - let's use what we've just worked out to work out how heavy the planet is around this pulsar First some data: we can measure the orbital period, how long the pulsar takes to wobble backwards and forwards which is the same time as it takes the planet to orbit backwards and forwards for one of the planets: this pulsar actually has three planets, but just take one of them 25.626 days plus or minus 003 - look at that beautiful precision. You can also measure in addition to how long it takes to do one oscillation, ow big the oscillation is, that is to say, how much sooner than average the pulses arrive at one end, and how much later at the other, and that turns out to be a whopping 3.0 micro- seconds. OK so that's our data, what do we do from here? Well, the first thing to do is take this orbital period and use this to find out how far out the planet is We use the equation we derived earlier We need to factor in the mass of the neutron star, which is about 1.4 times the mass of the Sun probably, as we will discuss in the violent universe course. and that will give us a value of 2.8 by ten to the ten metres, which is about 0.2 astronomical units. So this planet is 20% as far out as the Earth is from the Sun. OK - so that's got how far out it is, how about its mass? Well, for that we use the fact that the mass of the star over mass of the planet equals the radius of the planet's orbit divided by the radius of the star's orbit.

Now we know the radius of the planet's orbit - we've just computed it up here. We know the mass of the star, what we need is the radius of the reflex motion of the star, and we get that from the timing oscillation. If the star timing varies by three microseconds, we're going to assume the orbit is edge- on here that means that the radius is the distance light travels in three microseconds, so r star is three by ten to the minus six - that's the time times the speed of light, which is three by ten to the eight metres per second, which comes out as about nine hundred metres, so the reflex motion of the star is backwards and forwards and a radius of about nine hundred metres. So what we could learn from that is that m planet sine i is about 0.02 times the mass of the Earth.

So - this is probably a little baby planet If the orbit is edge on, so sine i is one, then the mass of the planet is only two percent that of the Earth. If the sine inclination is larger so it's nearer to a face-on orbit, it could be heavier than that, it could be all the way up to infinity in principle but odds are it’s a pretty small planet.

V1.7 Alright, so we can see that there's this change of arrival times which we can then convert to, effectively, an orbit.

When you do this for all of the data as best as you can, you realise that there's not just two planets, there's actually three, because these pulsars are amazing with how accurately you can measure things.

You can measure, for example, the masses of these things.

The innermost one is actually smaller than the moon, tiny.

So, two hundredths of the Earth in its mass, that is tiny.

There other two are a bit further out, they are both about four times the mass of the Earth, so there's nothing like that in our own solar system, these are big but not as big as the planets, but definitely bigger than any of the rocky planets.

But, when you say "far out", you don't really mean far out, I mean this one is two tenths, much closer than is to the sun, and even these two are about, as I said, they're sort of in where Mercury would be so they're all very close to the star itself.

We can also measure the eccentricity, this is the measure of how off-circular the orbit is.

Eccentricity of zero means the orbit is a perfect circle, eccentricity of one would mean that it's a parabola, and these things are actually pretty close to zero.

We can't really measure it for the innermost one so we're assuming it's zero, but for these two we can measure it.

The eccentricities are very, very small. They're close in and almost perfect circular orbits.

You don't expect planets to be born with nice circular orbits, especially after they've been slammed with a supernova or something.

They could have been born, some of the planets in our own solar system have circular orbits, but near after a supernova has gone off there certainly won't be any more.

This is an artist's impression of what these things might look like, not particularly accurate, in fact, from one of the planets, the other ones look just like dots, they'd be too far away to actually see the disks.

This is an artist's impression of what a pulsar might look like if you look at the very strong magnetic fields, but no one really knows if they're like that close up.

They've even put an Aurora, meaning that there must be some sort of atmosphere there, but I don't think I'd be going for a vacation at this planet. These are going to be cold, irradiated planets.

They're going to be zapped by huge amounts of x-rays from the pulsar and not much heat so these are going to be frigid, radioactive, probably very unpleasant places to live, I don't really want to vacation there, it wouldn't be much fun.

Yes, not nearly as nice as this picture says.

But that leads us to our puzzle. I mean, we've just agreed that this, around a neutron star, around a pulsar, is the one place where you cannot get planets because we know that planets form when a solar system forms.

But, after that, to get to a pulsar, you've got to get through at least one supernova explosion.

So, that's puzzle number one, how did the planets survive this immense explosion? Yes, and the other question is why are their orbits so circular? Almost certainly, they survive that supernova explosion, that's going to knock them into some eccentric orbit, and so something would have had to make them go into a nice circular orbit again but the pulsar isn't going to do it. It's a long way away.

Then you've got a third puzzle, remember, to form one of these millisecond pulsars, you need a companion star which will swell up and dump gas into it, and will then leave behind either a neutron star or a white dwarf, but we're not seeing that.

These planets are nothing like the mass enough to do this, so where is the companion star that got the millisecond pulsar sped up to these things? So, let's look at these possible explanations for how you actually form these things.

Okay, Paul, so we have a bunch of problems here of why I didn't think there should be planets here in the first place.

So, how are we going to actually go through and come up with a scenario to explain why these things are here? Well, let's talk through three of the theories that people have come up with that might possibly explain where these things come from.

The first theory is that they really are survivors. They were there before the star went supernova and somehow they survived.

So, let's see if this is, at all, feasible.

The reason we like this idea is because we know that planets form at the same time as stars.

Remember, when a giant collapses, it forms a spinning disk of gas and planets form then.

So, that's when the planet should form. Can they possibly survive? We have a couple of problems here. First of all, we know we need to have two stars in the centre, and if you're going to have planets going around two stars, they've got to be out a ways, or they're going to be ejected by these two stars.

I guess they've got to be much further out than the planets to actually see around the pulsar.

That's right, that's the first problem. The second problem is that these are big stars, and so as they run out of their in their core and start burning and heavier elements and infusing it, they become huge.

They become red giants or even red super-giants, and they're going to expand out to huge distances and, quite frankly, potentially engulf these stars or these planets, and when those planets get engulfed in the red giant, they will get drag and they will sort of get consumed by this star.

The second star will also be in the middle but that has got enough mass to keep in orbit, even inside the other star for a short period, but the planets probably don't.

That's right, so that's a pretty serious problem, and then that star explodes.

Okay, so let's calculate what happens, whether there is a planet that actually survives the explosion of a star.

V1.8 Okay, so what would a supernova explosion do to a planet? Well, let's say we have a supernova, a star that goes supernova.

These put out a power that can be up to about 10 to the 44 joules.

Well, that's the energy so that's the total power integrated over the time.

The supernova will be bright for a few weeks so if you add up the power of all that time, that's the total energy you get out.

Let's say we have a planet, some distance D, let's say about 10 to the 11 metres, a bit less than an astronomical unit, and let's say that it's a rocky planet, so it's on a radius of about, well it's got 6000 kilometres, that's a bit bigger than the Earth so 10,000 kilometres so it's 10 to the four, five, six, seven, about 10 to the seven metres in radius.

There's no point in trying to calculate it totally precisely, we're just after a rough figure to see whether it's even feasible that a planet could survive.

If it's up by many orders of magnitude, then the odd factor of two doesn't matter.

If it comes up as being close then we've got to go back and look at the calculation in more detail.

So, we're going to be two steps to the calculation, the first step is "what fraction of this power actually hits the planet?" The second is "what would that energy do to the planet?" So, let's look at the fraction that's hitting the planet.

Let's draw an imaginary sphere of radius D around the supernova.

Most of the radiation will just go straight through and out into space, but the bit that lands here will hit.

So, you can imagine replacing the planet with a disk of radius R facing the star, which therefore has an area of pi R squared.

The total surface area of this whole sphere is four pi D squared.

The fraction of the energy, the total energy that hits, the fraction of energy is going to be this area here divided by the total area, so pi R squared over four pi D squared. If you call the total energy "E", energy absorbed by a planet is going to be roughly E, the pi's cancel here, times E over four, R over D squared. So, how much is that? So, if we assume that the total energy is about 10 to the 44 joules, so that's going to be about 10 to the 44 over 4, and we've got about 10 to the seven metre radius planet about 10 to the 11 metres away, that's all squared, so that's 10 to the minus four, so when you square it, it's 10 to the minus eight, take eight off that, so that's about equal to a quarter.

10 to the 44 minus eight orders of magnitude is going to be about 10 to the 36.

So, that is a lot of energy, but planets are big.

The mass of the Earth is about six by 10 to the 24 kilograms, let's assume it's a bit bigger so three or four times bigger, like the pulsar planets, so that gives us a mass of the planet about, let's say, two by 10 to the 25 kilograms.

So, we compare this with that, we get an energy per unit mass, totals one over four times 10 to the 36 all over two by 10 to the 25, so that's about one eighth times 10 to the 11, which is pretty much 10 to the 10 joules per kilogram.

So, that's a lot of joules for every kilogram on the planet. Now this, of course, may not be totally realistic.

A lot of the energy of the supernova is in neutrinos, that might go straight through the planet.

Some of it might be in the blast wave which might curve in some fewer dynamical way around the planet, so it could well be that the energy that actually impacts the planet is less than this, but it's going to be something like that.

Now, let's ask, if you did get 10 to the 10 joules added to every kilogram of a planet, what's it going to do? Well, let's say we've got a kilogram of rock and you add large amounts of energy to it, whats going to happen? Well, the first thing is it'll warm up. So, let's warm it up to the melting point.

The melting point is going to be about a thousand degrees, depends on the exact type of rock, it might be 2000, starting at a temperature somewhere between naught and 100, so we've got to increase the temperature by about roughly 1000 kelvin.

The energy needed to do that is the change in temperature times the specific heat capacity.

Specific heat capacity for rocks is about 1000 joules per kilogram, so to bring the rock up to the melting point, you're going to need about 1000 times 1000, so about 10 to the six joules.

So, that's got it up to the melting point, now to melt it we need the latent heat of fusion.

This is the energy needed to convert a kilogram of a solid at the melting point temperature to a kilogram of liquid at the melting point temperature.

It's basically going into breaking the bonds.

Now, I don't know what that is for rock, but let's assume that that's about the same as water which is about roughly 300 kilojoules, 300,000 joules per kilogram.

That's to turn ice into water, and it's going to be roughly the same for rock.

It might be five times smaller or five times bigger, but about the same.

That five times factor doesn't really matter here. So, to convert out kilogram, we're going to need about, that's about three times 10 to the five joules, so less than that.

Then we've got to raise it up by another temperature difference to bring it up to the boiling point.

Let's say it boils, I have no idea what temperature rock boils at, I've never seen rock boiling, but let's say it boils at 2000 degrees, probably not going to be too far off.

So, we're going to have to raise the temperature by another thousand, let's assume that the heat capacity remains the same if it's liquid, so that's another 10 to the six joules, and then we've got to supply the latent heat of vaporisation to turn a kilogram of liquid into a kilogram of gas.

Just like it takes the energy to turn water at 100 degrees into steam in a kettle.

Now, once again, I don't know the value of that for a rock, I haven't tried boiling any rock recently, curiously enough, but for water it's about two by 10 to the six joules per kilogram. So, we'll assume that it's about the same.

So, add these all up and we've got about five by 10 to the six joules needed to turn a kilogram of rock at a normal temperature into a kilogram of rock vapour.

Now, remember, the energy available is 10 to the 10. All we need is a few by 10 to the six, so that's telling us that we have far, far lot's of energy so the energy supplied is much greater than energy needed to vaporise rock.

If it was only like two or three times as big, you might worry about maybe we've left something out, maybe we needed to look up more precisely these values, try melting some rock in the lab, you have to worry about whether the neutrinos are being absorbed by the radiation or flow around it, maybe as it starts to vaporise that will give it a very silvery clouds of vaporised rock that reflects much of the radiation off.

All of those things might bring the energy input down by maybe a factor of 10, maybe a factor of 100, but that's nothing like enough.

It would need to be brought down by 2000 times to save the planet.

So, it looks like planets are DOOMED!

V1.9 So, assuming that the planets can actually survive the supernova explosion, we have yet another problem.

As it explodes, most of the mass is going to get blasted out into space.

How much mass is left from a typical supernova explosion? Normally the neutron star weighs about one and a half solar masses after the explosion, but the star that exploded was 10 solar masses before it exploded.

So, you've only got maybe 15 percent of the mass left, but bear in mind, the planets before the explosion were in a nice orbit.

You'll see a circular orbit like in our own solar system, which meant that they were going just the right speed for centrifugal force to balance gravity.

The trouble is, the gravity now is 10 times smaller. These things have now been travelling 10 times faster than they need to be. So what's going to happen to them? Well, it means that they have higher than the escape velocity, of course, they're just going to go off forever, and even if they don't, their orbits are going to be really perturbed and be made into big, highly eccentric, elliptical orbits.

Exactly what we don't see.

These things are forever going in beautifully circular orbits, and you might worry that this star also has gravity, so that will counteract but we know that this star weighs less than this one, because the first one exploded first.

Yes, the more massive stars explode first.

But then the second star will swell up at some later stage, possibly engulfing the planets yet again, and feeding matter onto the neutron star to make it into a millisecond pulsar.

That's another problem, where's the remains of this? There should be a white dwarf left over, where did that come from? That's right, so we really have a problem of where that star went to.

So, the obvious thing to do is to come up with a different solution here, I think.

Yes, I mean, really the odds against the planets surviving have been stacked up here, there are just too many problems.

They'd have to be too far out, they get swallowed in the red giant phase, they get flung into an elliptical orbits or out into deep space during the explosion, they get disintegrated by the blast wave and where's the secondary star that should be there? This is looking pretty dead to me.

So, if we form it afterwards, how are we going to do that? One obvious possibility is that there were no planets before, they all got destroyed, but somehow we acquire planets after the explosion.

It could be that you get the thing exploding, leaving the neutron star in the middle, and some of the mass gets flung out into space.

Maybe some fraction, it doesn't need to be a very large fraction, goes out but then falls back in again and then forms a spinning disk, a bit like a and then this protoplanetary disk turns into planets.

Okay, I can imagine if maybe the first object explodes and does this, but the problem is that we have an angular momentum problem here because the supernova is a big, round ball, things explode so I know that in this case I really don't have much angular momentum to get rid of because I didn't have any to start with.

So, remember, in solar system formation, the trouble was that you turned a big, blobby cloud of gas which had motion as it got smaller and smaller, angular momentum was conserved and therefore had to spin faster and faster until centrifugal force balanced gravity.

But, in this case, everything has come out from the middle. It was probably spinning rather slowly then, but it certainly didn't have enough angular momentum to hold it out, otherwise it wouldn't have been a star in the first place.

So, the gas is meant to come out and fall straight back in again, so why does it end up in a spinning disk? I can imagine maybe a little bit of turbulence or something, but there's another problem here as well. There's still another star. Yes, where's the other star gone? There should be another star. So, maybe we can kill two birds with one stone.

We've got problem number one, "where are these planets coming from?" and problem number two, "where has the second star gone?" So, possibly we can combine these in some way.

One possibility is that we need to get rid of the second star.

Maybe it feeds matter onto the neutron star and it somehow gets torn to pieces or disrupted and so some of the mass end up in the neutron star but some ends up in a spinning disk and out of the spinning disk, planets form.

Well, that actually kind of makes sense because imagine that you're a star and you're next to this little neutron star, and you start giving it more and more mass, so it has a lot of gravity to begin with because it's small and compact and pretty heavy, and you're making it heavier and you're becoming lighter.

I can imagine that, for example, since the size of a star is really a relationship between how much gravity can keep it compact and how much pressure will push it out, that is, if I make it lighter and lighter, it'g going to have less and less gravity and the thing could, presumably, potentially rearrange itself and become larger and larger, making it more susceptible to the main star's gravity ripping it apart.

Yes, so normally you would think that if you have something, like a planet that took some of it away, it would be smaller.

But as Brian said, this doesn't necessarily work for some types of stars, sometimes with stars it does, but just like I imagine a pile of cushions.

The cushions on the bottom are going to be compressed by all the weight of the cushions above, so if you take cushions off the top, it can actually get bigger because the bottom ones will spring up.

Some sort of the stars can be like that. The stuff in the middle is compressed by the weight outside, so if you strip off the stuff outside, the stuff in the middle can expand.

So, you can imagine a star that gets bigger, feeds gas, gets bigger still, feeds more gas, until eventually there's nothing left but a little bit of gas which might form planets.

I like the sound of this! But it only relies on certain sorts of stars, fully convective stars and certain sorts of white dwarf will do this, so you'll need a very specific sort of star.

Another possible theory is that when you feed all of this mass onto the neutron star, that mass is going to fall down the intense gravity and generate huge amounts of x-rays, because x-rays will come out and zap the nearby star and that might cause it to swell up, and maybe even disintegrate it.

So, it donates material and sort of gets penalised, not dissimilar to a male Black Widow I guess, where you try and help out and you get killed for your efforts.

Indeed, this is called the 'Black Widow Model', the idea that this could be why so many of these millisecond pulsars don't seem to have companions because the neutron star ate its neighbour and destroyed it for the benefit of feeding it. Pretty nasty.

That's just one possibility. Now, how about another idea which is that we know we have two stars, and you can imagine that one star is a neutron star and one star is a normal large star.

Yes, so let's assume that the two stars were very massive stars and the planets were a long way out.

The star will explode and form a neutron star, the bigger one, and let's assume that these things are so far out that they can, more or less, survive that and the second star is so massive that it has enough gravity to keep these things bound.

They're not in a circular orbit any more, but they're still bound there.

Alright, so now we have a big star orbiting a massive star orbiting a neutron star.

It turns out that in some situations as this starts feeding that, what will actually happen is that the two will merge.

The neutron star will fall into the middle of the massive secondary star producing what's called a Thorne-Żytkow object.

So, that would be a really interesting star that's not a normal star.

Instead of having this normal core that's undertaking nuclear reactions in its core, instead here we have a neutron star, the core of a dead star, incredibly dense, and so you're going to get this kind of shell around it where things are going to be really hot and all sorts of wacko nuclear reactions will be occurring.

It turns out that the prediction is that around this core, the rest of the star will swell out to absolutely gargantuan proportions, so big that, even planets far out as they are, are going to be inside it.

Now that they're inside it they can continue orbiting, there's going to be a little bit of drag but it turns out that this drag will move them in and turn the orbits into circles.

So, they'll go closer and closer in and they'll become more and more circular which sounds like just what we want.

It has to be pretty well-timed, doesn't it? Because they're going to keep going in and the closer and closer they get the denser it is, the more they're going to be dragged, and the faster they're going to want to fall in.

You're going to have to turn off this process somehow.

The idea is to have these things spiral in, nice circular orbits and then ends its Thorne--Żytkow phase and just ends up as a neutron star at just the right moment to freeze them, like a game of musical statues, 100 just frozen when the music goes off in just the right places.

Hmm, so it's a very tuned model, although it does sound like it could do what we need it to do.

Except that maybe the neutron star in there isn't going to be spinning fast enough.

Ah, that's probably a problem because it has to be spinning at almost 1000 times a second and this isn't going to be easy.

There's going to be a lot of drag and all sorts of problems here to keep that star spinning. So, those are our three models, which of them is true? Well, in time honoured fashion of astronomers, we clearly need more data.

What we'd really like is to see some more planets around pulsars.

V1.10 So, since 1992 when this first planet was discovered, we've, of course, been out looking around all the pulsars, and we're very good with these pulsar measurements of making very precise measurements.

We're not going to miss many planets. But, funnily enough, we haven't really been able to find too many.

But we have found a couple. (Here's one that was discovered.) It's around the pulsar B1620-26, and this pulsar is a bit different than the one we've been talking about so far because it's not in our own galaxy but in the , M4, Messier 4, that orbits around.

This is an incredibly dense environment of close packed, very old stars.

There's about a million stars packed into this little fuzzy ball that we see up in the sky with your eyes.

It turns out that this is, rather, a different system from the first one we talked about, and what we have is a neutron star, and this one does have a white dwarf orbiting it, just like you predict, and another planet is further out.

So, this planet is actually orbiting around this binary neutron star and white dwarf.

How do you form something like this? Well, the current theory about how you form this one is that it relies on the very dense environment of the globular cluster.

Where we are in the galaxy, stars almost never come near other stars. It's just too much space between them.

The middle of a globular clusters stars do have close encounters with other stars quite a lot.

So, here's our current bet about what's happening. We started off with a planet orbiting a star, much like the Earth around the sun, and we had a white dwarf and a neutron star.

They came close to each other and got a bit muddled up, and the net result was, after they jiggled around and did their dance is that the white dwarf went out by itself leaving the neutron star orbiting around the normal main-sequence sun with a planet left in the outskirts.

Then at some later stage the main-sequence star swelled up, spun up the neutron stars into a millisecond pulsar and then turned into a white dwarf itself.

It's almost like the human relationship here, I guess, where we end up with a sort of new family after the fact.

This seems to work, we can do the numbers so it looks like it's a reasonably plausible thing to happen.

The main interest in this is that there are, in globular clusters, there are very few heavy elements. So, people thought that the planets were made of heavy elements and that there shouldn't be very many planets here, so the fact that we've seen a planet in this environment with very low heavy elements is quite interesting.

The second thing is that this globular cluster is extremely old, over 12 billion years old, so that's telling us that at least some planets were capable of forming around normal stars when the universe was very, very young, which you might not have expected.

So, this is an unusual system, maybe we should look at one which is similar to the first one. Have we found anything like that? Well, this is the closest one, it was only discovered quite recently by Australian astronomer Matthew Bailes and his team.

J1719-8, these are the coordinates on the sky. (They could come up with better names.) They could indeed. Well, this one, in fact, is generally known as the 'Diamond Planet.' Ah, that is a good name.

(Yes.) What we've got here is here's the motion and its oscillating velocity by about the same amount as the first one we saw, so about a millisecond.

You can see that we have exquisite precision. (It's nice, it's like a single sine wave this time.) Yes, this is what you'd expect from a binary, you have a second star, except the amplitude is much too small.

So, this thing that's orbiting around it doesn't have the mass of a neutron star or a white dwarf, it has the mass about that of Jupiter.

But this is going around every 2.2 hours. The Earth goes around the sun once a year.

This goes around in two hours, so its year is 10 times smaller than our day. It's incredibly close in.

In a sense it would actually be inside the sun to go that close in, but luckily a neutron star is much smaller so it can actually be outside and going around that fast.

So, this would be quite an interesting place to be because you have the whole mass of one and a half times the mass of the sun, crammed down into this tiny thing of 10 kilometres across.

(This is much too big to scale.) Then you have a planet orbiting it right next to it.

So, that is going to give you some interesting forces compared to what we're used to here on Earth.

You can do the calculations, what you'd find, of course, if it was something of about the mass of Jupiter, we don't actually know if it's the shape, colour or composition of Jupiter, but if it was, and every planet we know of that mass so far is a gas giant, the nearest bit is going to be much closer to the neutron star than the further bit; which means that gravity here will be much stronger than gravity over there.

Now, remember that to stay in orbit, the centrifugal force must balance gravity, because gravity is much stronger here, this bit must be orbiting much faster than that bit.

That's not good if you have a planet and the near side of the planet orbiting you 10 times faster than the outer side of the planet, that's not a planet anymore, it's been ripped to pieces.

Yes, so it's going to be ripped to pieces by these, effectively, tidal forces.

So, how can it be there? Well, the only possibility is if it's not this big. If we can make it much smaller, that means that the distances are more similar so the gravity is not going to be so different; also it's going to have much stronger gravity so maybe it's got enough gravity to hold itself together.

So, you can calculate the absolute minimum density and maximum size for this thing, it turns out to be absolutely tiny.

What you need is something like this.

Ah, so imagine that you go through and the heaviest thing we could make out of it was an osmium planet, that has a density 22 times of water, that's the heaviest element there is, but this thing is even denser than that.

Well, 22 times I'm prepared to do, so it could be an osmium planet.

Osmium, well okay, it's pretty crazy to do an osmium planet. (That's hard to imagine.) But it may be more likely for it to be formed from the star that spun the planet up.

Remember, this is a millisecond pulsar so once again we've got the problem, where did the star come from? So, maybe this very dense, Jupiter mass thing is actually the remains of that star.

So, possibly, it was a white dwarf and it fed the matter, spun this up and then we had the Black Widow phenomenon.

The x-rays, as the matter fell out, the x-rays came out and zapped the star and blew most of it away and all we're left with is the core.

Well, if you think about it, the core of a dead star, a white dwarf is, well the sun, for example, when it is becoming a white dwarf, it's going to be making helium into , and a little bit of happens on the outside, but inside it's effectively forming carbon.

So, the core of a white dwarf, you'd expect it to be carbon and this carbon, initially it's very hot when the sun becomes a white dwarf, but over billions of years it'll cool off and it becomes this giant carbon crystal.

We know what carbon crystals are, those are diamonds. This really could be a diamond planet.

It wouldn't actually be a shape like this, it would be spherical, but it would be made of diamonds, or maybe even some other forms of carbon even more compressed in the middle.

This is the idea that we might be talking about a diamond planet here.

That's what we've learnt so far, we've now found three planets around pulsars and they're all really wonderful in their own way.

Yes, but it's not exactly where I was expecting to look for life.

v1.11 So, we've finally found planets. But these planets are not quite what I would have expected to see.

Indeed, I struggle to get my head around how these things formed at all. They're really weird planets. We only know that they're there because of the exquisite precision taken to measure the distance to pulsars, so it's not a technique we could use anywhere else, and we don't know much about these planets.

We know a mass in orbit, but we don't know what they're actually like, but odds are that they're these bleak, irradiated, horribly toxic planets.

Possibly made of diamonds in one case. These are nothing like anything we see in our own solar system.

They seem to be very rare as well, it's very interesting, but it sort of leaves me with an empty feeling.

I was sort of expecting to go out and look for planets more like Earth, or like we see around our own solar system.

Yes, I guess what we really want is planets that potentially might have life or that we could go and colonise someday or we can set science fiction movies in them.

This is nothing like any of those.

So, that's what we're going to be talking about for the rest of this course, is how we actually try and see if normal stars, stars like our own sun have planets.

It's a much more difficult activity and that's what we're going to be covering in the rest of this course.

V2.1 So, what we really care about is "are there planets around normal stars?" Not opposed to these weirdo pulsar planets. So, Brian, how might we work this out? Well, a normal star doesn't have this nice little pulse of radio going off at an absolute perfect cadence.

We're sort of stuck with stars, like the sun, shining. But when we think about the Earth orbiting the sun, then, of course, the sun has to move around a little bit and so the sun and the Earth both go around the centre of mass of the two objects, and so we expect a planet to cause its star to wobble a little bit.

So, although it may be very hard to see the planet itself, we can, of course, look at the wobble of the star.

That's one approach, go and look for a star that's wobbling in little circles.

This will be the case if, like here, the orbit is pretty much face on.

Another possibility is if the orbit is more edge on.

So, that adds a complication, because it's not going in a nice little circle now, it's going in some little ellipse on the sky.

But it also gives you another thing you can possibly measure, which is that this thing is moving towards and away from us.

So, now it's coming towards us, now it's going away from us, the star that is, coming towards us again and going away from us. That could have a doppler effect.

For example, if that's the normal spectrum of the star with absorption lines of some description, when it's moving away from us, that might get shifted over to here, then when it's moving towards us it might get shifted the other way, so what you might look at is for small shifts in the absorption line wavelengths.

Okay, so that's two interesting ways that we can imagine going out and finding a planet going around a nearby star.

So, I'll go and calculate how big these effects actually are.

Okay, so let's work out how big a wiggle we would expect from a normal planet around a normal sun-like star.

We've got a sun-like star and a planet.

Now, let's model this on our own solar system, so let's give this the mass of the sun, and give this the mass of Jupiter because Jupiter causes the biggest wiggles in our reflex motion we've got in our own solar system simply because it's so big.

We'll put these at the same separation as Jupiter is from the sun in our own solar system, a little bit more than five astronomical units out.

Now, if you remember, we had an equation for the orbital period, which was the square root one over G, four pi squared over M1 plus M2, R cubed.

So, if we plug in the mass of Jupiter and the mass of the sun, and the distance between them cubed, we end up with a period of 11.84 years, which is indeed Jupiter's orbital period. Good to check.

That's the first worry. It's telling us that you can't just observe for a few months like you could for pulsar planets, to find plausible planets on other stars, you're going to need to look for decades to see a full sine wave.

That's worry number one. Now, how big is the reflex motion wiggle? Remember the equation for this, so R1, the reflex motion wiggle of the star, is equal to R all over one plus M1 over M2, which if we plug in everything here, gives us 7.8 by 10 to the eight metres, which sounds pretty big.

If you compare it to the radius of the sun, it's about, the radius of the sun is 6.9 times 10 to the eight metres, so it's a little bit bigger than the radius of the sun, so the sun's moving a little bit more from side to side than it's radius.

But can we actually hopefully see that? Well, let's say we're here on the Earth and we're looking at a star over here that's moving in a circle by that amount.

So, 7.8 by 10 to the eight metres. What angle does that make on the Earth? Because this is going to determine whether we can see it with our telescopes at angle Theta.

Now, this is going to depend on how far away the other planet is and let's say it's a pretty nearby star, only 10 lightyears away.

Remember, the closest star is just over four lightyears, there are a few stars within 10 lightyears, not too many but most are going to be further away, but we could, in principle, do this, it's quite a nearby star. Now, if you remember, we can use small angle approximation, which is that the angle in radians is equal to this, we'll call it R1 over the distance, let's call it "D".

So, that's going to be about, if 7.8 by 10 to the eight is about 10 to the nine metres over 10 lightyears, which is about 10 to the 17 metres, and that gives us the angle in radians.

To convert into other degrees, you'll have to multiply by 180 over pi.

We'll actually need to convert it into arc seconds because it's going to be very small angular degrees.

An arc second is 1/60th of an arc minute, which is 1/60th of a degree, so multiply by 60 times 60 to get into arc seconds.

So, it turns out for the reflex motion caused by something like Jupiter orbiting around a one solar mass star 10 lightyears away, we're talking about an angle of about 0.0016 arc seconds.

V2.2 So, Paul, you've shown us that if we were to look at a solar system like our own, with Jupiter going around the sun very nearby, 10 lightyears away, that the sun would be wiggling by 0.0016 arc seconds.

Now, an arc second is, there's 60 arc seconds in an arc minute, well an arc minute then has 60 of those to make a degree.

Now, a degree I think is something we understand, so an arc second is one 3600th of a degree, and this is almost a thousandth of that.

This is a very small angle, but of course we have big telescopes that are very precise.

How does that seem like we are going to be able to do that? Well, in principle, you might think that you'd look at a star, you see the disk of a star, it looks pretty small but you can pick it out, and then you'd go and observe it again a few years later and it would have moved.

So, you can try and look for something going from here to here. Not very big, but doable.

So, it moves by more than the star is wide across. (Yes.) Yes, okay, so that may be doable, but there's a problem, it is that when I go out and I observe, at least in the telescopes I use, stars don't look like that. They look more like that.

So, what we're actually trying to pick up is the difference between this and this.

Now, that looks a little harder.

So, why do your images of stars look so blurry? Well, unfortunately, life is not quite as perfect as it might be, all those stars are very small, the telescopes we use to observe them are very large.

Here's the Anglo-Australian telescope up near Coonabarabran, Siding Spring observatory, and you can see that this four metre telescope is many, many tonnes of equipment that all has to be lined up to a tenth of the wavelength of light you're looking at, and a tenth of a wavelength of light you're looking at is like on order of a tenth of a micron, or 100 nanometers.

So, you have to have hundreds of tonnes of stuff lined up to a tenth of a nanometer and that's not so easy. That's just the beginnings of the problems.

If there are any imperfections in the exact shape of any part of the telescope, that's going to blow your image.

But even if you had built a perfect telescope and we're fairly good at doing that, you've got this bloody thing up here called the atmosphere.

This is Mauna Kea Observatory, possibly the best observing site on Earth that we use, and that's me in front of one of the telescopes up there.

But you can see that even at this high altitude, it's about 4200 metres up, there's a lot of atmosphere above you and this atmosphere is not all uniform.

It's got bubbles of hot and cold air, which have a different refractive index, and they bend the light.

But this is called "astronomical seeing" and that was going to blow your image.

That's like the worst problem we have, really, but, okay, we spend a lot of money, we build telescopes in space.

We get above the atmosphere, and the , of course, really is lined up to a tenth of a wavelength, and it is above the atmosphere.

Clearly, this should solve our problem.

But the trouble is that even if you put the telescope in space, there's a fundamental problem that comes from the wave-nature of light.

This is refraction. As the light comes into the aperture of the telescope, it's refracted because of its wave-nature, and that blurs the images.

We'll talk more about this later in the course, when we get into direct imaging, but it turns out that even if a telescope is in space, the images are going to be blurry at some level.

Not as bad as from the ground, but still pretty blurry.

Alright, but let's say we have our star, and it's blurry, I can take lots of data, and if I can get enough data I should be able to maybe overcome my problem, right? I just go through and I use the fact, the law of averages, and I just average, although it is really, really blurry.

Yes, so here's the blur, so this is a cut through the image, so an image like this you might go across and even measure how much light is in each pixel as you go across here, and you might get something like this and if it shifted, it might change into something like that.

So, it shifts a little bit and it doesn't shift much.

But let's say that instead of looking at a few photons, I look at billions of them.

Yes, see you might be able to see that it's gone up a little bit on the side and down a bit on that side and so even though the shift is a tiny fraction of the blurring, you might be able to measure it.

But, even here, there's a fundamental problem, the problem is that we can't get perfect profiles like this. The reason is that in this profile, this is where you'd expect light to arrive, you expect lots of light in the middle and less going away, but quantum mechanics tells us that the arrival of light is a random process.

What this actually is is a curve of the probability of a photon arriving here.

Light comes in photons, they are more likely to be over here than down there, but the actual time when one arrives is a random process.

So, here's a simulation of that.

Here's what an image like that might look like as you built up over time, and what you'll see if photons randomly arriving, and they're more likely to arrive randomly over here than over there, but still, it's random, and as time goes on you start building up something.

But you can see that, because of the random arrival of photons, you're getting very noisy data. It's not a perfectly smooth curve.

Right, and so here we have the star emerging and here appears to be a bit of a background, because the sky, of course, isn't completely dark.

You see on a dark, moonlit sky, there's a glow due to molecules in the upper atmosphere.

Even if you go into space, there's a glow due to dust in our own solar system.

So, you're going to get some background, and then on top of it you're going to get this thing coming along.

There's this little funny thing like that, and you might think, well that's funny, but that's just random, and that's the way life is.

It is that Poisson Process as we call it, it gives you funny-looking things.

But Paul, we've sort of cheated here. This is a pretty faint star, why don't we look at Sirius, the brightest star in the sky, and then our telescopes should be literally able to detect billions of photons a second, and so we should be able to get something that looks pretty close to our ideal case.

Yes, what you saw here is when we had the very few photons like here, it looked like all this complete noise, but as the number of photons builds up and up it gets better and better, and sure enough you can get your hundreds of billions of photons, which you certainly can looking at a bright star like Sirius, then you will get back that very sharp image.

The trouble is that you've got a picture, and you've got that very sharp image, but how do you know where a telescope is pointing exactly? You may be able to measure it very precisely, say pixel number 47.539 on my detector, but when you go back and observe 10 years later, which you need to because this is in 10 year periods, your telescope is always suddenly pointing a little bit off, so the pixel will change even if it hasn't moved.

So, you'll know exactly where this star is in your picture, but you wont actually have any idea where it sits exactly on the sky.

The way you normally solve this is you reference it against some other stars in the field.

If you had two bright stars and connect those together, you may not know exactly where they are but you'll know where one is relative to the other one. The trouble is that the really bright stars where you get beautiful smooth data, like Sirius, there isn't another Sirius an arc second away from it.

Oh, okay so the fact that we have Betelgeuse 25 degrees away isn't going to help us too much.

No, we need the two to be so close that they'd be on the same part of the same image.

If they're even further apart, even the atmospheric blurring will move them differently around to muck you up.

Okay, so this sounds almost hopeless, so maybe we should look at the fact that the other idea when the star is coming towards you, it has a velocity we might be able to measure. Maybe we can do better that way.

So, let's calculate how big the shift in the lines, due to the doppler effect, is going to be.

V2.3 Okay, let's work out the predicted wavelength shift due to the movement of the sun forwards and backwards, because the planet is at a nearly edge-on orbit. For this, we want the velocity of the star.

Now, the equation for this is a simple one.

It's just the circumference the circle has to travel in divided by the time taken to go around, the period.

So, this member is R1, the radius not of the orbit of the planet around the star, but just of the little circle that's been done by the star, we've already worked that out for that case of something like Jupiter orbiting something like the sun.

That is a period of about 12 years in this case.

We can simply plug some numbers into that and we get the velocity of the motion of the sun, caused by something like Jupiter, of about 13 metres per second.

Multiplied by 3.68 kilometres an hour, so we're talking about 40 kilometres an hour or so, so the speed of a rather slow car.

Can we see this? Well, that will depend on the doppler effect.

The doppler effect equation tells us the change in the wavelength of light caused by the motion divided by the wavelength of the light when it's unshifted is equal to the velocity divided by the speed of light.

This is an approximation valid for speeds much less than the speeds of light and 13 metres per second is certainly much less than the speed of light.

So, let's assume that we're looking at a wavelength in the optical light, so say about 500 nanometers.

This gives us that the wavelength shift is equal to the velocity, so 13 metres per second divided by three by 10 to the eight times the wavelength, say 500 nanometers, which comes out as 2.2 by 10 to the minus five nanometers, a very, very small shift in the wavelength. So, Paul, you've shown us that as Jupiter orbits the sun, it's going to cause the sun to go through and have a small doppler shift equivalent to two times 10 to the minus five nanometers in wavelength. Now, that's not a very big shift.

Yes, it's very tiny, but in principle you could put in a really big spectrograph, these things typically weigh tonnes and the size of rooms, which can measure this sort of stuff so you might see a spectrum with wavelength against flux per unit wavelength with say, an absorption line, and it might move.

Okay, so it does shift a bit and so that should be measurable. As you say, is we get enough light and data...

The trouble is that, once again, the absorption lines are not going to be that narrow.

Ah, yes because stars do different things. For example, the sun rotates at two kilometres per second.

Yes, so if we look at the sun, and as you've said, we're not going to be able to see the star, we're just looking from parts of it, it's just going to be all one big blur. But, if we measure the spectrum of a big blur, say, this part of the star, let's say we're looking from down the bottom here, this part of the star is moving away from us, that parts moving towards us.

So, the spectrum of the left-hand side is going to have a dip over there, the spectrum of the right- hand side is going to dip over here, you can't pick them up as separately, you've got to imagine looking at the combined light from all the different places across here, some of which are moving away, some of which are moving towards us, add it up and you're going to get something that's quite broad.

We calculate how broad, so a typical surface speed of the sun is about 2000 metres per second, the change in wavelength over the wavelength is the velocity divided by the speed of light, so two over 300,000 comes out as about this.

So, that's almost a factor of 100 larger than the effect we need to measure.

Yes, so once again, we're in a situation of going from something like this to something like that.

Well, Paul, that almost looks as hopeless as what we saw before, we were trying to measure the motion of a star like the sun across the sky.

Yes, I mean, once again, we have the problem with the photon arrival noise.

It's not going to be perfect data, but we do have a few advantages here.

I mean, one advantage is that the shift does not depend on how nearby the star is.

The sideways shift gets smaller the further away something is, but this thing, it doesn't matter how far away this star is, the shift is going to be the same.

A second advantage here is that you don't get just one line absorption in a star, you get thousands of the things.

Oh, so you can average over many, many thousands, okay.

So, that gives you a big advantage, and another advantage is, for looking at the wobble of a star, you had nothing to reference against.

You didn't need another bright star nearby. But here, what we can do is we can feed in light from an arc lamp, or something that always omits a particular wavelength and compare it against that.

So, we can actually build a reference right into our own telescope.

Ah, so that sounds like a big deal because that, that's a big difference, compared to the previous method where we didn't really have that built-in reference.

We didn't have an artificial star we could put in the sky.

Maybe it's not totally hopeless here.

(Oh, okay.) So, over many years, a group of astronomers, this is not the glamour job of astronomy, you have the glamour job of astronomy.

Oh, we cosmologists have the glamour job, but these guys were still astronomers, right? They were out measuring very, very precisely and being very, very persnickety in their measurements of the motions of stars and having to really just beat down every little problem as they went along the way.

There were a lot of problems, I mean, here's how a spectrograph works.

You get the light that comes in from the telescope, it's brought to a focus here, it goes through a little slit at the focal plane, comes to a lens called a collimator, blips it into a parallel beam of light, that bounces off a diffraction grating.

For these mammoth spectrographs, it's a thing called "Echelle" normally.

Then that spits out the red and blue light separately, they're focused and brought to a detector where the blue light arrives in one place and the red light in another.

So, what could go wrong with this? So, for here on Gemini North going on, you can see that the telescope is following the star across the sky, the telescope moves over.

These are made out of metal and they're not perfectly stiff, and so they're going to bend a little bit, aren't they? They're going to actually not, everything is not going to be exactly still.

No matter how strong you build something, it's always going to bend a little bit as you tilt it around and point it at different points in the sky, so if your spectrograph is on your telescope then it's bound to bend somewhat.

You can try to build it like a battleship, really, really heavy and that might minimise it, but it's, again, it only needs to move by a tiny, tiny fraction of a wavelength of light to completely muck up your observation.

Well, presumably, we can go through and engineer the telescope to try and counteract that, right? We have this ability to put a reference built into the telescope so that's got to help on this.

Yes, well it's normally done here, it's actually bounced the light sideways down a combination of mirrors so you can actually put the spectrograph at least in a room somewhere else, it doesn't need to move around, or maybe run a fibre-optic cable so light goes into the fibre-optic cable and runs down to it.

So, that means that the spectrograph, at least, can be stationary.

Okay, so that's a big way to get rid of some of that bending light, but, presumably, we have another problem which is the atmosphere. Well, we have a high and a low-pressure system, the refraction, the refractive index of the air isn't exactly one, it depends a bit on the pressure and I think, just thinking about it, that's going to cause a bigger problem than the size of the measurement we want to make.

Yes, that's an issue, also the temperature is going to change.

You get a hot summers day, the spectrograph is going to heat up and that will make every part of it expand and also the air inside will expand, and have a different refractive index, again a very small effect, but even a tiny fraction of a degree is enough to move things by far bigger than the effects we're looking for.

So, we're going to have to overcome these as well, it seems like you're going to have to have a very, very accurate barometer.

There are other problems they've found out.

For example, at the Anglo-Australian telescope, the spectrograph had the problem that they were picking up this strange noise, this extra noise in the detectors and they couldn't figure out what was happening, so they would go into the room where it was stored and poke around.

They couldn't see what was causing the noise, then they'd go out and find that the noise had gotten 100 times brighter.

It actually turned out that the paint on the walls was fluorescing at very low levels, too faint to see with the human eye, but whenever they went on and turned on the fluorescent lights, the ultraviolet photons from the lights would be absorbed by the paint on the walls, and when they turned the lights out again the walls would glow a little bit, for the next day or so, and it turned out that titanium dioxide in the paint which was not known to fluoresce, but does at a very low level, was causing the problem.

In the end they had to go and take every paint in the hardware shop, paint blocks all on the walls and try and work out which one glowed 100 because it doesn't actually say on the paint can: "Beware: This paint will glow at incredibly low levels, do not use it near astronomical spectrographs." So, when you're trying to make measurements like this, every little thing ends up making it impossible to get to that level.

So, you just have to control every variable.

But it sounds to me like, okay so we're controlling all of these variables, you have a really accurate barometer, you have to get the right paint in the room, you stabilise your telescope, you use a fibre- optic feed, and you have a reference.

It turns out that the biggest problem is none of these.

Our problem was that in our spectrograph, the light comes in at this end, and here I've shown it going through the middle of the slit.

But, if instead the light was near the top of the slit, that means that it's coming in at a different angle here, hits there at a different angle, different angle, different angle, and it moves the spectrum up and down here a little bit.

Once again, not by very much, but still a hundred times more than what we're trying to look for.

Okay, but Paul, this is a huge problem. Clearly we can build a telescope that will be able to track that star really, really accurately, right? So, I've got a star, I need to put a slit across it, and so I go through and I write a computer program that says there's the star, put it right there and keep it there, I'll make sure that my hardware is stable enough to keep it right there.

Yes, in principle, the trouble is that if you look at the star image very quickly, here's what it's actually looking like.

Oh, that's the atmosphere, the turbulence in the atmosphere moving things around.

So, even if you got your telescope perfectly lined up, the star is going to jiggle around from the top to the bottom.

You could, in principle, avoid this by going to space, but the trouble is you can't actually get spectrographs this big in space.

The spectrographs on a space telescope, you simply can't have them.

A many tonne, 10 metre long spectrograph on a space mission, it won't fit into the nose of a rocket, so we'd have to do this from the ground, and this is going to cause our image to jiggle around all over the slit.

Alright, so with this, I know that the atmosphere moves around at like a thousand times per second, right? So, that becomes pretty difficult to control.

So, how do we end up controlling this? Seems almost impossible.

V2.4 So, we have a real problem. As the light from the telescope comes into the spectrograph, it'll shift around, due to atmospheric seeing, which will affect where it lands on the slit which will affect what wavelengths we actually measure. It will give a spurious apparent motion of the star.

So, how do we overcome this? Michel Mayor and Didier Queloz from the Observatory of Geneva came up with a solution to this.

The solution was to use something like this.

This is an optical fibre cable, a glass cable, in this case it's encased in plastic to protect it.

What happens is if you shine light in down one end of here, like I'm doing now, light will come out the other end, as you can see.

So, it's coming in here, it's going all the way around the loop and coming out over here.

The crucial thing about that is that it doesn't matter exactly where on this end that the light goes in, the light coming out remains pretty much, the same.

This is perfect. What you can do is put one end of this at the focal plane of the telescope where the slit would normally go, feed the other end into the spectrograph and then no matter how the light jiggles around, by the time it's travelled all the way around the loop of optic fibre, it's been randomised and comes out perfectly uniformly. So, that gives us the stability we need to actually see things, to see these very small shifts in .

The second problem was the problem of needing a reference position. Shift relative to what? Once again, spectroscopy can help. The idea is to use something like this, an arc lamp.

In this case it's a sodium vapour lamp, a voltage supplied through a gas cylinder containing mercury or cadmium or some other, in this case, sodium at very low pressure, and it causes it to glow.

In this case the characteristic orange glow that you often see in street lights.

But this is always going to be the same wavelength, the emission lines of sodium, in this case, a sodium D lines.

So, what you can do is get a second optic fibre, and feed the light from this down that second optic fibre into the spectrograph, so what you'll find in your spectrograph is two spectra.

A spectra of your star, which will be shifting, and a spectrum of this which won’t shift.

All the change in the slit will be taken out by the optic fibre, and so by referencing it too, you should get a really, really precise measurement of any relative shift of the star, compared to something that isn't shifting, the lamp which is sitting in your telescope on Earth.

So, this is a technique they use to get the precision down to a fantastic 30 metres per second.

So, Paul, you've shown us that, by being smart, you can go through and really design around all of the problems, perhaps, that are facing us and doing this experiment.

You can use a fibre bundle to scramble things so that even though the stars are moving around, we get all of its light all the time and it won’t mess up our observations.

A couple of groups had figured this out by about the mid 1990s, and they'd got the precision down to a staggering 30 metres per second, so you look at a star and measure its velocity by 30 metres per second.

But it still wasn't good enough, staggering as it was, to find planets because, remember, Jupiter is only going to cause the sun to orbit by about 10 metres per second. So, we weren't expecting to see planets.

What they were actually looking at was companion stars, the idea that around a normal star there might be a small, say a or star orbiting it.

Alright, so like all good things in Astronomy, or maybe not all, but almost all, you're out doing a very simple experiment and in this case we're looking at a nearby, quite bright star, known as 51 Peg as we short-hand called it, and it's a fairly ordinary sun-like star, relatively close so that it's nice and bright, and you can go out and hopefully see what's going on around it, but they found a bit of a surprise, right? Because, it wasn't just sitting still or not moving at all, and it wasn't moving a lot, it was moving a bit.

Here's what they found. Here's the velocity of the star against time, and what you can see is to begin with it was moving at about 120 metres per second, and when they observed away from us when they observed it next time a few days later, it was about the velocity of zero, and then it changed, then it changed, then it changed, then it changed, it was jumping all over the place. But it's changing very quickly, it's changing on an order of a few days, not months or years like we expected planets to be.

Yes, it seemed to be a 4.6 day period. Remember, Jupiter goes around the sun every 11 or 12 years, this is four days! The amplitude is enormous, remember, they were not expecting to see planets, they were expecting to see, a planet would cause about a 10 metres per second shift which is within their uncertainties here.

What they were actually picking up, however, was much bigger. It would shift by plus or minus about 75 metres per second.

We're talking about huge velocity shifts in an incredibly short time scale. So, what's going on here? Well, it seems like we need to go through and use the mechanics that you've put forth and calculate what type of object could do this.

So, what are the properties of this planet around 51 Peg? Well, I'll get to work out the properties as they would have been worked out by Mayor and Queloz back when first discovered.

Since then, measurement of the period and velocity has changed a bit, so the answers you see now is a bit different.

But the numbers they had to work with then were a period of 4.63 days, we now know it's a bit shorter than that, the velocity of the star of 74.5 metres per second, and a mass of the star, 51 Peg itself, you need this to work out anything else, it's worked out from a normal stellar modelling of 2.2 by 10 to the 30 kilograms, so 10 percent more massive than our own sun.

Given those numbers we can use the equation the radius of the orbit is the cubed root GM1 period squared all over four pi squared.

Plug these numbers into here, remember to convert days into seconds by multiplying by 24 and 60 and 60, and that comes out as 0.05 astronomical units. Very close in, 20 times closer in than Earth in our own solar system, let alone Jupiter.

How about the mass? Well, remember that we can't actually work out the mass, we all work it as M Sin i.

If it was edge on, we have the equation that V equals two pi over P, R, M2 over M1, if we arrange to make M2 the subject we get M2 equals M1, P over two pi R, V1, that's edge on.

If it's not edge on, actually we don't know if it's edge on, it should actually be M2 Sin the inclination angle, equals all that.

Once again, plug the numbers in, and we get M2 Sin i is 1.25 by 10 to the 27 kilograms, which is somewhat less than the 1.9 by 10 to the 27 kilograms, that is the mass of Jupiter.

So, this is, as it turned out, about half the mass of Jupiter if it's edge on.

If Sin i, so i, is 90, then the mass about half the mass of Jupiter, if i is larger or smaller, then the mass would be bigger.

What we've learnt is if, and it's a big if, this thing is at a nearly edge-on orbit, it's going to be something about the mass of Jupiter. So, there I've shown the dot here, maybe half the mass of Jupiter, maybe two times the mass of Jupiter depending exactly on what the angle is, and here's an actual scale diagram of it here and you can see, just about, the dot here. Here it is, coming around.

Oh, it's coming towards me. (Yes.) It's not very big compared to its star.

Yes, you often see the artist impression of it being very big and very close, this is actually a true scale diagram.

This doesn't look like it's very close, but in our own solar system it'll be much further away, you wouldn't see it at all, so this is actually what it looks like.

It is much closer in, but 10 times closer in than any of the inner planets in our own solar system, let alone where Jupiter is.

Alright, so Paul, this is well and good but you have said "edge-on", couldn't it also be the other direction so that it is face-on so that the planet is moving in the plane here of our screen, like this one? So that in that case, the motion of this star, the radial velocity is very small, and so you have to have a much bigger object like a star, rather than a planet, to account for what we see.

Yes, so this is entirely possible.

It could be that it's not a planet orbiting, but something much more massive like a red dwarf star like I've shown here, but for this to be the case, the orbit would have to be very, very precise within a degree or so of being face-on, which is actually quite a coincidence.

If it's more than that, the radial velocity would be too great because a thing like this would have much more mass, so I think it's a fair coincidence that it was so precisely face-on.

They didn't look at thousands of stars to find this, right? They only looked at a few, so it's not like we're just selecting the one out of a thousand out of a thousand objects.

It really was out of a few, so the odds are that it actually isn't this, it really is a planet.

But, you don't want to rely on odds like that. If it is a planet, it is pretty close on.

Here's the sunset at the Siding Spring observatory, that's what our sun looks like.

If we were watching the sunset on this planet, and it really was an edge on thing, that's what the sunset would look like.

Ooh! I think it would be pretty hot on that planet by the looks of the sun being that large.

Yes, so you certainly wouldn't be seeing gumtree covered hills down here. In fact, it probably is a gas-.

We know that the planets of that sort of mass in our own solar system are like Jupiter and Saturn which are gas giants.

They don't have solid surfaces, but we don't know anything about this planet.

It would be really cool if it exists, but I think the big question is, is it real? So, the data, as you've shown, are really, really hard to get.

They've had to go through and do all of these little things and, you know, let's face it.

It's pretty easy to make a mistake when you're on the bleeding edge like they were. You don't know for sure that it's not actually a star, another planet on an edge on orbit.

I mean, probability says it's unlikely, but would you be prepared to bet the bank on that? There's also forms of stars that pulsate. I study things like RR Lyrae stars or cepheid variable stars and there's a whole range of different ones, are we sure that this isn't just some form of stellar pulsation like we've seen before in a slightly different form that happens to be four and a bit days long? It could be that instead of the star moving backwards and forwards, what's happening is the star is getting bigger and smaller and pulsing.

As we're looking at the near side of it, as it gets bigger it appears to be moving towards us and when it's becoming smaller it appears to be moving away.

So, provocative but hardly compelling.

V2.5 At long last, we've discovered planets around normal stars, or had we? I mean, there was a lot of reasons to be sceptical about these things, and in fact a large fraction of the astronomical community were really not convinced. There had been too many false alarms in the past.

What we really needed was some independent confirmation.

Exactly, certainly, from my own experience, you need to have two teams looking at something that's really controversial for people to believe.

In this case, a team in California had come up with a novel idea to really make sure that they didn't have any, what we call, systematic errors.

Because, if we remember, when you need to measure these tiny, little velocities, any little tiny glitch will give you the wrong answer.

So, what they decided to do is they put a glass cell full of iodine.

Now, iodine has lots of spectral lines, like thousands upon thousands of them, and they're very narrow, and they put it before the light entered the spectrograph.

As the starlight shone through this iodine cell, it had imprinted on it each of these lines of iodine which could act as a reference stick for the wavelength of the light.

So, the spectrum you see at the end here would have both the lines from the star itself and the lines from iodine.

Now, the iodine cell is not moving, so if the spectrograph was all perfectly stable, they would always be in the same place.

In practice, if the light lands on different parts of the slit, or the temperature or the pressure change or any of the other things that can go wrong do go wrong, that would cause the iodine lines to shift a bit, but it would shift them by the same amount it would shift the lines of what you were looking at.

That's exactly right, so it was a way of getting rid of all those nasty little problems.

The trick is, these iodine cells are messy, and they really do make a nice looking spectrum and make it look terrible, so it's very difficult data to analyse. A lot of hard work had gone into the software. But nonetheless, the Californian group of Paul Butler and Geoff Marcy had been working on this and, in fact, they actually observed 51 Peg, but they just hadn't analysed the data because, after all, no one was expecting a planet. We didn't think we could see planets like our own solar system.

But as soon as they heard the result from Switzerland, they, of course, immediately went back and analysed the data, and they found the same thing.

What's more, when they dug through more of the data, they found more similar sorts of signals.

So, at long last, we had confirmation. We didn't just have one object, we had a whole bevy of planets suddenly come from essentially nowhere in a very short period of time.

So, here are a few problems we thought of, the first one was "were the data valid?" The fact that we now have two groups using different methods, so we've got the Swiss group who were using the fibre optic cable method, and we had the California group using the iodine cell method, and they both observed the same thing and saw the same velocities at the same time on different telescopes with different methods.

So, that's telling us that yes, these are very different observations, but clearly they're getting it right.

So, Paul, we still have that problem of, potentially, the object just being a brown dwarf nearly face on, so you only get tiny orbital motions.

It could be that the motions are real, in fact, they probably are now that we have two groups finding it, but maybe it's not a planet, maybe it's a star.

Of course, we've known about binary stars for a long time. But, the more you discover, the less likely that becomes.

Because if you imagine, let's say you have something really massive going around like this, if it's face on, then most of the wobble is going to be out not in your line of sight, you're only going to get a very small fraction of it, so it will look like a planet.

But for every one that's going to be face on, there are going to be many more that are at some other angle.

For these ones, you're going to see a huge oscillation, so you'd expect that for every one that looked like a planet, you'd see your 10 or 20 that look like brown dwarfs, and you won’t see anything like that many, these huge oscillations that could be a brown dwarfs.

So, with just one, you know, maybe it could be a fluke, it happened to be face-on, very close, but by the time you've got three or four or five, let alone the hundreds we've got now, it doesn't make sense.

Any individual one of them still could be, but as an ensemble, the whole population, no.

Okay, so what about the idea of it being some sort of stellar pulsation, like a cepheid variable star but something a little different that just mimics the sine wave of a planet.

Well, this was seriously considered, that maybe it was some sort of strange pulsation of the stars surface rather than the actual whole star moving, the trouble with this is kind of two-fold.

First of all, when you get a pulsation from a star, it very rarely looks like a sine wave. It tends to be a slow rise and a sharp drop or a steep drop and a slow rise and a slow fall.

Secondly, when stars pulse, they don't pulse at one period. They pulse at multiple periods simultaneously.

They've a resonance, right? They're almost like a musical instrument, that when you blow your trumpet, it doesn't just give you one tone, it gives you multiple tones.

Like a bunch of harmonics, although they're not very harmonic, they've all got funny ratios, it would sound horrible if you listened to it. Sort of like bagpipes.

Bagpipes and bells are two instruments that have harmonics that aren't nice at regular intervals.

But people only see the one sine wave, so that made it very hard to come up with any model of a star that would do that.

Okay, so it looks pretty solid.

What were they discovering? Well, most of the ones they were discovering were something like this, the , where a planet's in a near circular orbit very close in. This is a schematic, it's not really to scale.

To scale it looks more like this. There's a dot coming across. (That's less impressive.) Much less impressive, which is why most people don't give you scale drawings of these things.

So, were all the objects going in these close circular orbits? The bulk of them were, but there was also another class of things, what we call the 70 Virginis systems after the first one discovered, 70 Virginis.

These ones, the planets are much further out, this one again is not to scale, they're actually maybe as far out as the Earth, an astronomical unit out, but they're very elliptical orbits.

They came very close then whipped around very close and then way out slowly then in and close.

So, you can really see them when they come close, the way you find these things is the fact that they are elliptical and they have big radial velocities here and very tiny ones out there.

That's right, at least to begin with, that's how they were discovered.

V2.6 What we've seen is that two groups had gone through and made painstaking measurements of, effectively, the spectra of stars over time. By making those measurements with exquisite accuracy of wavelength, they were able to use the doppler shift to convert the shifts wavelength into velocities.

When they did this work, they discovered planets.

But these were weird planets. It's nothing like our own solar system.

In own solar system the big massive planets, like Jupiter and Saturn, are a long way out.

But here, we're talking things with a comparable masses of gas giants, but these are practicably skimming the surface of the star or in highly eccentric orbits very close in, so it's very weird. Well, you say it's weird, but who’s to say our solar system should be typical? I mean, why would we not expect to have these types of planes out there? Well, the reason why people didn't expect these sort of planets is because of what's called the 'Snow Line Theory', this is a theory of how gas giants form. If you remember, when we talked about solar system formation, the idea was you started with tiny, little grains of stuff that stuck together to make bigger and bigger lumps until, eventually, they end up with planets.

In the inner solar system, the only lumps we can have are lumps of rock, but in the outer solar system, where it was colder, you have lumps of ice, and because ice is mostly hydrogen, there's a lot more hydrogen out there, that's the most common element in the universe, so there should be a lot more ice out there than there are rocks closer in. There's also rocks further out as well.

What this means is that the planets are further out, in our own solar system the snow line is probably somewhere in the , things beyond there should be able to get much bigger because they can be made of ice as well as rock.

In the inner solar system, the ice will just all evaporate away.

So, what that means is that the planets further out will get bigger, not much bigger, maybe three or four times bigger, but once they're three or four times bigger, their gravity is stronger and they can then start sucking in all this hydrogen and helium gas that's around, at which point they get very much bigger, like 300 times bigger like Jupiter is.

This is the standard theory, and this said that you should only be able to form really big planets out beyond the snow line.

Okay, so we have a mystery on our hands of why we have these objects, these gas giants right next to their stars and so, once again, another mystery confronts us.

So, how are we going to solve this? Well, clearly we're going to need more data and some good theoretical thinking and that's what we'll cover in the next lesson.

V3.1 So, Paul, at last we have a method for reliably finding planets.

All we have to do is monitor a star and its radio velocity to a few metres per second for a few weeks, months or years and we can pick out its reflex motion caused by its planets.

It's not the way anyone thought this would happen, but it turned out to be quite effective and suddenly it became very trendy.

These people who hitherto were very obscure were suddenly showered with grant money and jobs and telescope time.

They got to build their own spectrographs and huge amounts of time on the world biggest telescopes, and so the data rapidly got better.

Yes, it really became a huge industry where there were multiple groups around the world and they, of course, got a lot of time so they made a lot of discoveries.

So, here we've got a plot, which we'll loop over, showing the discoveries against time. So, what we're plotting here is the mass and, remember, they don't actually measure the mass, they measure the mass Sin inclination.

On average, for things randomly distributed, its real mass is going to be 14 percent above that.

To begin with, there were only a few things which were a pretty high mass close in.

But as time goes on, first of all they start finding things down here with lower and lower masses and that became because they got better and better at their techniques.

They got better software, better at correcting all of these different problems we've talked about and also they got to build their own spectrographs; which were purpose built for this purpose, rather than just borrowing someone else's spectrograph, which gave them more precision.

The second thing that's improving is they're starting to see things out here, further from the sun.

When you get further from the sun, you're talking about longer periods.

These things might have periods of five, 10, 15 years.

So, you're not going to see them in a one week observing one, you have to actually observe over many, many months, years.

As time goes on, this is where we're at at the moment, at the time of writing this talk.

These are the hot Jupiters, these are the things very close in, and you see that they range from maybe less than a hundredth the mass of Jupiter up to 20 times the mass of Jupiter, much higher than that and they'd be a star, and you also begin to see more and more objects further and further out.

It turns out that these are relatively rare.

The bulk of the things, now that we got 10 to 15 years worth of data, are out here, maybe about an Earth orbit out, so it would be a period of a year or thereabouts.

We're even beginning to see things with periods and masses close to that of Jupiter.

Well, so if we look at this diagram, we see that there are a lot of Jupiters where the Earth is, so our solar system isn't obviously the norm. I guess though we can't yet see our solar system because we simply haven't looked.

We're getting close to being able to see something like Jupiter, something with a sort of Jupiter mass in a Jupiter orbit.

We're not yet in a position to be able to see things like the Earth or Venus, let alone Mercury or Mars which are way down here.

So, these are still not like our own solar system.

We're still talking about the hot Jupiters down here and these things, we'll see in a moment, tend to be in the highly eccentric orbits.

You've got the hot Jupiters and we've got the eccentric giants over there.

So, Paul, we have all of these big, Jupiter-like planets in quite close to the sun, so not at all like our own solar system. If you remember, that's a problem for our normal theories.

Our theories say that you should only be able to form these big things out beyond the snow line, beyond the asteroid belt where Jupiter is.

It's a real problem that we're talking massive things that should form a long way out, very close in.

So, let's not give up yet, maybe we can form them out where they're supposed to be formed, and move them in rather than trying to form these big planets close in in the first place.

This leaves, for a long time, the standard theory for how these hot Jupiters got there, and it had a benefit that it was actually predicted before the observations.

It's always, you know, have more faith in the theory if it comes on before the observations.

Theorists are very good at explaining things after the event. There's actually a theory of migration.

This came as a solution for some problems in our own solar system. The idea is that when the planets are first forming, they're still embedded in this protoplanetary disk, which is a very massive disk primarily of hydrogen and helium, and some smart theorists had calculated that there would be a reaction between these things.

There's not going to be much gas drag, but the planet will generate ripples in the gas and the ripples would have a gravitational pull back on the planet and this then causes planets to move.

This was come about as maybe an explanation for where Uranus and Neptune come from in our own solar system.

Basically, the time to take them to form out where they are is so long they should never have formed.

So, the standard theory was that maybe they formed in close to where Saturn is now, and then moved out.

But the theories could get them to move either way. Here's some simulations.

This is a simulation of a fly-by of a protoplanetary disk, which is in red, with a planet forming.

What you can see, this is a fairly massive planet, and it's gravity has actually carved out a gap in the disk, and you can see where it catches a ripple pattern coming in through there.

Gas is falling in here and spiralling around the planet to actually form the planet, this is how you might actually form something like Jupiter.

We'll zoom in on this in a second, and you see the whole complicated ripple pattern out here, and these ripples can either move it in or outwards.

In this case it will probably move it inwards, but depending on the exact density of the disk and its temperature and how many planets there are, you can get this thing to move in or out, or even turn around.

So, since this is a very convenient model, you can expend anything you like from it.

It sounds very complicated. It is a very complicated model, and because we know so little about what these disks are like in the first place, it's very hard to say what it would do, but it's certainly possible for these things to move around in huge factors.

Now we're going to zoom in on the centre here, and we'll see a disk around the planet, and this might be the disk of gas, like the disk of the whole solar system except smaller one around a planet which might have formed, for example, the Galilean satellites of Jupiter, or the big satellites.

We know these ripples happen, because you can see them in our own solar system in the rings of Saturn.

You've got tiny, little moons forming gaps in the rings, just like we see in there, and they form this rather complicated ripple pattern on the side, and so we know that when we do have a disk and you have a mass in it, it can indeed open up gaps and produce these ripples, so it's confirmed in that sense.

Here's a simulation showing how one of the planets had actually been moved in.

So, here you've got the planet, it had actually been spinning around in an enormous time, but they've cancelled that out and left it in the same position, and what you can see is, as time goes on in this particular simulation, the planet's moving itself in.

The ripples over here and there produce a net backward torque, slowing down it's orbit and moving it in.

These other ripples were also caused by the planet as well, so, presumably, a big planet like Jupiter would effect everything else in this system as well.

Of course, in reality, we might have several planets, each of which direct their own ripples, the ripples start interfering with other ripples and it becomes incredibly complicated.

How can we form hot Jupiters? Well, one idea is would be that we have the protoplanetary disc, and the planets start migrating inwards.

The gas giants form out where they're supposed to form and then fall steadily inwards, and you've got an endless stream of planets all falling inwards until, at some point, the protoplanetary disk goes away.

This is thought to be about 10 million years after the solar system starts forming, and at that point it's like a game of musical chairs.

Everyone suddenly freezes where they are at that moment.

Because all the gas is gone and this rippling effect that's sapping energy from the system disappears and so you literally get these objects coming in and whatever's left is left, as you say.

So, here's another simulation of that, so here you've got a planet and a star embedded in a disk and a planet orbiting around, so as time goes on it's setting up ripples which, of course, gets to spiral in closer and closer, faster and faster, and then at some point, there we go, it just goes away, leaving it where it is.

If you get it just right, you might be able to leave it like this is a hot Jupiter.

But the trouble of this is it needs a lot of fine-tuning. These disks are supposed to hang around for about 10 to the seven years, so about 10 million years, whereas the time to migrate something, that's only about 10 to the five years.

100 It sounds to me like you would probably lose almost all of your planets you formed into this scenario.

That is indeed the case. You'd expect that maybe only one percent of planets survive, the one that happened to be just at the right place at the exact moment.

But that's kind of okay, because we actually only know that about one percent of planets have hot Jupiters.

The other 99 percent they didn't see anything. If you remember the survey, we can only see things that had massive and closer in, and it turns out that if you did the sums, we're seeing that about maybe half a percent to one percent have hot Jupiters, so it could be the case that maybe this happens everywhere.

All of the solar systems form planets and the vast majority is just destroyed or still a long way out and then a half a percent or one percent is just caught at the right position.

So yes, it's very destructive, that's one possibility.

Another possibility is that, for some reason, there's a hole on the inside of the disk, so the things migrate in, but then they stop migrating when they come to the inside of the disk, as there's not more ripples around them, and so you just build up something really, really rather big here.

Okay, so in this case, you get the first planet that comes in, it quits migrating, and then it sort of bumper-cars with everything else just piling in on top of it as they come in and so you get to build a great big object up.

But you have to make a big hole, so you say magnetic field, that's convenient.

Yes, whenever astronomers don't know what's going on, they say "magnetic fields", "turbulence", we have our hands and look goofy, so, yes.

Well, let's magically assume that the magnetic field from the sun goes out and magically clears a hole in the disk and magnetic fields can do whatever you like so maybe it'll work.

We know that stars have magnetic fields, we know it'll interact with the disks, so it's not maybe totally crazy.

(It's not completely crazy.) But it's fairly crazy.

This will have the benefit that these things coming in could be quite small because they pile up on the inside, whereas in the previous model, you'd have to have a bunch of big things coming in.

But, you know, there's lot's of mass in the solar system.

Maybe there are, maybe our solar system did form a hundred Jupiters and 99 of them fell in and one got left behind.

The problem with this is that it's actually a bit too good a solution, this whole migration stuff.

I mean, bear in mind that the migration timescale is much too short, you can explain these hot Jupiters, but what about our own solar system? We've got Jupiter out where Jupiter's supposed to be. I mean, why didn't it migrate in or out or somewhere like crazy? It could do so very quickly.

In fact, it probably predicts the that most solar systems don't have any giant planets at all, because they all might have migrated in long before they had a chance to stabilise anywhere.

Right, we've seen that, as we've found more and more objects, there are a lot of Jupiters and not really, really close in, a lot of them are out by the Earth, and it looks like there may even be even more out, sort of where Jupiter is supposed to be, so maybe our solar system isn't completely weird.

Yes, so this may be too good an answer.

You get things closer in but maybe it gets everything too close in.

So, we still have a mystery on our hands.

V3.2 Okay, so that's a possible explanation for these hot Jupiters, but what about these eccentric giants like 70 Virginis? These things that are further out with very elliptical orbits. What can we do about them? Well, is it just on its own? Is that just an isolated case so we don't have to worry about it or is it pretty common? Well, here's the data again, we've got a time lapse showing how these things were brought up, now we're plotting, once again, how far out they are, but now we're plotting the eccentricity.

Eccentricity of zero means a perfectly circular orbit, eccentricity of one would mean a parabola, so the more up here, the bigger the ellipticity is, the close and further it goes.

What you can see is that the ones that are close in actually aren't very eccentric. Eccentricities of 0.2 or 0.3 or a bit less.

But that kinda makes sense because if you're a big planet and you're near the sun, you're going to get bent all out of shape by the tides where the sun's pulling on one side of you and then the other, so that's going to cause friction, which isn't going to mean you're going to try to limit that the best way to do that is to go in a circle.

Yes, so it turns out that if you do the calculation, you bring a planet closer and it'll raise big tides in the star and these tides will actually tend to, what's called, circularise the orbits.

So, you expect that anything this close in be pretty much in circular orbits, and indeed they are.

But you look at the ones further out and, my goodness! Yes, so this is 1AU, so that's the distance of the Earth, and here we have Jupiter and we can see all these things.

I mean, these things are coming in on comet-like orbits, they don't look at all like planets.

They certainly don't look like the Earth or Jupiter.

Yes, everything in our own solar system, Jupiter has an eccentricity of about 0.05; which will mean that almost everything we're seeing is far more eccentric than almost anything in our own solar system.

That's a bit weird, how are we going to produce this? The problem is, you're forming things out of a protoplanetary disk, the disk is going to be in circular orbits. It has to be because gas can't be in elliptical orbits because it'll bump into other gas and equalise out.

You're forming things out of a circular spinning disk, they should, damn it, be in circular orbits! So, what happens if you just go out and try to simulate it and see, make sure that your intuition is right.

So, now we're going to do the reverse.

What we were talking about last time was that we were using the disk to cause things to spiral in.

It does that, very slowly keeping them in a nearly circular orbit as it spirals in, but let's say we form the planets and get rid of the disk.

In this case, there's nothing left to stabilise them, if you've got enough planets close together, they'll start influencing each other.

Here's a simulation. I'll give you the code so that you can play with it yourself.

So, I put a bunch of things in random orbits and you can see them all interacting with each other.

Like this one had a close collision, and, presumably, when things interact, they get too close, one of the ones gets thrown out.

Usually the smaller of the planets.

You can see that this green one here is now in a pretty eccentric orbit.

Oops! It crashed in. Oh well, it wasn't anymore.

But this whitish one over there is now in an eccentric orbit.

So, in this case, everything will start off in a circular orbit and you did actually end up with some elliptical orbits simply because of the interactions, but it doesn't always work.

Here's another one of the same code. Once again they start in circular orbits.

So, here you've done exactly the same thing, you've just started things out with a different random set of conditions.

That's right, and if you have the code you can play for yourself and see what you get. What are we getting over here? Lots of collisions again, oops! There's another collision in the middle, and this time you end up with this on, oh it crashed into that one.

That's one way to make a big new planet.

So, there we've got something that's actually fairly big, fairly close in, but it's in a fairly reasonable circular orbit, not too eccentric.

Maybe this will do it, like a game of Billiards or a game of Crap Shoot if you like, where there's random interactions.

You need to have lots of things, get rid of the disk and then have them interact by their own gravity.

Okay, so you end up with one object here, it seems to be that whatever you get, you're going to end up with one object because everything else has kind of 'goneski', it gets thrown out of the system, it doesn't look at all like our own solar system.

This is our own solar system and you can see that the things are pretty damn-near circular. So, once again, the problem is that it might be too good an explanation.

If you do get these huge numbers of planets all playing Billiards, first we get lots of collisions, and secondly, you don't get anything like our own solar system.

Right, I mean, the advantage of going in these nice circular orbits is that they don't cross each other, and you don't play billiards.

As soon as you start throwing planets in on these elliptical orbits, there are going to be collisions and you're going to rearrange the system in pretty short order.

Guaranteed.

V3.3 So, Paul, so far we've been talking about distant solar systems or different systems that have one planet.

Now, our own solar system has eight planets and nine or 10, depending on if you count Pluto and Sedna and things.

Are there any systems that look more like our own that have multiple planets? We have to bear in mind that with current technology, if it was our own system it would look like a no-planet system because none of our planets are within current sensitivity.

But there are some now which show multiple planets.

The most famous one is Upsilon Andromedae. Here's the original discovery data.

So, you've got these points over here and they've managed, I don't know how, to fit that particular sine wave to these things.

You do have to be a true believer, I think, but actually the data does speak volumes.

Yes, I mean, the velocity is jumping around by an enormous amount.

But there are a couple, like that point is kind of deviant.

Back in this paper in in 1997, Paul Butler came up with the idea that there was one planet.

That was a classic hot Jupiter and a period of 4.6 days very close in.

But then as the data got better, they got more data over a bit longer, they started finding that there was some residuals.

If they take that one sine wave they've got here and subtract that off the data and see what's left over, here's what they were getting.

Ah, so here you get something quite complicated. It's not just another sine wave, it actually looks like two sine waves.

That seems to indicate two things.

So, indeed it's very fast, your four day oscillation, you've got a slower oscillation here and an even slower one like this. So, it looks like here you need not one, not two but three planets.

Three planets! Okay, so a three-planet system.

What do the planets look like? Well, here's an artist's impression but really, we don't know what they look like.

Here's the architecture of the system, so here's the star and you've got one planet here which is a classic hot Jupiter in a nice circular orbit, low eccentricity, about 0.7 Jupiter Masses.

The second one is much further out, 0.7 Astronomical units.

That's about where Venus is in our solar system, and it's two times the mass of Jupiter, so much bigger, and right over there...

Oh, so this is a five times Jupiter, so it's a really big planet, two and a half AU out, so it's sort of Mars- ish, but it's very eccentric, 0.4.

So, there's no planet like that anywhere near that eccentric in our own solar system.

We've talked out the two classes, the hot Jupiters and the eccentric giants; we've got both in one system here.

One of one, one of the other and one that's kind of in the middle.

So, this thing's going to be like a giant mix-master, you would think. Are we sure that this thing actually wont self-destruct? Well, one thing that saves us is that these things are quite well separated; so even though they're elliptical, they don't come that close.

The other thing that saves us is that these things are actually in, what we call, resonant orbits.

We get this in our own solar system, for example, Pluto, which is highly eccentric, is in a resonant orbit with Neptune so that for every two times that Pluto goes around, Neptune goes around exactly three, an integer ratio of periods, and that means that as they go around, they always avoid each other.

It's a bit like wandering around campus trying to avoid your PhD supervisor.

If you know their schedule, you can carefully make sure you're always at the place they were at a different time.

These planets are doing something like that.

They've got these particular ratios of their motion so that even though they might get close to them, they're never get there at the same time.

So, presumably, that's not designed, it's actually a survival mechanism.

Yes, so either there were many more planets to begin with and the only ones that survived were the ones that happen to be in these resonant orbits, or there was a fair bit of migration and the migration had went off and will often tend to leave things in these resonant orbits as these are the most stable positions.

One way or another, these multiple systems do seem to be stable.

So, Paul, we can go through and we can find "planets", but it's all kind of unsatisfactory because we measure the mass multiplied by this sine of the inclination. Are we really finding planets or are we just finding things because of this inclination effect? Yes, we don't really know the mass of any of these things.

On a statistical average might know, but it's really a bit unsatisfactory as you've said.

What worries me is do we even know these things are planets? All we know is that it's a mass going around the star.

They've got about the mass of a planet, but we don't know if it's a planet.

It could be some sort of giant death-star or some weird crystal- lattice or who knows what.

So, we go through and we say, well, here's a planet about the size of the mass of Jupiter, and so we say it must be like Jupiter.

We have to make that assumption because we have no measure of, for example, its density of anything, do we? Yes, and also we've only been finding these things around a small fraction of the stars.

If you do those calculations, it turns out that about one percent of sun-like stars have these hot Jupiters and maybe about seven percent have these eccentric giants. What about the other 92 percent? Oh, so the other 92 percent could be normal or they could be even weirder.

We just don't know yet.

V3.4 So, this radial velocity method has been a great triumph. At last, we've found huge numbers of planets around other stars.

The people who did it became famous, household names.

They wrote books, they get huge amounts of telescope time and all the good things in life.

These weird things we're discovering, they're not finding anything like our own solar system.

We're discovering these hot Jupiters and these eccentric giants.

So, Paul, whenever we measure things, we always have the inclination, right? So, we're throwing a lot of faith in the idea that we're really getting a random selection of stuff.

It strikes me that we would really like to pin down that inclination a bit better.

That's one worry about the solar system, for any given planet we don't know the inclinations, the mass could be much than what we're talking about, so when we talk about your resonances and Upsilon Andromedae, whatever we've been talking about, maybe we're talking complete crap because there's actually a ecliptic system there, they're nearly face on giant stars.

The other thing that really bugs me is that we're not actually sure that these things are planets.

All we know is a mass and an orbit. I mean, it could be black holes orbiting or who knows what.

It could be a huge alien space civilisations or what. It would be nice to actually know we're talking about planets here. So, Paul, why don't we think about doing what Captain Cook did when he was on his way to explore Australia.

He, as you recall, was actually employed, not to look for Australia, but to look at a transit of Venus and the idea was back then was that if you could see the planet Venus go in front of the sun, you could quite accurately measure the distance to the sun; which, back in the 1700's was not well known.

Captain Cook, of course, that was the things he did and, in an interesting twist of fate, the science subsidised the military outcome afterwards, which was to go out and, essentially, claim Australia for England.

Yes, we always tell when politicians ask "what use is astronomy?" We say "well, it does have spin- offs like Australia." In the case of these extrasolar planets, we're not going to actually see the dot as it goes across here.

Bear in mind, we're not seeing the disk of the star, we're just seeing a bit of blurry...

It's just a point of light, right? Yep, but we could tell that as it goes in front, we get the dip in brightness.

That's only going to happen if the planet's in an edge on orbit. Is that likely at all? Well, some fraction is going to be.

Certainly those hot Jupiters are going to quite likely be.

They've got quite a good chance to be, but bear in mind, this is not to scale.

The planet here is actually much too close in to be to scale. (Right. They aren't really this big.) But if it's much further away it could be edge on.

What a bunch of people did is they went out and got all the planets, which we knew from our radial velocity had planets, or so we thought, and we were hoping that one or two of them might actually, by a fluke, be edge on enough that we could see the transits.

So, this is a great experiment, right? A young astronomer, named Dave Charbonneau, literally went out with a tiny little telescope in the parking lot of his university, and stared out at one of the stars with the very sexy title of HD209458, and this is what he saw.

He knew when to look for the transits because, in radial velocity, you can work out exactly when it's going to pass in front, and here's the brightness.

So, one is the normal brightness and you can see it dropped by about one and a half percent, wow! At the right time, and then he observed it again and it did it again.

Well, so this is a great idea because if it's going directly in front of the object, we know the inclination exactly.

It's effectively, you know Sini is one, as good a precision we need, and so there is no ambiguity.

Let's see what we can work out from this data.

Okay, so what can we deduce from a transit like this? What we know is that the observed brightness against time goes down, so what we can measure is how long the transit goes for.

Let's call this Delta T, and the change in brightness, Delta B. We can also measure the normal brightness of the star when it's not in transit B.

What can we learn from that? Well, the easiest way to think about it is to imagine the disk of the star, which is all glowing, and from our point of view every bit of the star will have about the same amount of glow.

We won't be able to see the star, it'll be a point, but nonetheless we'll get a contribution from this bit, a contribution from that bit and so on.

But now, something dark has moved in front of part of it; which means we're losing the amount of light coming from this bit.

Now, that's got a radius R-planet (RP), as the overall thing has a radius R-star (RS), so the fraction of the light we're losing, so lights fraction of light lost, is going to be Delta B over B is going to be the fraction of the star's surface blocked from out point of view.

That's the area of this divided by the total area which is pi RP squared all over pi RS squared.

So, the pi's cancel, equals the radius of the planet over the radius of the star squared.

We need to rearrange this because what we actually measure is this, and what we want to know is the radius of the planet, so take the square root of both sides and we end up with RP equals radius of the star times the square root of Delta B over B.

Now, this is assuming that all parts of the star has the same brightness as viewed from us, in practice the edge bits of the star appear a little bit darker, it's called limb darkening, so a problem one would have to take into account.

But if you measured Delta B in the middle of the transit, this is actually pretty accurate.

So, what's the radius of this particular planet? We have Delta B is one and a half percent and in this particular case we know that the radius of the star is 1.1 times the radius of the sun, so in this case the radius of the planet equals 1.1 times the radius of the sun, which is 700,000 kilometres, close enough, times Delta B over B, that's 1.5 percent, so that's 1.5 over 100, the ratio, which comes out as about 94,000 kilometres.

Now to compare to Jupiter, which is about 70,000 kilometres. So, that's looking like a gas giant.

A bit bigger than Jupiter, in fact, but roughly comparable.

Now, that's the simplest thing to work out.

Just look at the dip in brightness divided by the normal brightness and that gives you the ratio of the sizes.

You can also, if you look at the brightness versus time, and if you see more than one transit, you can measure the orbital period from the middle of this transit to the middle of that transit.

We've already derived the equation for this, the orbital radius.

How far the star is from the planet is equal to the cube root GM star period squared over four pi squared.

Now, in this case, that was already known from the radial velocity measurements, but if you discover something purely using transits, that's the useful thing to be able to work out. A final thing we can work out is to get the exact inclination. We know it has to be nearly edge on, and that's usually good enough, but if you think about it, here's the disk of the star, now from our point of view the planets moving across.

If it's exactly edge on, it's going to go at a velocity of V across there, so the transit time, Delta T, is going to be 2R-star over the orbital velocity of the planet.

But if it's slightly off edge on, then it's got less distance to cover, and in principle, you could have a glancing transit where it's going to be very, very short.

So, you know the angle of inclination is nearly 90 degrees, but you can work out exactly whether it's 87 degrees or 85 degrees or something like that by looking at the Delta T, you know the orbital velocity from the radial velocity measurements or you can calculate it from this.

We wont do this calculation, it's a bit complicated and fiddly, but this gives you the exact inclination.

It doesn't really matter too much because it's going to be nearly 90, but it's sometimes nice to know.

V3.5 At long last we actually know that this thing really is planet size. It actually looks like Jupiter.

This is actually a real scale picture of the thing with all the right properties, which means it's almost invisible, but you can see the transit every now and then and dimly make out the planet as it whizzes past.

But we now know its radius, it really is not just a black hole or something, it really is a planet of about Jupiter size.

But Paul, this is only one object, and there aren't that many planets discovered by the radial velocity method and if we're going to go out and look at all those objects, the odds of finding another transiting planet are not that large.

Maybe we'll find one or two more, but we really need more because we can get caught out by only using single objects.

Yes, a lot of people are scratching their heads and wondering how we're going to find more of these things.

We can't just rely on following up the radial velocity ones because most are not going to be edge on.

But for a radial velocity measurement we can only measure one star at a time, it takes a big telescope a lot of time.

But imaging, you're taking pictures of these things and trying to measure the brightness.

That needs much smaller telescopes to have bigger fields of view and look at many more stars at a time.

That was the idea, you might pick some region of the sky with lots of stars, like this one up here, and point a medium or small telescope like this at it and take a picture and you might measure a few hundred thousand stars at a time and do that over and over again and look for the transits. So, the only problem with this is that when you try to take pictures of big pieces of the sky, you have the problem of actually doing the photometry as accurate. We need to do it, it looks like, to better the half the percent accuracy.

That's the trouble. Photometry is the art of measuring how bright something is and these dips are only like a one and a half percent, or maybe even smaller if we get small planets, so you have got to get very high precision brightness from maybe a hundred thousand or a million stars across the whole field of view, and that's difficult for all sorts of reasons.

I mean, one reason is that you've got your detector which has pixels and let's say the light's falling over here.

It'll fall on this bit of this pixel, every pixel with slightly different sensitivity.

Of course, as time goes on, it's going to move around because of the atmospheric seeing, so it's going to be jumping from pixel to pixel to all over different sensitivities.

In fact, it's even worse than that because even within an individual pixel, that bit of the pixel might be less sensitive than the middle of the pixel.

Right, and so we really do have the problem of trying to deal with what, unfortunately, this is what a star really looks like to a telescope, it doesn't look like the beautiful pointy thing that you often see in pictures unless you stare at it for a long, long time and are able to average over things.

Well, a solution to this was to actually put the telescope deliberately out of focus, which is what they do, so replace it with something like that.

In this case, if it's jiggling around, it's going to be almost the difference because it's spreading over so many pixels.

Each pixel might have very different sensitivity, but if you average over a hundred pixels, that's going to average to not much.

So, this is the first approach.

Consider, it goes against everything we know as an astronomer to deliberately put your telescope out of focus, but these things are so bright you can measure them well anyway.

Well, the advantage, of course, is that these digital detectors can only count up to, typically about 65,000 and, for some of these stars, you're literally getting millions of photons per second; so this is a good way to count up to a bigger number which means you can average over better in addition to just the atmosphere itself.

The atmosphere itself is another problem.

Here's a time lapse at Mount Stromlo that I took a couple of nights ago, and you can see a number of things here.

First of all, there is a whole bunch of clouds around and there's some kind of clouds moving up there.

Those are fairly obvious ones, but at night you're taking your data of something and some tiny little wisp of Cirrus goes, or you might not even notice especially if it's a dark night, so that can give you variations of brightness as well. So, I think "yay! It's a planet!" What you've discovered is a cloud in the atmosphere above you.

Secondly, even when it's a perfectly clear night, there's dust in the atmosphere and you're looking for these transits over multiple nights and on different nights there's different amounts of dust.

For example, the observatory in the Canary Islands has trouble with this dust being blown off the Sahara Desert over them.

Depending on the wind direction, there's a lot of dust coming over, you can't see it but then it drops the light.

Then again, if you imagine looking at a particular star, you can see all these stars around here, the whole sky is rotating, compared to the Earth, it's moving down.

So, you follow a given star, as time goes on it's getting lower and lower into the sky, we're looking at more and more atmosphere which is going to cause more and more absorption.

So, you've got all these things that are going to cause the brightness to vary with time. What can we do about that? Well, it strikes me that we're going to have to be very clever about how we measure things, but if we looks at a big part of the sky, we can do everything to sort of inter-compare with everything else we see, so we don't really care about absolutely how bright the star is, we only care how it's brightness changes over time relative to everything else.

Because the vast majority of this is that we're not going to have a transit at a particular moment, so if we average across all of the other stars, that will vary as the atmospheric emissions vary, and then you look at the brightness relative to that.

If, for example, a cloud comes over, it's going to affect not just one star, it'll affect all of the stars around it; and so you can say oh well, this star is still this much less bright than that star and you can inter-compare everything and maybe be able to get rid of this problem of the atmosphere.

So, people using this technique has developed this.

The current state-of-the-art is to actually not look at a small bit of the sky with a fairly powerful telescope, but have a whole bunch of much smaller telescopes.

This is the HAT-South Telescope centre at Siding Spring Observatory in those boxes over there, and when they open up you see, once again, a bunch of fairly small telescopes.

The benefit of the small telescopes are that they can look at a very wide area of the sky and because you've got a very wide area of they sky, you can pick out some really bright stars.

You don't need a big telescope to get decent counts on them and also, because they're so bright, they're going to be really easy to follow up.

Yes, and so this is a project which we're doing up at Siding Spring and each time it looks, it's actually looking at four identical pictures offset in the sky and we can look at almost 250,000 stars at a time with this telescope.

V3.6 Today, Paul and I are up here at Mount Stromlo's observatory talking to Dr. Dan Bayliss about the HAT-South Telescope. So, what is HAT-South? HAT-South is a global network of telescopes. We've got telescopes in Australia, Namibia and Chile, and they're small telescopes that are looking for transiting exoplanets around bright stars.

So, why is a global network a good idea rather than just having one telescope? Yes, good question. So, the first transit surveys were just from a single sight, but what happens there is, because of the day-night cycle, we miss a whole lot of the transit events.

They only last for a few hours, so by having global coverage, it means we can continually monitor the stars and we can catch all of the transits that are happening.

So, if you had a transit that have happened, let's say, every four days or so, you can imagine it happening, in a regular telescope would only have one, it could happen at every daytime, at noon and you just never would find it, presumably.

Yes, exactly, and with a network for HAT-South, it's always dark on one of the sites so we would, therefore, catch a transit each time.

What is HAT-South Telescope in terms of the telescopes themselves? The telescopes are actually quite small. The primary mirrors are only 18 centimetres, but we have four mounted on one unit.

What that allows us to do is cover a huge area of sky, about 128 square degrees.

We need that because we need to monitor tens of thousands of stars just to catch one of these transiting planets.

How is the network of small telescopes better than a big telescope for this? A big telescope can obviously gather more light, but usually what you get with a big telescope is only a small field of view, so even though you can monitor stars that are fainter, you don't cover a wide area of sky, so you can't monitor all of the bright stars.

Now, the reason we're really interested in bright stars is that if you see a transiting planet around a bright star, there's lots more exciting follow up work you can do to work out things like how hot it is, what the atmosphere is made of and its orbital orientation.

So, this sounds like an interesting idea that, presumably, other people are doing.

How have you found it? Has it been an easy experiment to do or has it had its challenges? It certainly had its challenges, for example, the HAT-South network runs in an automated and remote way, so I don't stay up each night checking on the telescope. To get the telescope to run automatically is actually quite a challenge.

It actually has to be able to sense the weather and know when to open and when to close.

The other part of it that's been a challenge is working out which of our stars really have planets going around them.

We see a lot of signals that look like they could be transiting planets, but there's a lot of work to then go and look at those candidates afterwards and see if they really are transiting exoplanets.

What fraction of your candidates actually turn out to be exoplanets, would you say? Probably, in the end, only about 10 percent of our candidates turn out to be exoplanets.

There's many other things that look like exoplanets which aren't. For example, eclipsing binary stars often look like a transiting planet signal, but when you investigate more carefully, you work out that it's a star rather than a planet.

So, it sounds like you've made some discoveries. What are the types of discoveries you've made now with HAT-South? Yes, so this year already we've published three transiting planets that we've found. They've all been interesting in their own right.

For example, HATS-2B is one of the planets that we found and that transits in front of a star which has got a lot of star spots on it, just like the spots we see on our own sun, except much much larger.

When the planet passes in front of one of these spots, it actually appears to get brighter because the planet isn't passing in front of a dark spot on the sun.

So, we've been able to start characterising, not just the planet, but the star itself using transiting planets.

So, we can use this method literally to see tiny little sun spots on a star on the other side of the galaxy.

Yes, that's right, as the planet passes in front of the star, it gives you a little map of that part of the star that it passes in front of, so if there are spots, we can see them.

So, HAT-South is currently the cutting edge for ground-based transit searches, what's going to happen next? Where do you go from now? Yes, so the real challenge is to try to find planets that are even smaller than what we can see at the moment.

To do that, we need to get to a higher precision on our light curves.

One of the ways to do that is from space, so the Kepler mission in space has been very successful in monitoring stars and the next transit mission that NASA is planning is called TESS and that is similar to HAT-South, it's quite small telescopes, but from space, it doesn't have the Earth’s atmosphere to interrupt the starlight, so the precision of the light curves is much better.

It's hoped that, with a mission like that, we might be able to find much smaller planets right down to the size of just a few Earth masses.

What would be the most exciting thing that you could imagine discovering with one of these transit surveys? Well, ultimately, we'd like to see planets that would have some possibility of having life.

Now, of course, we don't really know what that means.

On planet Earth, it means liquid water, so I guess finding a transiting planet that is a similar size to Earth and in a zone around a star that could have liquid water would be really exciting, and if that happened, I think we'd focus all of our attention on trying to work out what the atmosphere of that planet is because there's some chemical signs that might give away life being on that planet.

Well, thank you very much for talking to us. (Yes, thank you.) Thank you.

V3.7 There's been this huge waves of projects looking for these transits. It sounds pretty easy.

You just photograph stars repeatedly and look for very small dips in brightness every now and then. You were involved with one with Dan, Brian, is it as easy as that? Well, unfortunately, there's a lot of things that can make a star dip in the way that mimics a planet and so we have to worry about getting rid of things, for example, of two stars, a bigger and a smaller one orbiting, where you just sort of clip the edge of the one star with the other.

It turns out that puts a little dip, and the reason why the dip is so small is because you just clip a little bit of one star with the other.

So, we have to get rid of that effectively by looking at the velocity of this star, because this system will have a much bigger radial velocity change, so it's a lot easier than measuring with the way you find planets, so you can get rid of that type of thing. But there are other problems as well.

So, in this case, we have an eclipsing binary again where the star really gets eclipsed, but there's another star that is behind or in front and, of course, when we look through the Earth's atmosphere, one pixel is much, much bigger than this screen, so you're averaging or adding up everything that you see here.

So, these two, if just by themselves, are making quite a big dips because they're big things partly in front of each other, but because their light is diluted by this star over here, it makes it look very small.

Right, and so that's a real problem and so there's a couple of ways we can get rid of this.

One way is just to make sure that, for example, the star that we're looking at doesn't look like two or three different stars, the other one to make sure that this star isn't a because it turns out that when you're looking for transits, a giant star has a huge radius compared to the planet and so you just can't see transiting planets in front of giant stars.

So, how many candidate planet things do you see and what fraction of them turn out to be real planets? The fraction that we're having to get rid of, it's almost a hundred to one in the end.

I mean, we're able to pretty quickly get it down to sort of ten to one, but in the end we have to go through and do radial velocities of the transiting objects we see to be confident that they are planets.

So, this is a bit of a nasty surprise. It looked like a great method.

You could do it with small telescopes and the trouble is, because of this huge contamination of things like this, you had to actually still go to the big telescope for the follow-up.

So, huge amounts of big telescope time, once again required to follow all of these things up.

But it's been done, and continuing to be done and here now is our discovery chart.

Once again showing the mass of the planets against the orbit, only now we are going to start showing red dots for the ones discovered using the transit method.

There's the first one, and what you can see is that these things are primarily hot Jupiters.

Right, and you should realise that it's not that suddenly we've discovered a bunch of missing hot Jupiters, it's just that this method is really good at finding objects here in the diagram, and it's really bad at finding objects down here. The basic reason for that is, let's imagine that Brian's head is a star and we have got a planet it over here, if it's close in, if it's edge-on it will cause a transit. It can actually be at quite an angle and still cause a transit.

But if it's way out over here, it doesn't have to be very far a line before it goes above or below Brian's head.

So, basically the probability of seeing a transit goes down quite deeply as you go further out, simply because the odds of it being edge-on enough to go in front becomes very, very small.

So, Paul, we can find all of these kind of wacko hot Jupiters, we already know they existed, it seems, well I won't say it's pointless, but it's not obvious why it's so interesting.

Well, why it's interesting, I mean yes, we knew hot Jupiters existed, but now we actually know the mass, not just M Sini because it's got to be pretty much edge on, more importantly, we should know the radius of these things.

We're always assuming, when we call these things hot Jupiters, that they were gas giants like Jupiter, with a density of about 1000 kilograms per cubic metre.

But maybe they were actually giant rocky planets.

In our own solar system, the things of mass of Jupiter are, there is only one of them and it's made of gas, primarily, no density, but maybe there can be masses of things that are more like the Earth, the density of more like 5000 kilograms per cubic metre.

So, how can we tell? Well, here's a plot of the transiting objects, what we're plotting here is their radius in units of Jupiter radius, that's one Jupiter radius, and up here is the mass in units of Jupiter mass.

There's Jupiter, there's Saturn and Neptune and this line here is what you'd expect from something that's primarily made of gas, so about Jupiter's composition, and these error bars up here in purple are the actual planets we're seeing.

So, you can see that there is an object that looks about like Jupiter, but most of the objects are a lot bigger in radius, and remember, the volume, because it's the cube with the radius, being a bit bigger means you're a lot less dense, you really are puffed up.

This is the first big surprise, it looks like these things are actually mostly, not all, but mostly considerably bigger than you'd expect from their mass. These things are very low in density.

Actually incredibly low densities that some of these things up here, I mean, Saturn is actually a low enough density that it would float if you had a really big bath tub, these things are more like the polystyrene type densities, incredibly low.

So, we do know that they're very near to their stars, so maybe they're being puffed up by the fact that they're close to their stars.

Well, this is the first idea people had, you take gas and then you make it that it's heated up, and then as it heats up it becomes less dense, so these things are very close in.

So, just how hot are these Jupiters anyway? Now, if you remember a while back, we derived an equation for the temperature of a planet in equilibrium. We balanced the radiation in from the sun with the radiation out, assuming it absorbed and emitted perfectly and was all the same temperature, which is not very realistic, and we found out that the temperature is the fourth root of the luminosity of the star all over 16 pi Stefan Boltzmann constant sigma and D squared, where D is the distance between the star and the planet.

So, we can use this to work out the temperature of a hot Jupiter.

Let's do an example, so let's say we have a solar luminosity star, so in that case that's the luminosity of the sun, let's assume that it's 0.05AU out, then if you plug numbers in, we end up with a temperature of around 0 kelvin, so pretty hot.

If the star is less luminous and the planet is far away, the temperature will be less.

So, Paul, to explain why these objects are so much less dense than Jupiter, and you kind of expect Jupiter to be how a planet would form, you would think.

Let's plot it as a function of temperature and have a look at what we see, because that's one possible idea to explain things.

Here we have the planet radius, versus the planet temperature and there does seem to be an effect.

You also see that the symbols here indicate, for example, the size or the abundance of elements in these planets and it doesn't seem to correlate with any of those, so it really looks like temperature is driving it. So, problem solved, isn't it? Well, yes, to me it seems like if you're going to shine heat onto the planet, it'll puff up because that's the way gas is.

You heat it up it puffs up, but there may be a problem.

Yes, I mean, the trouble is that we think that a planet like, for example, Saturn, a gas giant like this, Here's an optical picture of it, but if you look at it in infrared, it looks much more evil.

When these things formed, you had a big cloud of gas that shrank and shrank and shrank until it formed these things, much like when a star forms, and in the process a huge amount of heat was generated in the middle.

It turns out that, for gas giants, this heat is still mostly there.

The inside, as you can see from this infrared image, is glowing intensely.

The middle of the planet is much, much hotter than the outside.

So, when we talk about the heat coming in from the outside and warming it up, it might be quite hot on the outside, a thousand degrees or so, but that's nothing to the heat in the middle already, so it's very hard to see how anything you do to the outside of the planet, it might only affect the outer half a percent or so, but the middle of the planet is so hot anyway, it's almost not going to care what's going on out there.

We sort of need to somehow get what's going on on the outside into the inside somehow.

This is currently very controversial. Here's three possible models for what's going on.

If you remember earlier on, we talked about when they might have started off in an elliptical orbit and had huge tides raise when it came closer, that's a possibility.

Maybe when this thing came close, it was pulled out of shape by the intense gravity and as it spun and was pulled all out of shape and that stirred it up and heated it up in the middle. So, that's sort of like what makes Io's volcanoes happen, where Io is getting bent out of shape by Jupiter 100 so it gets heat in its centre, so that's one way to do it.

A second possibility is that there could be winds. Now, we generally think that, because of this tidal effect, the planets are always going to face one side towards the star, so just imagine that Brian is a star, I'm going around him, I would always, as I moved around, rotate so I'm looking at him from the same direction.

That's sort of what the moon does when it goes around the Earth for the same reason.

Exactly the same reason, but this means that if I'm staring intensely at the sun, this side of me is going to be very, very hot and that side is going to be pretty cold, which could well drive very strong winds from one side to the other.

I mean, on Earth, the equator is hot and the poles and cold.

They're nothing like as much of a difference as we get on these planets, and that drives the winds on the Earth.

Maybe temperatures can drive winds here, or maybe they don't.

But, if you're talking about these very strong winds, once again they're at the surface level, but maybe a very strong wind can dredge up and cause some turbulence and stir up the stuff underneath it and that will start the stuff further and further down so you might have some cascade of turbulence further down to warm it all up.

Hmm, yeah I don't know, it sounds a little dubious to me.

What about magnetic heating? I mean, we have our friend, the magnetic field, I bet you that we can do some magic with it here too.

So, of course, we know that planets in our own system have magnetic fields, gas giants have very strong magnetic fields.

Maybe if you have this gas on top that's ionised, that means it will pull the magnetic field lines along with itself and they will then pull on the stuff inside, so maybe that's a way to communicate maybe the winds at the surface down into the middle.

Alright, so we have some models here, but maybe not a solution yet.

V3.8 Here's another really sneaky trick you can do with this transit data, what's called the Rossiter Mclaughlin effect.

The idea is that you can actually use the transit to find out about the rotation of the star that you're orbiting.

So, here we have a star that's going and a transit is going to occur and so this shows you where the object is as a function of how bright the star is as a function of time.

But, of course, the star is rotating. This part of the star is coming towards us, that part is going away from us. Let's colour it now, so the blue is the bit that's coming towards us, because the spectrum from that is going to be blueshifted, and the red bit is redshifted.

As the planet goes across, it'll block out some of the blue light, and then block out some of the red light.

So, as it's blocking out the blue light, the star will appear to be moving away from us a bit anomalously and when you're blocking out some of the red light, the star will appear to be moving towards us, so the velocity of the star will appear to go away and then come towards us.

Right, and so you can actually go through and measure, literally, how this stars rotation compares to the motion of the planet.

What you'd expect is that the planet would be going around the star, in the same sense that the star is spinning by itself, like in this diagram here.

In our own solar system this is the case.

The direction the sun is spinning and the direction all the planets are going around are the same.

You'd expect this to be the case because both the sun and the planets form from the same protoplanetary disk.

This is what you'd expect. But I suppose, to complete this set we should consider the alternative possibility which they are going in the opposite direction, in this case, stars been the same way but now the planet is going to come in from Brian's side.

So, it comes here, blocks the red side first and so it's going to appear like it's moving a bit bluer towards you, it's going to be moving towards you when it comes on this side, relative to when it blocks out the blue light; which is the part which normally indicates motion towards you.

This can be measured and has been measured multiple times, and here's one example of this.

The results were pretty surprising.

It turns out that between 45 and 85 percent of hot Jupiters are misaligned, are more than 30 degrees out from the same plane as the stars going around.

So, these are completely different than our own solar system, and it's really bizarre because, clearly, these objects are being formed by the same gas as the sun.

I mean, they're not being drifted in from inner-planetary space or something, and yet we're looking at this and it's like they almost don't even know about what made the angular momentum that made the star in the first place.

So, this is pretty baffling at the moment, we've got a couple of ideas of what might be going on here.

One idea is that maybe you actually had two protoplanetary disks.

Maybe you had one disk that formed the star and then it went away and another disk got dumped down at some later stage with a different angle and formed the planets, I mean, why not? Another possibility is that this whole Billiards stuff, the planets scattering off each other.

But if you have a play with the simulations, it's quite hard. You tend to end up with things still going the same way around, but if you work on it a bit and have enough time and allow them to very slowly work themselves up, maybe you can get them into these really weirdo orbits.

Alright, so still another mystery on our hands.

V3.9 So, we're really getting somewhere now.

Now that these things actually are planets because we can measure the radius and, not only do they have gas giant masses, but they actually have the radii of gas giants, they really must be planets.

Well, yes, but they are a little bigger than they should be, aren't they? They're quite a bit bigger than Jupiter, for example, and we don't really understand that, and we don't really understand how they got there in the first place.

Yes, and we have talked about a couple of theories, the migration one, which was looking good for a while, but the fact that some of them seem to be going backwards seems to imply that, actually, the Billiards theory is a better one for these things.

Right, okay so we still have a few mysteries here to solve, and these gas giants are interesting, but I kind of want to know about normal planets. Planets that might have life.

Nice and smaller ones.

Yes, I'd like to find some smaller ones, I kind of would like to know more about the planets, rather than just say "yeah, it's about a planet that's sort of looks like Jupiter".

It would be nice to find some ones that are further out, I mean, these things are all very close to the star and probably too hot.

It's nice to find some ones that are actually out where big planets are supposed to be, like in our own solar system.

That's right, so, presumably, we're going to have to rethink a little bit of how we find these objects.

I mean, we've got the basic idea here, but it doesn't seem to quite be delivering what we really want.

V4.1 So, we've got two tools, radio velocity measurements and transit measurements and between them, we find that there really are planets and we can actually measure, not only their mass, but also their radius.

So, does that mean it's all solved? Well, I personally, Paul, would like to know a little bit more about things other than these giant Jupiters, things about smaller planets and then I really kind of want to know what's going on on these things.

What are they made out of? What's going on in these planets? Yes, I guess a smaller planet one would like to potentially live on would be nice to know about. So, why can't we just find smaller planets with transits? I mean, in principle, we could look for really small dips and see really small planets.

So, the problem we have, once again, is our atmosphere and so this is a movie of what a star looks like going through the atmosphere.

We've seen this before and it moved things around from pixel to pixel, so that's why we defocused the telescope to average over that.

Right, and so the reason why it's doing this is because the atmosphere is really bubbly and turbulent and those bubbles of slightly warmer or cooler air act as tiny, little magnifying glasses, effectively.

So, not only is the star moving around, it's becoming brighter and fainter at over a rate of like a thousand times a second.

It changes so it's real problem.

Yes, but it's not like if you get a bunch of cold air in front of the telescope, cold air is denser and so it bends the light more and has a higher refractive index so that it focuses the light on the telescope and makes it appear brighter.

If you get a bubble of hot air coming across, that has the reverse effect and defocuses it.

That's right, and so it's a problem, you might think that we can average over things, right? You go through and, okay don't take a picture every thousandth of a second, take one for an hour and presumably, the average will be okay, but it turns out that you need to observe longer than an hour because the atmosphere doesn't just do this, it changes over all types of frequencies, so you really are stuck.

Yes, a change in brightness is something you can't fix by defocusing the telescope and it doesn't fix very well by having very long exposure times.

Yes, you can fix it a bit, but ultimately you just need to somehow get rid of the atmosphere.

How do we get rid of the atmosphere? Spending a lot of money, it turns out, and going into space. That's the best way to do it.

So, this is the Kepler Space Probe. People have realised that to get these really accurate transits they need to go into space for a while and a number of missions have been planned or launched.

This is the 'great grandaddy' of them or the most powerful one, NASA's Kepler Mission.

What this does is it's specifically designed to go into space and look at lots and lots of stars and measure their brightness with the exquisite precision that's only possible when you haven't got this bubbly atmosphere in front of you.

Right, and so this telescope is a little different than the Hubble Space Telescope.

The Hubble Space Telescope is able to go through and it, essentially, magnifies the stars to, what we would say, that the diffraction limit is so as good as it can see.

This telescope doesn't bother doing that.

It says we don't care about making a precision picture of each star, what we want to do is just measure how bright it is and not have that messy atmosphere, and so each star comes on and really is a tiny, little point. You can't actually see that much information on each star.

Yep, so what it does is it's basically spent three years pointing at the same bit of the sky.

It's got lots of different detectors and so these are the places they look at in the sky, up in the Northern Hemisphere and it just stares at about , 140 000 typical sun-like stars for three years.

It sees with each one of these images, which is made up of a bunch of different little detectors and mosaic together.

It sees this huge piece of sky, that's like 200 times bigger than the full moon simultaneously, all out in space.

So, it is really a technological marvel.

You can see the quality of the data it gets.

Here is ground-based observation of a given transiting planet and so here are all the different measurements and you can see that there's a fair bit of scattering and that's because of this atmosphere jumping up and down, and over here you can see there's a transit and the points have moved down, and if you average over them enough you can see clearly that there's a dip there, but it's all quite grainy.

Now look at this with Kepler.

This is actually some of the very first data it came out with when it was only up for a few weeks, and the scatter is almost gone.

It's still there, but very much smaller. You can measure this with absolutely exquisite precision.

The amazing thing is the technology used here and here is almost identical. It's really the same type of detectors.

The problem is the atmosphere. It's not like going to space, you're spending a lot more money, well you are because you've got to get it to work in space, but it's really the same stuff.

It's not like there's anything magic, it's just been put up there.

So, with this exquisite precision, from the ground you're lucky if you can measure the brightness to better than 0.1 percent or so, whereas Kepler was designed to get to better than maybe about 50 or 60 parts per million.

It's not going to quite achieve that, it may be more like a 100 parts per million, but that's still an awful lot better than you can possibly do from the ground.

It means that you'd have to observe, essentially, a thousand times longer from the ground to do as well as you do at Kepler.

Even then, you probably wouldn't.

Even then, you probably wouldn't, that's right.

V4.2 Alright Paul, so Kepler has had its three year mission, it's gone and taken all this data and, unfortunately, its mission has ended about the time we thought it was going to and normally these missions go a little longer than that.

You try to get more out of them than you intended, but these reaction wheels that allow it to point precisely in the sky, they're sort of like giant gyroscopes, have broken, two of them have broken so we can't do that anymore. So, what have we learned? Well, from the ground you can only get, say, 0.1 percent precision, so you only see a planet that blocks out 0.1 percent of the light of the star, so it's area is 0.1 percent of the area of the star radius, square root of 0.1 percent.

So, those are big guys.

(These are big guys.) These are going to be things the size of your Jupiter, Saturn gas giant planets.

The hope with Kepler was, because it can get to a much higher precision, it can see much smaller dips and therefore can see smaller things.

So, there's the question, what lurks out there that's smaller than the gas giants? Right, so in our own solar system, it's always kind of puzzled me because we've got Mercury, Venus, Earth and Mars which are these relatively small, rocky planets, which are kind of interesting for living in, and then we've got these big monsters, you know Jupiter, Saturn, Uranus and Neptune out there which seem completely different.

It's like we sort of have A and B. Now, do we see that same type of thing out there? Yes, I mean it all seems to be a bit strange to use the same word 'planet' for both of these things, because they're so different.

I think you should use 'gas giant' and 'rocky crap' or something like that.

This is one of the big challenges. Were we going to see the same dichotomy, the same division? Were they going to see a clear break between big things and small things and nothing in the middle? Or maybe, in other, our system is unusual, maybe there are actually lots of things in the middle.

So, what they find, well here's a recent attempt to work out all of the stuff.

What we're plotting here in the top plot is the radius of the planet relative to the Earth, so the Earth would be here, that's about the absolute limit of what you can see, getting up to your Jupiter as about 11 times the radius of the Earth.

What we can see is the number of planets at all these different radii and what you can see is basically small ones drastically outnumber big ones.

These are the ones you've been seeing before and the small ones hugely outnumber them.

What we can also see is that there's kind of no clear gap. Maybe, there's a bit of a jump up there, but by and large you can probably fit one curve through the error bars all the way from here to here.

So, it kind of looks like the number ramps up steadily from one to the other, or maybe it ramps up even faster than steadily.

But there do seem to be huge numbers of things bigger than the biggest rocky planet in our solar system, the biggest rocky planet in our solar system is the one we live on, the Earth, which is right down the bottom here. So, all these things up here, Neptune is 3.8 Earth radii so the smallest is gas giant is there, what we can see is the vast majority Kepler are finding are bigger than Earth but smaller than Neptune, so they're bang in this gap that we have in our own solar system.

Okay, so that's kind of interesting. That means that maybe our solar system is a little unique in the big picture of things.

Although, we have to remember that we're not looking out at very large distances here, we're really looking at the inner part of the solar system still.

Yes, these are things with periods of up to 50 days, so these are all much, much closer in than anything in our solar system.

In an attempt to do the same thing with mass rather than radius, Kepler, of course, measures how much the light dips and that's the radius.

To get the mass, you then have to go to a very big telescope and measure a spectrum and look for the radial velocity which they can't do for most of the things found with Kepler.

In fact, most of what Kepler finds are never going to get confirmed.

There's probably about a 90 percent chance they're a planet, but there's always a possibility that there's some sort of eclipsing binary.

They try their best to eliminate them but without getting spectra with giant telescopes, which is impossible for most of these faint Kepler stars, you're never going to prove it.

Yes, so one of the problems with Kepler, and maybe the only problem I can really think of, is that to make it so they can see ,000 stars at a time, they had to look at pretty faint stars and so it turns out that faint stars are hard to measure radial velocities because there's just not enough photons arriving at Earth, even with our biggest telescopes, to get those accurate measurements.

We can do it for mass as well, and the radial velocity people have been trying to measure the same thing.

To begin with, you're finding the larger objects, I suppose that, as you remember, they got better and better precision, they started finding smaller ones.

The other way they can find smaller ones it to look for smaller stars.

If a star is only one tenth the mass of the sun, then a planet is 10 times smaller and can still cause it to wobble by the same amount.

So, they're also finding the same thing, it's the yellow dots here, that the number of planets close in climbs drastically as you go into smaller masses, just like smaller radii.

It does actually seem that both sets of observations, then we've got very little idea about the things down at the Earth's mass from the radial velocity, but one or two have been found around really tiny dwarf stars at the highest possible precision and it's kind of looking like the same picture.

Yes, it is remarkably similar, so it's unusual for things to agree that well given that we're doing things in very different ways here, so that seems to be that we have a pretty good idea of what's happening. Yes, so these things have been coined 'Super-Earths', maybe they should be called 'Mini-Neptunes', but 'Super-Earths' sounds a bit sexier I guess.

So, the idea is, what are all these things that we don't have any analogs like we do in our own solar system, bigger than the Earth, smaller than Neptune and so we're calling them the Super-Earths.

Maybe they're rocky planets like the Earth, just bigger.

Well, we can, I think it seems to me, we have the right type of information to look at this further because we have mass and we have radius, so presumably, that's going to be able to tell us a bit more about what they're made out of.

Yes, this is the question, are they actually your Mini-Neptunes, so gas giants smaller than anything we see or are they rocky planets bigger than anything we see? Well, what you can do is plot the mass.

This is for ones which have the radial velocity measurement which is only a very tiny fraction of the Kepler ones, because it needs huge amounts of big ground-based telescope spectroscopy time, and the planet radius Earth radii.

So, this is our own solar system, that's Venus and Earth, Uranus and Neptune, Saturn and Jupiter as you go up here.

What you can see is all these dots, all the different things measured which have both radial velocity and transit measurements whether from Kepler or from the ground, and what they've plotted here is theoretical models for what you'd expect for different sorts of material.

So, if it's hydrogen, you're expected to sit on this line here, so as the mass gets bigger and it get's bigger and bigger until this point, the hydrogen is so heavy that if you add more mass it actually makes it compress, like what we were talking about earlier, like having a pile of pillows.

You put more weight on top of a pile of pillows, things actually start going down.

This is where they started eventually turning into stars if you make them too big.

Yes, and here is a planet that is made entirely of water, one entirely of rock and entirely of iron.

Clearly and is going to be smaller at a given mass because it's got a higher density.

Right, and so when you did these models, it's really a matter of figuring out how the gas or the rock or water behaves as you put more of it, it exerts pressure, it pushes back and different things push back differently, but, of course, gravity always cares about how much mass there is, so gravity is really just related to the radius and the mass.

You can put these all together and these models are actually pretty secure.

They're things we can sort of test here on Earth, so we really do know what a ball of hydrogen is going to do.

Yes, the ones that you can see is if you look at Saturn and Jupiter, they lie near the hydrogen line, whereas Uranus and Neptune, while they look like gas giants from the outside, actually lie nearer the water line and, in fact, people in our own solar system call them 'ice giants' rather than 'gas giants'.

While they have the gassiest atmosphere, on the basis of their density and radius, they're probably made mostly of a thick ball of ice with a thin layer of gas on the surface of them. These new planets, where are they sitting? 100 Well, some of them are down here around the rocky ones, but only the very smallest, and there's almost a continuous progression.

Rocky ones, iron ones up to water ones, which may well be ice ones, and then there's sort of a gap in the middle and it drops up to hydrogen ones.

There are a few things in the middle all the way through.

But these little guys down here, they really do look like Super-Earths, they really look like giant analogs of Earth.

They're as dense, they're probably going to have iron cores and rocky mantels and so, aside from being really, really close to their stars, and so presumably pretty hot, they look like at least something that we are used to living on.

This looks like we've got a range. One thing that's caused a lot of interest is one was lying near this line, which was quite a lot of them, the idea that these actually might be water planets.

So, what we know is the radius and the mass, unfortunately there's more than one way to get the same radius and mass.

So you have two possible ideas.

One is something like you've got an iron core, then rocks, this is iron, magnesium, silicates, various things that we would call rock, and then a rather thick layer of water.

On the Earth we have your iron core, 6000 kilometres of rock and, on average, maybe a couple of kilometres of water, whereas here we're talking maybe a thousand kilometres of water.

This would be a very, vey deep ocean and then the hydrogen and helium gas up there, or it could be, if you get rid of the hydrogen and helium and actually just have water all the way with just a little bit of hydrogen at the end once again, around iron and a rocky core.

Both of these things can give things that lie around on this line over there.

We expect it to really be water and not ice, because these things are in a solar system.

Is that enough to make it water as opposed to the outside? Well, probably it has got some water, it's very, very hot presumably, but actually, the pressure is so intense that even at the high temperatures, it's going to be solid, so it's hard to imagine hot ice, but if you put enough pressure on, water will turn into a solid, even at very high temperatures.

So, quite what form it's in, it's probably got water layers somewhere in it, but in the middle it's a form of H2Os like nothing we've seen on Earth.

V4.3 So, Kepler has shown us that this is a massive population of Super-Earths.

It would be nice to actually work out some statistics of these.

For example, how many very heavy Super-Earths as opposed to lighter Super-Earths, how many that are as in close-in orbits as opposed to further out.

The trouble with doing that is the last sample is all vey biased. For example, the closer something is in, the more likely we'll be able to see it simply because it's more likely to be on an edge on orbit.

When something is further out, it has to be more precisely edge on to be seen.

Likewise, the bigger planets with larger radii are going to cause bigger dips, they're going to be easier to see.

In some stars, the star itself is very stable.

It's always the same brightness even a very small dip produces a measurable effect, whereas other stars have flares and sun spots, so their brightness is jiggling around all the time adding more noise, so a planet has to be really big to be measured there.

So, all this means is that the population of things we see is not a fair representation of the overall population.

So, is there some way to actually unbias statistics to go from what we see to what's really there? I mean, how would you go about unbiasing something like this, Brian? Well, this is a pretty common problem throughout astrophysics is going through and figuring out what you have compared to what's really there.

So, I really like using, what we call, Monte Carlo simulations where you sort of roll the dice, or you sort of fake-roll the dice, of what's out there, put it through your system and how you observe it with your telescopes and the weather and anything that you know about the stars and you see what's out there and what you actually detect on the telescopes.

So, you're generating a random bunch of, in this case, planets of a range of sizes and inclinations, they put them in random positions and then faking what you see and running it through the same software you can use.

Yes, so we would typically go through and we would take a first guess of what we think the population looks like and then we would see what we end up with and compare that with our observations and say oh, we're missing... we have some extra ones here... and some of these planets are missing and so we tweak what's out there until we get the right answer and it's a very powerful technique.

You can throw almost anything into it, but you can only do what you know. That's the problem.

So, that's one possibility and some analysis have used that.

Another method is the method of binning. What you can do is take all of your detections and bin them up.

What we've got here is a plot showing the planet size in Earth radius, that's one Earth radius, two Earth radii, four Earth radii, some sort of log scale and across here is the period in days, so from five days to 50 days so they're all very close in.

(Very quick things, yes.) Each dot represents something found by Kepler.

But what you can do is break it up into these little squares, and for each square, so if you look at this square it's things between 2.83 and four times the Earth's radius, and between five and 10.8 days period and there were two dots in that box and you can calculate that, for things in that situation, 98 percent of them are going to be seen. They're so close in and they're so big that they're very easy targets.

On the other hand, down here, things are between 23.2 and 50 days and between one and 1.4 Earth radii, we have found six things in this box, but there's only a 59 percent chance of seeing them, and when you go down here, the chances get even lower, so 13 percent and one percent down here.

So, what you can do is you can take the numbers that you actually see and divide by the percentage, so if the percentage is 100, you're not changing it very much but for things that's only a 50 percent chance, that means that instead of six there should have been 12 and we've missed half of them.

So, you can correct for this sort of way as well.

Yes, that works well. Either way, this one's maybe a little easier to understand.

It has the trouble that by the time you divide them up to lots of different boxes, there's not many left in each box. (That's right.) Anyway, once we get from these sort of analysis, well it's very early days yet, but here are some initial numbers.

What we're looking at here is the number of these planets as a function of their orbital period.

So, we're going from less than a day up to 50 days and what you can see is that the numbers go up as you go out.

It will possibly start levelling out once you get near 50 days. There aren't so many that they're really big ones.

These eight to 32 Earth radii ones, as the top ones are two to the 32 Earth radii.

So, what this is saying is that almost five or six percent of all stars have a Super-Earth, more or less, within a period of 50 days.

So, I mean, five percent doesn't sound like very much but, I mean, our solar system doesn't look anything at all like that.

That's five percent in each bin, so that's five percent there, another five percent over here, so that starts adding up pretty fast.

Right, and so if you add it all up in total, it almost looks like about 30 percent to have a Super Earth here.

Yes, earlier on we were thinking there were lots of things very, very close in because we saw all of these hot Jupiters.

What it was telling us is that for the things where the period is down to three or four days, there are actually a lot more periods up at 30-40 days. So, these ones are very easy ones to see to begin with, these very massive things close in, but it looks like they're much outnumbered by the somewhat further out, less massive things.

That's something you learn from unbiasing the sample.

Alright, so that's great, but it sort of tells us that to really get going we need to keep observing so we can look out in the interesting part of the diagram where we inhabit. (Beyond 50 days.) Exactly.

Here's another rather unexpected result. You can actually look at what the odds are of having one of these planets, mostly Super-Earths, within a 50 day orbit as a function of the temperature of the star. So, the sun's got a temperature of about 6000 degrees, so most stars in the Kepler field are dwarf stars, red dwarfs down here.

What we can see is for the massive stars, you can't tell very much, it's kind of flat, they're about the same numbers all the way up and it's so few. (Not very common, yes.) So few of them you can't tell very much.

When you look at the smaller near two to four Earth radius ones, you find that the numbers go up a lot, you get to cooler stars.

So, the red dwarf stars, which are by far the most numerous stars in the galaxy, also seem to have a higher fraction of these close-in planets, so that means the galaxy is pretty full of red dwarfs with Super-Earths in close-in orbits.

That's quite remarkable, because, of course, those red dwarfs are the most common stars in the galaxy by an order of magnitude.

(That's a lot of planets.) So, the universe will literally be teeming with planets.

You can also, and this is more tricky, do some statistics about multiple planet systems.

A number of the Kepler stars have multiple transits, so you see, say, one set of dips that appear over your four days and another set of dips that appear, say, 10 days or 15 or 100 or something like that.

This only happens if both the planets are in edge-on orbits.

So, you could ask, let's say you have six planets in a system.

It could be some are edge on and some of them are going over the poles.

In that case, even though there are lots of them there, you're only going to see one set of transits, because the odds of two orbits going over in the line of sight are very remote.

But if they're all going around in the same plane like the ecliptic in our own solar system, then if it's edge on it'll be edge-on for all of them.

So, you either see no planets or lots of planets.

People have done the statistics and it seems like when you do see planets, you very often see lots and lots of them, and so it seems that in fact, multiple planet systems are very common and they do all seem to be in the same plane.

Well, that's convenient. That's at least a lot like our own solar system, so that's a little reassuring I guess.

It doesn't tie in with the Rossiter McLauchlin effect we talked about last time where the star seems to be misaligned quite a lot of the time with the planets.

So, maybe it's telling us that those Super-Jupiters, where that Rossiter McLauchlin effect is sensitive to, are really a different beast than the average solar system. We only know they're only one percent.

Or, it could be that you might have had two discs to form this. One disk that forms a star and then another lot of gas comes down from a different angle and the planets form out of that, so they all have a different orientation to the star. I mean, weird but...

Well, I guess we'll just have to wait to find out the ultimate answer.

V4.4 So, Paul, we've come an amazing way here.

We're able to find out all these interesting things about planets, but I want to know more.

I really want to know, what are these planets, how hot are they? What are their atmospheres made out of? What's going on? Do they have winds? Do they have spots? I want to know more.

Luckily, the data with the exquisite precision of Kepler can actually get us some more facts, rather than just the radius and the mass.

Now, here's a plot we've seen before. It's showing the brightness versus time for ground-based data and the exquisite precision of the ground- based data versus time with the Kepler data.

But now, let's zoom in on just the top bit here.

We can't really see it here because it's so small, but if we zoom in on that, we might expect to see something else going on.

Let's imagine that we've got a transiting planet like this.

Look at brightness versus time and you get the big dip when it goes in front, but there's also going to be a little dip when it goes behind because you'll still see the star, but you'll lost the light from the planet.

Because the planet is much smaller than the star, it's going to be a much smaller dip.

So we'll see it going along here with a big dip that goes in front and then the small dip when it goes behind.

So, the planet is actually reflecting the star's light, so it does contribute a little bit.

Yes, let's zoom in on the planet here, so you see a planet that comes on the far side we're seeing the reflective side and then it disappears in front of the star and then comes out.

Okay, so we expect the planet to be quite dark here because, essentially, we don't see it, maybe a crescent or nothing.

On this side it's full so we expect it to be as bright as possible when it's behind.

There's two effects, one is the so-called secondary eclipse, which is when the planet goes behind the star, but also you'll notice that in between the curve isn't quite flat. Let's go back and play that again.

So, it's going around. You'll see here that we're looking at it face on, we're now looking at it half on, and now we're looking at a crescent. That causes a dip here. So, when it's on the far side, like it's coming out here, it's quite a bit of light from the planet and then as the planet goes closer around towards us, it then drops off because we're only seeing the dark side of the planet.

The planet is only shining because it's reflecting light. So, in principle, we can see two things here.

We can see this oval sort of sine wave type wobble due to being able to see the illuminated as opposed to the dark side of the planet, and we'll also see this secondary eclipse when it goes behind. Can we actually see that? Well, so here's the plot we were looking at before magnified seven times and now magnified 100 times.

You see a little dip there, but if we magnify it, it becomes pretty defined.

Yes, you can see the secondary dip just about there, but with under a much higher magnification, we now just see the uncertainties in the Kepler data, very much smaller than the ground-based one.

On this scale, the primary transit is way off scale, but you can see that there's definitely a little bit of a dip here, but also you can see that there's a slope in between.

So, we really are seeing the light of the planet here dramatically and you're seeing it disappear, so that is how bright the planet is and that should tell us that, at some level, what its albedo is,how much of its light it's reflecting.

That's what's exciting.

Yep, so there had been five of these things seen now by Kepler, and this number will go up fast I imagine and most are reflecting curiously little light.

Most planets actually reflect quite a bit of the light that bounce off of them, but with these ones it's less than 30 percent, so that's actually quite dark, which is a bit weird.

So, we have five systems, they are very interesting, but the fact that they are curiously not reflecting much light makes them, well, I guess the question is "is that what we expect?" I mean, the Earth reflects about 30 percent of its light because it has clouds.

Yep, and we think that these things are gas giants, and gas giants also reflect light from clouds.

Clouds are tiny droplets of something that's condensed in the atmosphere, in that case with the Earth there, water droplets typically, maybe ice if it's high enough up. In the case with Jupiter, these would be hydrocarbons of various descriptions, you can see the beautiful swirling coloured patterns of the gas giant, there's Io in the front of Jupiter.

Jupiter reflects a lot of the light and it's because of these cloud droplets.

People have done predictions and, because these Jupiters are so hot, these hot Jupiters that Kepler were looking at, it could well be that there are very few things that actually form droplets.

So, mostly, you've probably got a transparent atmosphere and all the droplets have sunk down where we can't see them.

That might be why they're so dark.

The light is just going right down into the gas until it can't come out rather than being reflected off by clouds up high. Certainly with things like water vapour and hydrocarbons, it would be far to hot for them to be up there, they'd just fall out in the form of rain.

Oh, okay so maybe this isn't such a surprise after all.

Yes, so many artist impressions show things that look like Jupiter, odds are that these things are actually much darker than Jupiter, they may not have these beautiful bands and be rather more boring to look at.

That's not always the case. Look at this data, Brian. This is another transiting object.

So, this is another transiting object where we've zoomed right in and so, we don't show it but there's this primary transit that goes way off scale, but this one is a little different and I not that it has this nice little transit, that's great. (A secondary eclipse.) Yes, sorry, a secondary eclipse, but I note that when we fit that, it gets brighter here, that sort of fits the data a little better.

For example, this green curve where it reaches its maximum brightness of the planet reaches when it goes directly behind.

So, it seems kind of funny. It seems kind of asymmetric in this case, like there's something funny going on.

You'd expect it to. as it goes behind, so let's say that the light and I'm going behind it, you'd expect it to be brightest here or here just either side, because the light's shining full on my face.

What we're seeing is it's actually darker just before and brighter just afterwards.

It keeps on getting brighter, so it's actually brightest around here when some of it should be in shadow.

Right, so it's almost like that there is this bright spot on the planet, so since it's reflecting light, it's almost like there's a bunch of mirrors or clouds on one part of the planet, but not on the other part.

Yes, and indeed this is what people actually believed is happening in this place, that most of the planet is actually very dark, but one side is actually much brighter.

Maybe it has cloud and the clouds are all on one side.

Maybe it's got some sort of circulation of the clouds forming on the cold side of the planet and not the bright side, or something and carried on one direction for whatever reason.

This, if you like, is a first actual map of a planet from another star, and the map seems to say that one half of it is shiny, maybe from clouds, and one side isn't. (Okay, so that's rather curious.) There's been another case where, actually using the Hubble Space telescope, so once you've found the planet using another technique you can then use the Hubble, which also has the benefit of being in space, but is a much bigger telescope than Kepler, and once again they look at the secondary transit and in this case they find that the dip in brightness varies by wavelength.

What you can tell is that, in fact, the planet is very blue. It's actually a deep blue colour.

This is an artist impression of what it might look like. That also seems to suggest clouds.

The model they come up with here is actually clouds, we need some chemical that can survive this very, very hot environment, I mean, water vapour won’t do it. So, it's not something like our own atmosphere which is kind of a deep blue as well, I mean Earth's blue because, well actually because there is an ocean, but... (And oxygen in the atmosphere, yes.) Yes, but it does scatter a lot of light, maybe preferentially blue.

But this one, I guess, we think is truly a different type of colour than something like the Earth.

The best guess is that the sort of thing that might condense and form clouds would actually be glass, silicon dioxide or quartz, because of the temperature we think that this planet is at, that's something that actually could form droplets or crystals.

In this case, it may well be that we've got clouds of glass and therefore your winds of glass, there's probably very strong winds on these things, maybe even rain of glass.

So, you'd literally be sandblasted there if you were there.

Yes, I mean you'd be fried long before you get sandblasted, but nonetheless, not a very pleasant planet but it might look quite pretty.

Oh, okay well that looks like an interesting place to visit, at least from space.

So, we're beginning to get a first few clues as to what the planets are actually like, and they're coming out quite interesting.

V4.5 Now, the secondary transit stuff is all very difficult, I mean, you're looking at, even though the original transits are too small to see from the ground and in this case you're trying to find secondary transits at slight slopes, it's very, very tough.

Yes, well it strikes me, Paul, that maybe we're looking in the wrong place in the spectrum, because in an optical light, the planets like Jupiter are just reflecting the sun, so they're going to be very, very faint.

But, if you have a Jupiter in close it's going to be hot and glowing on its own.

Now, it might be in the infrared, but if we look at the infrared, it strikes me that we're going to maybe have some bigger signals to get our hands on.

Yes, so here's the spectrum in wavelength going from something with maybe a temperature of 6000 degrees like a sun-like star and in this case it peaks at visible wavelengths.

But, if you look at something that's maybe at a thousand Kelvin, like one of these hot planets they also will glow but the glow might be out at your three microns, five microns, which is what we call infrared light.

So, if we look at visible light like Kepler does or the Hubble Space telescope do, we're looking in the worst place where the light of the star completely dwarfs the planet.

But if we go out, the actual green curve here is grossly exaggerated, it wont actually be as high as the red curve, but nonetheless the ratio is going to get much better in our favour, the effects are going to be much bigger.

Right, well that sounds good, the problem is that observing in the infrared is hard. On the ground, the whole atmosphere glows and if there's anything I hate doing, it's going to the telescope and observing in the infrared because it's just so hard.

Yes, you're struggling with the glow because, of course, your telescope is glowing with these wavelengths.

These atmosphere is glowing and also the atmosphere is largely opaque because of the greenhouse effect on Earth.

You've got lots of particularly water vapour absorption which blocks you in a very unpredictable way and constantly changing.

So, trying to do this from the ground, even though it's a bigger effect, is going to be hopeless.

So, what we need is an infrared space telescope.

Exactly, so fortunately NASA has provided us with the Spitzer Telescope.

This is one of the great observatories and was done in the series that brought us the Hubble Space telescope and also the Chandra X-ray telescope.

Spitzer is a space based infrared telescope and even though its mission, it needed to operate very cool to do its most precise measurements.

Yes, its primary mission had a huge basically tank of coolant that kept the detectors and the mirror very, very cold.

That eventually, after many years, boiled off, but nonetheless, at wavelengths of a few microns, it can still work very nicely, out at near 20 microns and so on, it can't work anymore since the coolant boiled off.

But those few microns were good for looking at things with a temperature of maybe 1000 degrees, which is exactly what we're looking for for these transiting planets.

So, a great resource for us to go out and look at these things.

It's not going to find them in the first place, but if you found them by some other method, whether it be Kepler or a ground-based survey, this is a great telescope for following them up.

Because it's in space, it has a sensitivity and also because nothing is changing for it, it doesn't have to worry about day and night and varying amounts of water vapour and everything else, it can look for very small changes.

Okay, so what have we seen? Well, the question we're dealing with here is "what might the weather be like on hot Jupiters?" If we look at the weather on Earth, it's driven by the fact that more sunlight falls near the equator than near the poles, and so it's very hot here and that causes wind from the equator or equatorial regions to rise and move out and fall down.

Because it's spinning, that produces sideways motion, the trade wind.

You can see all of these storms around the centre which is the air rising up and then it moves further out and distributes heat away.

If it was just an equilibrium, if heat couldn't move from the equator to the poles, the temperature difference at the moment, or it may be typically 30 degrees near the equator and minus 20 or 30 near the poles, so maybe a 60 degree difference. If it wasn't for the atmosphere, it would be more like a 200 degree difference.

Oh, okay so, very substantial, yes.

So, what's happening is a large amount of heat is being carried by atmospheric currents and ocean currents as well on the Earth from the hot regions to the cold regions, so the temperature gap is nothing like as big as it would be if we didn't have an atmosphere.

Alright, so all we have to do is look at one of these Jupiters and see how it behaves and we can, you think, get a sense of its weather.

Yes, now Jupiters would have very different weather because they almost certainly are tidally locked, as talked about before.

They would tend to face the same side towards the star.

So, we've got a star over here and we've got a hot Jupiter and this side is always going to face it, so as it goes around the star, it is always going to look at the star.

So, we are going to have a hot side and a cold side then.

Yes, so the orange and the blue side, as I've drawn it here, and the question is going to be "is there any weather to carry the heat from the hot side around to the cold side?" If there's not many winds going from one side to the other, assuming that they're gassy things, maybe the gas on this side is just sitting there incredibly hot, and the gas on that side is maybe sitting there incredibly cold and nothing's transferring.

Or maybe, like on Earth, you've got winds, but with a pretty different pattern because it's spinning only every few days as it goes around the star, but it might still be enough to drive some quite interesting weather patterns.

The answer is, well at the time of producing this video, there are about three systems which have these data.

This will go up dramatically, probably even by the time this course goes live, so it's probably out of date even today.

One of them is Nu Andromedae, which is, we've already talked about the one with the first one they discovered three things, that a hot Jupiter and two eccentric giants further out.

In this case, there's a huge day and night temperature difference.

So, that's sort of telling us that there's not a lot of wind there to redistribute things.

Or maybe the winds are just doing loop-de-loops around the hot air but not carrying too much heat around the cold and, well, to others finding similar sorts of results where there seems to be a huge gap in temperature between day and night.

Alright, so these may be kind of boring places, but is that always the same? Do we get the same answer wherever we look? Well, here's another one which is a different answer.

Here we've got the overall light curve of the main transit and the secondary transit and again you see a little slope up here.

You can see how much bigger that transit here is compared to that one. Remember in the previous ones, you couldn't even have these ones on the same scale but in infrared, you can suddenly see them.

That's the power of the method.

If we zoom in, you can see this clear change here and what you're seeing is the difference in brightness there and there, it's telling you the difference in heat between the day and night side of the planet and the dip here is when you lose the entire planet.

So, if the gap there is telling you how much radiation you get from the day side, and the gap from the bottom there to here is telling you how much radiation you got on the dark side.

So, even the dark side, this one is glowing quite a lot. It's hotter in the day than in the night, but not very much.

In this case we may be talking maybe a 200 degree difference, so maybe you're 0 degrees in the day side and 1000 on the night side.

So, in this case, there does seem to be some sort of wind, 200 degrees would need a wind to carry it around.

So, somehow the heat is getting moved from the day side to the night side in this particular case.

Okay, so not everything is the same. We seem to, again, have a very large range of phenomenon.

This pattern is maybe slowly becoming clear here.

It kind of looks like if when you find the planets that are really close in the very classical hot Jupiters.

In those cases there seem to be very big day to night temperature differences.

But when you get the ones that are a little bit further out, some of them still have the very big temperature differences, but some of them have much smaller ones.

So, it looks like that maybe there's something about being very close in that actually stops winds.

Maybe it's just such a big difference and maybe the tidal force in the star, I don't know what could be doing it, seems to shut down this heat transfer, but the ones a little further out can do more like the Earth do 100 and have currents that carry the heat from day to night.

But it's still early days, we only have a handful of these, so we'll learn more as we get more data.

V4.6 BRIAN: So Paul, strikes me that spectroscopy would be really useful here as almost everything has a signature of light that you can identify.

We can identity almost anything if we can only have a spectrum of what's going on, but it's not going to be easy.

PAUL: Yes.

Because now you've not merely got to measure the total brightness, but the brightness broken down to wave length beams, but it has been done. So the idea is you wait until the planet is just outside the secondary eclipse, take a spectrum, and then when it's in secondary eclipse you take a spectrum.

So the spectrum that's just outside will be the star light plus apparent light.

When the planet's behind, it'll be just the star light.

You subtract one off the other and hope that the difference is the spectrum of the actual planet, and here's one.

BRIAN: OK, let's see.

So this is an infrared.

PAUL: They're claiming they see a bump here.

BRIAN: I see.

So the idea is that you don't see anything, you don't see anything, and then you see a little bump of emission of something.

You really have to be a true believer, I think, to believe that.

PAUL: Well they claim it's real.

81 of these individual points is only about 1 error bar above, so that means there's a 32% chance it could be outside the error bars, but there's quite a number of points up here.

So maybe if you add them all.

But if you really believe you've got your systematic errors under control, maybe it's real.

But they claim this is the right wave length speed from silicon, so very suggestive of other reasons.

There might be silica clouds in these things, it could be looking at this hot Jupiter which actually, again, has silica glass or quartz, clouds in the atmosphere.

And what we're actually looking at is a bump in the spectrum just below 10 microns caused by silicates.

BRIAN: All right.

So here we're looking in the infrared for something that is emitting in that line, sort of like a sign emits a line of neon.

PAUL: It'd be nice if it could do something in absorption.

BRIAN: Right.

That sounds easier to me.

PAUL: Well first of all because it's the primary eclipse in fact goes in front much deeper, so you'll get a much bigger effect.

And in principle you can, but here's a picture of Saturn taken by the Cassini space probe when the sun was on the other side of it. And what you can see is a little glowing arc around the side here, which is the light of the sun refracting through the atmosphere.

It's like all the sunsets on Saturn at the same time.

BRIAN: So the beauty of this, you've got the light of the star shining through.

And of course when we see things-- this one, Saturn completely eclipses the sun.

But in reality what you'll see is-- you can actually see light coming through, you'll see the light of the star at same time, and then you'll see the absorptive fingerprint of material.

PAUL: Yeah.

So what it kind of-- Another way to think of it is the radius of the planets might differ as a function of wavelength.

At wavelengths where the atmosphere is transparent, it'll just be the radius of whatever solid or the cloud banks.

And other wavelengths where the gas in the atmosphere absorbs, the radius might get a little bit bigger, so you'll see a bigger dip at some wavelengths than others.

So once again, you take the spectrum when the planet is not in front of the star, it's just a star spectrum, and when the planet's just in front of the star you'll get a star spectrum minus a bit of light from the planet, and that light that you've taken off may vary as a function of wavelength depending on the atmosphere, because of this arc around the side.

BRIAN: OK.

So it sounds like a promising way forward.

So what have we seen? PAUL: Well here's one results in a very recent paper.

What we're looking at here is carbon monoxide.

So here's a spectrum, and you can see there's a little bit of a dip along there.

Once again, it's not something you'd want to write home about.

BRIAN: I can see it.

There's a real slash there.

PAUL: Well that's just a simulation, that's not real data.

These are the real data.

BRIAN: Well, I sort of see it.

I reckon that looks better to me than the previous one.

PAUL: Yes.

And what you're seeing here is the darkness along there, it's a sloping line.

The reason it's a sloping line is as it goes in front of a star, its velocity is changing.

So if it was just going straight in front, the velocity wouldn't change. But it's actually doing a circle, so it's going away and towards.

So you're getting a bit of a slant across here.

BRIAN: So this diagram, just to be clear is plotting, how bright the area of CO is, the little signature if CO-- PAUL: This is the wavelength along here.

BRIAN: So this is wavelength and we're actually measuring, in some sense, the velocity.

And then this is telling you what phase in the orbit it is.

And so we do expect there to be a change because the object is moving.

100 PAUL: So what you're seeing is the right pattern here for the Doppler effect.

As the velocity of the planet relative to the star changes, we expect the slide to slope and it slopes exactly the right way, which is looking good.

BRIAN: So this planet looks like it has CO in it.

PAUL: but there's a surprise in here.

It turns out that the velocity, while it's sloping the right way, it's not quite at the right place.

It's a bit different from the velocity of the star-- BRIAN: Oh.

PAUL: --by about two kilometers a second.

That's about 7,000 kilometers an hour.

What it seems to be is that the CO is not just sitting in the planet's atmosphere.

It's actually moving from a hot side to the cold side at about 7,000 kilometers per hour.

BRIAN: Wow.

So our jet stream is maybe 350 kilometers per hour.

So this is 20 times faster than the fastest stuff we see on Earth.

PAUL: Yes.

It's even seven or eight times faster than the winds on Jupiter, which are much stronger than the winds on Earth.

BRIAN: And Jupiter's orbiting very quickly.

So this is pretty funny.

PAUL: So it looks like at least at the altitude where you're getting carbon monoxide, we're seeing an incredibly fast wind from the day side to the night side, in this case.

BRIAN: OK.

PAUL: Here's another surprising case.

This case, the planet causes a, typically, sort of 0.5% dip. But if you look not at the general optical wavelength, you can look at the wavelength where you get absorption from hydrogen. This is actually in the ultraviolet it's been done with the Hubble Space Telescope because the ultraviolet can't penetrate the Earth's atmosphere.

But if we look at the Lyman alpha line, which is where an electron to level 2 to 1 of hydrogen, which is in the ultraviolet, .6 standard meters, something I spent a lot of my life working on-- BRIAN: Yes.

PAUL: --instead of blocking 0.5% of the light, this thing's blocking 15% of the light of the star when it goes in front.

BRIAN: So it can't be that it's atmosphere puffs up to 15% of the radius of the star.

That seems crazy.

PAUL: Yeah.

So maybe that'll be-- we do have a planet that's got an atmosphere this big of hydrogen.

But more likely what's happening is an atmosphere that big of hydrogen wouldn't stay there, it'd get blown away.

So our best guess as to what's actually happening is evaporating planets.

It's losing huge amounts of hydrogen, producing what's the cometary tail of the stuff.

So as it goes in front, you get this huge amount of hydrogen absorption, plus a small amount of absorption all solid wavelengths caused by that stuff.

BRIAN: OK.

So this planet sounds to me like it's going to be doomed if it's losing too quickly.

I guess it really depends on how quickly it really is losing it because hydrogen in that Lyman-alpha line is so sensitive you just need a little bit of hydrogen and it really is good at taking out all the light.

PAUL: So we've had a planet with incredible winds, we've got an evaporating planet, but even, it turns out, that seeing nothing can be interesting at times.

Here, remember, we had two possible models for these super Earths that might be a potential water planet, one of which had a hydrogen and helium atmosphere.

One of which was mostly water and water vapor all the way out.

And for one of these things, people have tried to measure the transits of different wavelengths.

So you can see going from the red-- well these are actually all red wavelengths, but slightly less red to slightly more red.

And you can see the dip of the transit and you can compare the shapes of all these different wavelengths here.

So what they've done is they fitted the average of all these things and taken it off.

And what you can see is the transit actually looks exactly the same all the way for 1,000 nanometers down to 780 nanometers.

BRIAN: OK. So that means that the planet is really exactly the same color at all these different wavelengths.

Now that's-- well, I mean it is interesting.

PAUL: If I had a water surface or a cloud service, that's fine.

Clouds absorb or solid surfaces absorbs at all wavelengths.

But if had mostly a hydrogen atmosphere, it would not be like this.

It would absorb more at some than others.

BRIAN: Right.

Because hydrogen ends up having this signature, or in this case scattering, at some point.

So it would change things.

OK.

So that's telling us that this object is interesting, perhaps.

Maybe it has a dense shroud of clouds.

Interestingly enough, clouds turnout very conveniently for astronomers because they're around, they really have no color to them.

So when we look through the atmosphere, there are effectively a neutral density filter that you 198 would use on your camera that doesn't change the color.

PAUL: So whatever it is in this particular possibly water world, something with the right density to a water world, which we don't know-- whatever it is in its atmosphere, so that it doesn't have different effects at different wavelengths.

So not conclusive yet, beginning to give us some interesting results.

BRIAN: OK.

That would interesting to see if there are more of these

V4.7 So, we've found this great bonanza of Super-Earths.

Previously we knew about the hot Jupiters and a half a percent of systems and we knew about the eccentric giants.

What we've seen is that these completely dwarfed in numbers by these things that are bigger than the rocky planets but smaller than the gas giants.

Yes, I really like the name Super-Earth, but it seems maybe a tad bit misleading given what we know, because we don't really know if these are rocky giant things like Earth or if they're sort of small little versions of Neptune, do we? Well, they might even be giant water worlds for all we know with their huge amounts of water over a great distance.

We also mean to find out something about the atmospheres of these planets. It's a very incoherent story at the moment that will develop very quickly over the next few years, but we're seeing signs of enormous winds, at least in one case the planets evaporating and there seems to be some planets where the heat is being distributed from the day side to the night side really well and some ones where it isn't.

Okay, so despite all the promise of discovering things like Earth, we really haven't been able to find anything using Kepler and the transits that really looks like Earth, have we? But that might just be a matter of time, we haven't analysed all of our data yet.

Right, so there is more data coming, but Kepler has, sadly, its mission has ended after about three years because its reaction wheels that allow it to point very precisely in the sky have stopped and so, consequently, we're sort of stuck with the data we have. So, you think there might be still an Earth in that data set.

Yes, I think people are hoping with, especially with a longer base line, so with the Earth you're only going to get a blip once a year, so you need the full three years worth of data to try and find these things.

So, maybe we're going to be able to find hundreds of objects like Earth or even objects that go out like Jupiter and Saturn in our own solar system.

If we do, it would probably be before we've had a chance to put this film together, we'll have to film a variation on it.

It'll happen quite soon if it happens at all.

But once Kepler's dead and gone, where to now? I mean, the really big gap, first of all you may not find any Earths or similar things, the real gap is things further out.

Even with the exquisite sensitivity of Kepler, you're only going to find things close in because when things are further out, the odds of it being so precisely edge on that it gives transits is very, very low.

Oh, so we're probably not going to find a Saturn or a Jupiter then with Kepler.

Well, given you have a 10 year period for Jupiter...

It was only a three year mission. It's pretty much Earth.

You might see one transit but there's not much you can learn from that.

Yes, okay, fair enough.

So, in fact, either with radial velocity or transits, finding things further out is going to be very hard, and further out is where most of at least the big planets in our solar system are.

You're going to need to find Saturn your 20 or 30 years of data, either with the radial velocity technique or transits.

I suppose that, in principle, you could survey a very, very, very large number of stars for those tiny fraction where the transit is edge on, but you're going to have a look at every star in the sky for 20 years with incredible precision.

So, we really need to come up with a better idea of how to look out in these outer longer-period objects to really hit the pay dirt of our own solar system.

That's what we're going to talk about next time.

V5.1 We've learnt a lot about close-in planets, but it would be really interesting to find out about ones that are further away.

Things like Kepler are telling us wonderful things about things that are orbiting within 50 day periods.

As they get more data, it might get out to a hundred or a few hundred day periods, maybe out to Earth radius or beyond, but both transits and radial velocities don't tell us much about things at five, 10, 15 astronomical units out where Jupiter, Saturn, Uranus and Neptune are in our own solar system.

Yes, it's going to be pretty hard as well, because these planets have many, many decade long orbits and so you can go through and you can beat on them for decade after decade so you can see the whole sine wave.

But you also have the problem that things like Uranus and Neptune for example, they're a long way out and so the amount that they perturb the sun is very small and so the reflex motion, very long periods mean it's not a good strategy to go out and find them this way.

Yes, for transits, the odds of something that far out being edge on enough to cause a transit are very remote.

You'd have to look upon millions and millions of stars to find one and then you'll see a very small dip that recurs every 40 years or so.

Right, so even if you do find one, you won't be sure it wasn't just a butterfly that flew in front of your telescope.

Odds are you've retired before the next one happens and you really want your four or five of these things before you've got to say very much.

So, clearly we need a different technique here. (Yes, we need another technique.) The technique that's being used for this is something we've talked about before when talking about Dark Matter which is gravitational lensing.

So, here's the basic idea and the fundamental equation.

Let's say you've got a beam of light that's passing near an object of mass, M, passing at some distance, R, from it.

Then, as an approximation valid when R is fairly big, it deflects the light by an angle in radians, that's equal to four GM over RC squared, so G is the gravitational constant, M is the mass of whatever this thing is here, R is how far the light passes from it and C, the speed of light all squared.

This really comes back to the foundations of general relativity and how we realised general relativity came into being, Einstein, when he had the idea (Yes, he came up with this equation) and he came up with this equation and was tested.

He then went out and found that the sun deflected the light of background stars by so much during the eclipse during the first World War. (Right.) So, it's fundamental physics here. We've seen this before for gravitational lenses, in this case we're looking at a background galaxy that's been lensed by this cluster of nearer galaxies over here so you see the multiple images and they're on different sides.

So, its been very powerful in cosmology, but it could potentially, one could imagine, maybe using it here to look for planets I guess.

How would this work? Well, here's an edge on galaxy, it would look a bit like our own galaxy, what the Milky Way would look like edge on, and you see that these galaxies puff up in the middle.

This is called the 'bulge' and most spiral galaxies have one of these bulges including our own.

Now, we're out here in the outskirts of the galaxy and the idea would be that we'd look at the bulge.

Our line of sight would pass just skimming the top of the disk of our galaxy.

If you look at the stars here, we might look at big stars, giants or something over there, bright stars.

Then every now and then a planet or a dwarf star somewhere on the line of sight will pass in front of it and cause some amplification.

So, the reason why we're looking out here is because our galaxy is full of dust and that dust means you can't see through things very well and so we need to kind of skirt around that dust so we get a clear view of as many stars as possible.

Here's a view of the galactic bulge from Mount Stromlo.

That's the dome of the 74 inch telescope in the foreground, and what you can see up here is the bulge.

The middle of the galaxy is hidden behind this layer of dust along here, but you can see the bulge poking above and below it.

So, what you do is you find somewhere along here, and what that gives you is very large numbers of stars that are quite a distance away.

The bigger the distance away is, the smaller the mass can cause the lensing because it gives a very small angle and still focus things on the Earth.

So, looking at lenses with focal lengths of tens of thousands of lightyears, these are very small lenses.

You want the biggest distance you can get away with and also, because you're skimming just above the surface of the disks as you look out there, there's a fair chance there's going to be stars and planets in the foreground to see it.

So, you get a lot of stars in the background, we get some in the front and occasionally we can hope for these things to line up.

Yes, so let's calculate how big the lensing angle is going to be in this situation.

V5.2 PAUL: OK. Let's see what our gravitational lens image is going to look like.

If there was nothing in the foreground, what we might see in our telescope field of view-- say here's our telescope field of view-- is we'd see the background star.

But because of the lens, instead we should see two images-- or maybe even a complete ring-- at distance-- angle of space, alpha, from where the single image was going to be.

So if alpha isn't too small, we can see these things.

Simple geometry here-- here we have the background star.

Here we have the Earth.

We've got the ray of light going either way around.

And for the sake of simplicity, we'll put our dark thing-- whatever it is-- exactly halfway-- there's the distance-- to the background star.

And we have r here, r there.

That's in the middle of the mass.

And we know from the lensing equation that this deflection angle here, theta, is given by the equation theta equals 4gm over r c squared.

So from that, we want to measure this alpha here, which is this angle in there.

From symmetry-- that's going to be theta as well here.

That's going to be theta.

And all the way across here is going to be theta.

So we know that alpha equals half theta.

We also know that this right angle triangle here-- 10 theta-- equals opposite over adjacent, which is half d.

But the angle of alpha and theta are going to be very, very small.

Sorry, that should be 10 theta over 2, then 10 alpha.

The angles are very, very small.

As long as we measure everything in radians, we can get rid of the 10.

So what we get is this that theta over 2 equals r d/2.

So r equals theta d over 4.

So what we can do is substitute this one in here.

You have two unknowns-- r and theta-- and two equations.

So that should be solvable.

So substitute this one into here.

And we end up with theta equals 4gm times 4 all over d theta c squared. So 4 times 4 is 16.

Want to take the theta up here-- so that gives us that theta squared equals 16gm over dc squared.

Take the square root of both sides and substitute.

We know that alpha is half of theta.

So we end up that alpha equals the square root 4gm over dc squared.

And this angle alpha is so widely used it's got a particular name.

It's called the Einstein radius.

This is the equation when the lens exactly halfway between.

There's a slightly more complicated equation for the Einstein radius when the lens is not midway between.

Halfway between is where it has the most lensing influence.

So what is this number? Let's assume you've got a Jupiter mass planet halfway to the middle of our galaxy.

In that case, d is the distance from the sun to the [? bulge, ?] which is about 25,000 light years. m is the mass of Jupiter, which is about 1.9 by 10 to the 27 kilograms. c is the speed of light. g is the gravitational constant.

Stick this into here and you end up with alpha equals 1.5 by 10 to the minus 10 radians.

We need to convert that into some unit we can understand.

So a radian is pi over 180/pi degrees.

So multiply 180 over pi.

That will give us degrees.

But the angle is going to be much smaller than a degree.

So then we have to times 60 for arc minutes times another 60 to get it to arc seconds.

Because an arc minute is a 60th of a degree and an arc second is a 60th of an arc minute.

So I multiply by 180 over pi times 60 times 60.

It gives you 31 times 10 to the minus 6 arc seconds-- so 31 micro arc seconds.

Now bear in mind a typical telescope can see its images fuzzed out by about an arc second.

So we're talking 100,000 times smaller than that.

Even the Hubble Space telescope gets about 0.1 arc seconds-- maybe 0.03 at very good times.

It's still vastly smaller than that.

So this is an incredibly small angle, which means we're basically never going to be able to see these multiple images.

V5.3a Well, Paul, that was depressing.

I mean, those angles are so small, we're never going to see anything like we see in cosmology; where you can see the lens split and giving an angle that's actually measurable on a telescope.

Yes, it is a bit depressing.

But, if you think about it, splitting the image, while very neat, is not the only thing that lensing does, it also actually focuses the light on the Earth, so it makes things brighter. It amplifies things.

Well, that is true, because this is one of the techniques we use, not to just see that this exists, we actually use this to magnify background galaxies so we can see things much further away than we otherwise would.

Yes, so how are we going to calculate this? Well, the way you do it, or the most common way, is ray tracing.

The idea is we have a background source here, and it fires out photons in random directions past our dark thing, our planet or whatever it is, towards the Earth.

We have drawn an imaginary plane through the Earth and we count where each of these photons arrives.

You see that whenever a photon gets near here it's deflected, the ones that are very close gets deflected a lot, because the equation at one over R is the deflection angle, the ones that are further away are deflected less and so we end up with a pattern over there in the background.

Okay, so in this case you shoot things all out and, presumably, you're shooting them out in this direction but we don't care about those, so the ones that come by and through here collapse.

Now, if there was no star here when you do this, you just end up with the same number of rays anywhere on this side of the diagram that we're going to have.

But if this changes that and gives you perhaps a different pattern over here.

Yes, it's acting a bit like a lens, but a rather crap lens.

So, here's an example of a crap lens, my water bottle.

You can see it's focused the sunlight coming through into a rather weirdo pattern over there.

It's got a sort of almost lines and caustics and things over there.

Right, and so a real gravitational lens, maybe more analogous, is maybe more like a funnel of glass where there's sort of this little thing of glass that spreads out and it gives you a pattern very similar to what a gravitational lens looks like.

Okay, so we can simulate this, the way we do it is to go back to the firing range and now do it in three dimensions.

What I've done is I've put, in the background, a source that's firing photons out in all directions and I've put a foreground mass, a stellar mass this time, and that's bent some of the light that's come close but not bent the light that's further away, and then I've put an imaginary plane where the Earth is, and here I've counted I think about 10 million points here.

So, you sort of have this plane which is your target and it's like shooting arrows. (Yes.) The arrows get bent and wherever the arrow hits, "boomp", you get a little dot here. (Yes.) So, you don't end up with a uniform pattern anymore when you take into account that ray tracing.

Yes, what you find is that the rays that come to the planet are deflected way off and so they're actually off the plot and in different directions.

The ones that go a very long way just end up where they were going to go anyway.

What happens is that the ones that are sort of an intermediate distance at just the right angle get focused rather vaguely towards the middle.

It's not a very sharp image, but a rather blurry image in the middle.

Okay, so if we are here on Earth looking at an object directly lined up with another object like you've seen, then that's why we'd be right in the centre, then we're going to get a lot more light from that star than if we're off here, so it's going to appear brighter.

That's right, but of course, this is space and everything is moving.

I mean, the background star is moving the bulge of the galaxy, whatever this lensing star or planet is moving, and we're moving.

So, we have three motions. We've got the star, the other star and us! (And us!) That's three motions, but probably all more or less travelling on straight lines, at least over a few days, I mean you can break up the Earth's motion and our sun's motion in straight lines, so we have three straight lines pointing in different directions.

So, you just add them up with the normal vector sum and we're just going to get one line.

You add three lines together, you're going to get one line.

What that means is that you've got this plane, which is the image, and that's going to move across the Earth, and the Earth's going to move across that, and so you can pretend that the plane is stationary and the Earth is moving or pretend that the Earth is stationary and the plane is moving.

It's usually easier just to assume that this is stationary and calculate, with respect to this image plane, where the Earth is moving.

Alright, so we can break it down, all those motions into one motion, and then we're going to plot how that plane moves across the sky.

Yes, so it could be that the Earth is going to go up here or down there or something like that.

If the Earth just, say, goes over here, it's not going to see very much, so for when there's not much magnification.

Presumably, we don't care about the angle, this looks like it's completely round in this case.

Yes, so let's put a random motion in here. Let's say that the Earth moved across this image plane like this. Of course, in reality, it would be that all three things are moving, but we can approximate that as everything being stationary.

So, what would happen here? When we're out here, we're going to see the normal brightness of this object, but when we get here, if you look you'll see that there are more dots per unit area here which means you're going to get more photons from this object and up here we're going to get quite a lot more.

So, what we can do is we can go along this path, and for each point, calculate how many photons arrive there, and here's what we get.

Okay, so there's kind of a curious looking shape, it's sort of pointy with little wings out the side.

Yes, it's a bit noisy because I only simulated 10 million particles, I've simulated a billion billion or something, which is probably what you'd really get, you'd get a nice smooth curve because of the noise we talked about before.

But yes, what you'd expect to see is over some period of time, in this case it would typically be a few days, a star that normally had a particular brightness would appear to get much brighter.

So, it started off with a brightness of maybe about 50 photons and got to about 500, so in this case it's a magnification of about 10 times.

Presumably, if you were to cut across on that line would cut across at a different point, you'd get even brighter or fainter.

Yes, if you went right through the middle or very close to it, you'd get a much brighter magnification, if you're out here you might get a very small magnification and so on.

Okay, so that gives us a clue of maybe figuring out what's going on, of how bright thing are.

Yes, certainly for a star, but we're not very interested in stars, we know stars exist.

A red dwarf star, you might not be able to see it, it will be so much fainter than the background bright star, so we can pick it up from this, so it might be of some interest, but all we really care about is planets.

Let's put a planet in front. So, here's a planet going in front.

Okay, so it's a lot less massive and so the effect is much, much smaller. Okay.

Yes, so if we draw a line through this, once again it will depend whether you go right through the middle or further away, but if you went the same sort of distance you went in the last time you will get something like that.

Alright, so it's a lot fainter, so how are we going to distinguish that from a star? Well, you can't really use the magnification because going right through the middle of a planet will give a much bigger magnification than going a long way away from a star. What you can use is the time here.

This is going up and down in just hours, as for a star, it's probably going to take days to go up and down.

So, there's two things that we have. The amount of magnification and the time that the magnification happens.

Yes, so combining the two, we could probably work out this sort of mass that's going on. However, it's a bit more complicated than this because imagine you do have a star and a planet and a photon of light coming through, it's going to get bent one way by the star and another way by the planet.

But the two are going to act together, so, for example, if something that went right through the middle, it might be able to get straight through.

So, it's not as simple as taken the pattern from the planet and pattern from the star and superimposing them.

So, the scale of the solar system is such that you have got to worry about both things at the same time, you don't get to just break it into one or the other.

Yes, it turns out that if you have a planet and a star near each other, in fact any two masses near each other, you get rather interesting patterns.

I've done this movie here, what I've done is I've put a star here, and I've moved a planet across on a line through this and what you can see is the pattern in the image plane.

You really get an interesting pattern, which we call a 'caustic', it's not dissimilar to the pattern at the bottom of a swimming pool.

Or the pattern of my water bottle.

What you're getting is actually lines, you can see along there, which aligns where it so happens the bending of the two objects cancels out a lot of photons and end up at the same place, the so-called caustic lines.

What we can see is that when the planet is a long way out, it doesn't have much lensing effect, similar to if it was all by itself.

When it's right in close, like now, it's actually very much like a star, just lensing.

But, when it's out a little bit, you get some very interesting big caustic patterns all over the place.

So, that's a very complicated pattern and complicated patterns have the advantage of you can learn a lot, because if you can really see that pattern and, presumably, you're going to be able to nail exactly what's going on in the system.

Now, to nail this, what we would need is a two dimensional array of telescopes spread all over several solar systems.

If we had telescopes scattered all over space within a lightyear of us, we can actually measure the brightness here, here, here, here, all over this and do that. We can't do that.

What we can rely on, once again is a track.

So, for example, let's say we were moving through like this, we're going to hit a caustic here, it'll glance a caustic at another one there and so we can do the same sort of calculation.

(So, it's still a very complicated pattern.) Here's what you get for this particular situation.

Oh okay, so you get these little blips and those little blips tell you what the caustic pattern looks like and that caustic pattern tells you, presumably, how big the planet is relative to the star and where it's orbiting. Yes, so you've got the overall big blip due to the star and superimposed a number of spikes.

So, what you've got to be looking for is a normal star pattern, but with weird spikes in different locations as you cross the caustics in this diagram.

But, of course, for this to happen, the planet needs to be at the right distance.

It can't be too close, in which case all you're going to see is a star or too far out you're going to see two quite separate glitches.

To get this neat caustics, you have to be at the right sort of distance in the middle.

So, let's calculate how far away a planet would need to be for a star to give these neat caustic patterns.

V5.3b PAUL FRANCIS: Now one question a number of students have asked, we've referred a lot to caustics.

Now what actually is a caustic? So were going to in this short video explain the definition of this term "caustic" for microlensing.

Now if you remember, when you're looking at some background object which has a planet near it, the brightness will go up and have these sudden sharp spikes, which are due to planets orbiting the star.

And that's enormously powerful.

It tells a lot about how big the plant is.

That it's there.

How it's orbiting.

But why do you get these sudden, sharp spikes? So we've talked a bit about what caustic is with a hand waving type explanation.

If you have light going through a glass you get these sort of patterns here.

BRIAN SCHMIDT: Yep, and so those little patterns are the caustic, and essentially where light shining here gets added up into specific spots.

PAUL FRANCIS: So generally, whenever you shine light through any sort of distorting lens, instead of getting a fuzzy image you get images with rather sharp lines, like this one and this one and this one.

And these sharp lines are the caustics.

Here the same things at the bottom of the sea.

Here what you've got is the light coming through the surface of the water, which has ripples.

It's a distorting lens.

And once again you tend to see rather sharp, constantly moving lines, which are also the caustics. For gravitational lensing, remember what we did is I imagined being in a background shooting out a whole bunch of rays.

And the rays get bent in different ways by-- in this case I put a star on a planet in the foreground-- and then you look at where they land on a plane through the earth.

And once again, it's much like sunlight coming through a disturbed water surface and landing on the bottom of the sea.

And so once again you get these rather sharp patterns.

And the reason why we see these peaks in brightness is because in this plane the earth, say moving along like that, and when you hit one of these lines you get a sudden peak in brightness.

But what actually is a caustic? How's the definition of it? I mean, we said it's a line.

So what do you do if you don't know what word is? BRIAN SCHMIDT: I don't know, I usually look it up.

PAUL FRANCIS: Wikipedia.

BRIAN SCHMIDT: Yeah.

PAUL FRANCIS: So here's what Wikipedia said.

A definition of a caustic is "envelope of light rays reflected or refracted by a curved surface or object." What does that mean? BRIAN SCHMIDT: OK, so I think we know what everything but the envelope.

That sounds like an interesting term.

What does envelope mean in this case? PAUL FRANCIS: Well of course, I then clicked on the link to find out what envelope meant as far as this is concerned.

And here's how it's defined in the mathematical term.

"Envelope of a family of curves is a curve that is tangent to each of them." So what we need is a family of curves.

Here's example they gave on Wikipedia.

So here's a family of curve.

So each curve starts here and you move down and around.

And when you do them all you get an envelope which is tangent to all of these things.

BRIAN SCHMIDT: Right.

So this almost looks like the string art that I used to do when I was a kid, where I take a bunch of nails and then take string and go between them and you end up with a pattern, which is the envelope of all those lines.

PAUL FRANCIS: OK, so what we seem to need is a family of curves.

What's the family of curves in microlensing? If you remember when we did the simulations, what I'm doing is I'm just firing a vast number of background rays, but instead of firing all the rays out at once we could divide them up into lines. What I can do is I can be at the background and say fire a bunch of rays this direction, then a bunch of rays in that direction.

So I have a line, and each line sets out as a perfect line, something like this here.

But then by the time it's distorted-- for example let's have one of these lines along here-- the ones in the middle are going to bend this way a bit whereas the ones on the outside are a bit less.

So you're going to end up with a curved line here.

And if I fire a line over here that might be curved the other way.

And if fire to the middle it might be rather more complicated.

BRIAN SCHMIDT: That's right.

PAUL FRANCIS: So that's going to be our family of curves.

What I'm going to do is fire a bunch rays along here and see where they end up in the plane of the earth distorted.

I'm going to add them all up.

So I've got a little simulation here where I start off on the side and go through firing vertical line, vertical line at different angles and then see where they end up.

And what you'll see is the envelope of these.

So it's going to start up from this side.

We'll see the black line.

Here we go.

BRIAN SCHMIDT: So it's distorted to begin with.

100 PAUL FRANCIS: It's bulging in because of gravity there.

And now it's actually doing loops around it.

BRIAN SCHMIDT: Now we're going to pop out on the other side.

PAUL FRANCIS: So what you saw was that the family of curves did have and envelope.

There were a whole bunch of curves that added up along this line, along this line, along that line, for particular times.

And so that's what the caustic is.

It's just you have this whole family of curves as you send planes of light outwards.

And they do indeed give you caustic patterns.

BRIAN SCHMIDT: It essentially means that that's where the light of the object you're looking at adds up.

Where it's instead of shining out to the entire part of the universe, it all gets directed towards you when it passes through that little part of space.

V5.4 Now, for a planet to cause lensing as it orbits a star and to give it lots of caustics, we need the angle, here's the Earth, here's the star and here's the planet.

We need the angle to be about the Einstein Radius, which, if you remember, was given by the equation root four GM, M is the mass of the star in this case, over DC squared, where D is the distance to the background thing that's being lensed.

Now, for a planet mass, so if M is about the mass of Jupiter, which is about two by 10 to the 27 kilograms, we knew that the Einstein Radius angle was about 1.5 by 10 to the minus 10 radians.

But, in this case, the mass we want is not the mass of the planet, but the mass of the star.

So, the mass of the star is about 1000 times the mass of Jupiter.

Mass is under the square root here, so that means the new Einstein Radius is going to be a square root of 1000 times bigger than the old one, the square root of a thousand is roughly 30, so it's about five by 10 to the minus nine radians.

So, that's the angle, what's the actual distance? If the distance here is half way to the middle of the galaxy, so about 125,000 lightyears, then you have to multiply that by the angle to get R, so R is going to be the distance, so that's about 1.25 by 10 to the 20 metres times five by 10 to the minus nine radians, this is using the small angle approximation as usual, which comes out as about six by 10 to the 11 metres; which is four astronomical units.

So, to be an effective lens, you need to be a few astronomical units out, which is roughly where Jupiter is in our own solar system.

You don't want to be hundreds out, you don't want to be 0.1 out, so it looks like this is ideal for finding Jupiter-like planets.

Well, Paul, this is great because you've just shown that the scale where things happen is like our solar system, so we're going to be able to see the things that we know exist, at least in our case, and furthermore, those caustics amplify the effect of little things like the Earth.

It seems to me that we're on a real bonanza here.

Yes, so we clearly need to find some of these things.

So, we need some telescopes pointing at the bulge of our galaxy, looking at it over and over and over again and monitoring the star, so ones that start getting brighter in just this right pattern that suggests that there is a microlensing event going on, because there's some dwarf star in the foreground lensing it, and then we monitor really intensely to look for some spikes in the light curve.

So, very conveniently, the Milky Way and its bulge is best seen from the Southern Hemisphere, and here in Australia, starting in 1993, we had a program to go out and use the 50 inch telescope, known as the MACHO Telescope, to go out and do a survey specifically to do this event.

To go out and, as it monitored the night sky, it could look at the large and small magellanic clouds, but you couldn't look at them all night long, it turns out that they do get pretty low, so they could also go through and monitor the centre of the galaxy and look at hundreds of millions of stars. So, let's remind you of what this telescope looks like today.

So, in 1993, in this telescope, astronomers started an experiment that did exactly this.

The MACHO experiment looked at 16 million stars continuously.

As you can tell, this telescope is no longer in working order.

It was burnt down in the great Canberra bush fires of 2003, along with the rest of the observatory.

Before it was burnt down, the telescope was fully automatic.

It would actually open itself at sunset if the weather was clear, check the weather, focus itself, pick its targets and analyse the data and even ring the astronomer up if it discovered something interesting.

Yes, I remember it fondly because it used to send me messages on my telephone, and on the 18th of January 2003 in the afternoon, there were fires about and it sent me a message that said: "Temperature out of range. 73 degrees celsius." And I knew the telescope was in trouble.

Here's the remains of the superstructure of the telescope.

This is winched out of the burnt out dome and dumped over here after the fires.

The main mirror used to sit down here, it would take the light and focus it.

That was originally bolted on the bottom here, that would bounce the light up towards the middle there.

So, the light came up from the primary mirror, entered the top end of the telescope here and was split into two colours, red and blue, by a device we call a 'dichroic'.

Part of the light went off here to the side and the other went out to where Paul is standing out the back.

Now, this telescope was unique because it was equipped with a 64 million pixel CCD array, the worlds largest digital camera.

It was able to collect data faster than any other telescope before its time.

So, in the 1990s, the 50 inch great Melbourne telescope up here at Mount Stromlo was able to do a survey where it looked at the magellanic cloud, which is over your shoulder there, Paul, and that magellanic cloud, of course, as the Earth rotated, sometimes it went down very low, so you need something else to look at.

Because they were trying to search for dark matter, they needed to sort of calibrate with some other object that, for example, shouldn't have very much dark matter in front of it.

That was the bulge of the Milky Way, where we could go through and we could see lots and lots of stars and have lost of test things.

So, in the end, the MACHO experiment didn't find dark matter.

It was able to rule out many possibilities.

But it did find lots of lensing towards the bulge of the Milky Way and in the end, I think that was probably the more interesting part of the experiment as we look back 10 years later. It was also working with another experiment at the time called EROS that was done out at Chile by a French group.

Yes, so they found lots of lensing events, in this case probably dwarf stars, red dwarfs in the foreground lensing things in the background.

There was no clear evidence of planets.

They didn't observe every star often enough.

To look at these little planetary glitches, you need observations every few minutes, while this one only observed any given star once a night if it was lucky and the weather was good.

So, you needed more rapid observations.

But it got people excited about it, the possibilities, I think.

It became clear that the lensing did actually work.

Einstein was right and we did get these events and you could feasibly, with modern telescopes, see these things.

There's been a whole bunch of follow-up surveys, for example, OGLE in Chile and MOA in New Zealand, and these things more or less do what the MACHO project did, only better with more modern technology, they have telescopes mapping large areas of the galactic bulge over and over again very rapidly, looking for stars that suddenly start getting brighter.

Some stars vary in brightness all the time, we just throw those ones out.

What you want it a star that normally doesn't vary, it just sits there not changing at all.

If a star that has been doing nothing for the last several years suddenly starts getting brighter at just the right shape of the curve... Woah! Alarm! Right, and so these guys have got great software systems in place and they have many, many years of monitoring, so they're able to sound the alarm very quickly and tell everyone in the world: "Hey, one of these magnification events is happening, let's all go look at it." Once you know one of these events is happening, you're going to need lots and lots of follow ups.

These big telescopes have to keep doing their survey to look for more things, so what they really want is to hand off to follow ups to other telescopes.

But they're also only located in one place and, of course, the Earth rotates and so day time happens or the object gets too low in the sky so you can't see it, so you really need to have objects or telescopes scattered across the globe because if a planet happens, it might just happen when it's daytime at one telescope.

Yes, so these planet glitches are going to be very quick, so what you'd need is a large consortia that are going to go around and, when the trigger goes off, start monitoring 24 hours, every 24 hours from around the world, as the Earth rotates a different telescope picks it up, high precision observing every few minutes to look for these sudden glitches.

V5.5 So, Paul, I'm really excited about this. So, what have we learned? Well, lots. A number of these things have now been seen. Here's one of the early ones.

This is a star and you can see that here's the data from OGLE that the star didn't change in brightness for a very long time, about 1000 days.

It was a very boring star. Then suddenly, around mid July 2005, you see that it started inching up in brightness.

Right, okay and so it started getting a little bit brighter and so they would have been able to send the alerts, presumably.

Yes, and then it started really climbing around here, it got a bit less data, I assume it was cloudy or something around there, but by this point it's climbing quite fast and they were able to fit the microlensing curve and realise what they were looking at.

At this point a warning went out and people around the world started following up.

So, for example, telescopes in Australia, in Perth, the Danish telescope in Chile, MOA in New Zealand and as the world rotated these three telescopes would come online.

You see this happening over several days, so it got brighter and brighter and brighter, peaked at about magnification of three.

So, presumably, as you watch this coming up, it looks like it's just a big magnification event and just a star.

So, just a star, just a star, just a star, just a star, just a star... Ooh! What happened there? Ooh, there's a little glitch in it, yes.

If you zoom in on that, you can see that these glitches are a long way outside the arrow bars, so what's a very small glitch is very real and that's exactly what we're expecting. We're expecting a big star pattern with a glitch on the side.

Right, and so the fact that that glitch is really narrow tells you that it's something that's not that massive.

Yes, in this case it's a caustic, you've crossed a caustic here most likely, so caustics are very narrow.

You can see that this is only going over a few hours, this narrow spike, and so without the whole network of telescopes around the world, we wouldn't be able to follow this up.

So, their analysis of this, and because we have a fair bit of information here, they were actually able to be the first group using this very tricky technique to find something that looks like a Super-Earth, that is, a planet that is bigger than the Earth but smaller than a Neptune.

Yes, so this is the first one, because this came before all of the results from Kepler and the transits. We're talking 5.5 Earth masses.

The arrow bars are asymmetric, so there's a big uncertainty in the upward direction and a smaller uncertainty in the downward direction, so it could be twice that.

It could be 11 or it could be half that down to maybe two Earth masses, but anyway it could be just about as big as Neptune or something like that.

So, we don't know if this is a gas giant or a rocky planet. Yes, once again, all we know is the mass.

(So, we know the gravity and that's it.) So, the Super-Earth, you've seen lots of Super-Earths before, but the interesting things is this one is a long way out.

All of the Super-Earths that have been found by Kepler, they're all very close in with orbital periods of within 50 days.

This one is 2.6 astronomical units out. That's a little bit like where Mars is in our own solar system near the asteroid belt.

Okay, so this is getting to being something that looks and smells a bit more interesting with the respect to our own solar system.

So, it looks like Super-Earths are not only close in, but they're also further out and we're for the first time been able to see planets out at a decent distance.

Is this the only one we've seen? No, there are more. Let's show you some examples.

Here's a rather more complicated one.

They got data from both OGLE and MOA, the two surveys.

Here's the old data ones showing that it didn't do anything, didn't do anything, didn't do anything... until suddenly it started climbing, likewise, OGLE found the same. Didn't write that trigger.

MOA found the same, so here's their data, nothing, nothing, nothing, nothing, spikes.

Doesn't look like there's much follow-up data here, so it's probably just their own data from the surveys on these ones.

So, they weren't able to sound the alarm in this case, obviously, or maybe the surveys weren't in place yet.

But, nonetheless, it looks like something's happened.

The model says there's a big glitch here, it didn't actually manage to zoom in on that. Let's zoom in a bit.

So, certainly it was climbing here. It would have been nice to get an observation right up there but it'll probably be just a gap between two exposures or a cloud went over or something.

We went down again, this time, the seconds spike, they actually managed to get an observation from the top.

They nailed it, yes.

They also nailed the shape around here.

So, it's a very complicated shape which means that you could learn a lot about the system.

Yes, and in addition to these two big variations, there are a couple of small ones off elsewhere that you can hardly see, and combining these all you've got multiple caustic crossings and in this case it turns out that you've got a 1.5 Jupiter mass object about three astronomical units out.

So, that is something that's very similar to Jupiter, it's not quite as far out as Jupiter. A bit bigger and not quite as far out but beginning to look like a...

But it's going to be the closest thing we have to Jupiter,at least, I mean, this was in 2004.

Yes, now it's not always that obvious.

Here's another example of a microlensing event, and that pretty much looks like there's just a star if you eyeball it like this.

This is a very quick thing, looking at only a few hours across here, you can see that it was being observed by telescopes in New Zealand, that it was picked out by an amateur astronomer in South Africa and followed it through the maximum, then down here it started getting picked up by telescopes in Chile as the Earth rotated.

But the South African got lots and lots of data very quick, very accurate things.

If you try and fit a model for a single star lensing event to this, you see it doesn't quite fit.

There are a few little wiggles around it.

So, these are tiny little wiggles in this case, which means that the thing probably just wasn't lined up.

It didn't really didn't go through a caustic as much as other things.

Well, it turns out in this case, most likely the reason why the wiggles are small is what's called 'finite source problems'.

Here's a model fit to the data and you can see that you can fit the wiggles, this is actually a hard thing to fit, but you can actually can fit it all very well.

The idea is that here's the image plane and here are caustics, these green and blue lines through different models.

Everything you're doing so far has been assuming that the background source is a point, but in fact the background source is a star, which is a finite diameter which is comparable size to the caustics in this case.

So, say this part of the star, as it drifts across, will be lensed quite a lot because it'll go over a caustic that part won’t be very much.

Okay, so a tiny little piece of that star is magnified.

Yes, so because in this case the star is comparable in size to the caustics, bits of the star are being magnified, bits are not and you have to allow for that.

But if you allow for it, you see a pretty good fit.

Since most of that data is from an amateur, it really goes to show that amateurs with modern equipment can really be at the cutting edge of astronomy right now.

Yes, and in this case, we've got something a little smaller than Saturn which is 1.25 astronomical units out.

So, something like Saturn at the approximate place of Earth.

This could be one of the elliptical giants that we talked about.

This is actually a similar thing to what's been found by some of the radial velocity searchers. Okay, so we're sort of finding where we can find overlaps, we are finding some overlaps, that's good.

We're finding some new ones. Now, lots of people were involved in this. This is an author list of one paper.

It almost looks like something from the Large Hadron Collider.

Yes, so huge numbers of people from around the world doing all this sort of stuff.

Here's the result we get in this particular case.

This is a really neat one because there's a lot going on here.

You see lots of different observing situations, so there's a little glitch over here which is only caught by one or two observations.

Then up here, this is not a symmetrical curve, it sort of tilts a bit over there, then spikes, drops, comes back up again, comes back down and has another spike over here.

It's a really complicated pattern and comparable to lots of caustics here and big caustics.

Normally I would think, when I see something like this, it's a train wreck, it's hopeless, but because we understand the physics of gravity and gravitational lensing so exquisitely well, we can fit every little piece of this puzzle in something that makes sense.

Yes, and as it says down here, we've got a Jupiter mass planet, it's about 2.3 astronomical units out, and a Saturn mass planet about 4.5 astronomical units out.

So, that's really beginning to look like our own solar system, just a little more compact.

But the star is only half the mass of the sun and therefore much less luminous than the sun, so in fact, in regard to the snow line and the habitable zone, it's actually almost an exact analogue to our own solar system.

Well, that's really exciting.

Yes, so we see a lot of neat stuff with this technique.

V5.6 So, Paul, this is really neat stuff. So we've found some things, but are we able to make any conclusions based on a statistical basis so we know how frequent these things are? Well, here's the data on what we've currently seen.

So, the red dots over here are the planets discovered and confirmed by the transit method, so we're plotting the mass here against separation and, of course, the ones found by transit are all very close in.

This is not including most of the Kepler ones because they are not confirmed, but they'll be down around here, and we've seen the radial velocity, which finds some of these hot Jupiters but it's finding more and more of these eccentric giants up here.

The green dots over here, I hope you don't have red/green colour blindness like Brian does and discriminate them, they're about what you'd expect these things to be, so that in this region over here, so about the Einstein Radius out, a few astronomical units out, and you can see things down to quite low masses and also quite high mass ones. We are indeed finding things where you'd expect.

So, we know we have different selection effects here, and so we think that the selection effects for the green points are pretty much just how far away they are, so the fact that they scatter down further down here tells us that maybe the blue points are a little biased because, of course, the blue points don't find things down there.

Yes, so we've already talked about how we go about working out biases, whether we do a Monte Carlo simulation or try and work out for each bin here what the odds are of seeing things, and so we can try and recreate what the true population is.

Given we only have seven or eight points here, it's pretty hard.

However, basically about half of the high magnification events are followed up, the other half is just bad weather or they don't find them early enough for something like this, and of those half that are followed up, about half show planets with different deviations, and the half that don't could still have them, they're just too small or just happen to fit in the gaps in the data which wasn't very well sampled or something.

It's looking like of all the half of all these, typically dwarf stars that were in the foreground of our line of sight to the bulge, have planets big enough to see out in this sort of range.

Okay, so we can make some preliminary conclusions.

We should compare the radial velocities.

Remember, this is just the radial velocity plot now, and they're now getting to the stage where they can see Jupiter mass things out at Jupiter-like orbits, and a recent paper by Robert Wittenmyer concluded that they are seeing baby Jupiter-like things in about 3.3 percent of the stars they study.

However, that's almost certainly a gross underestimate of how many are out there because they haven't got that many years of data, a lot of them you can't measure enough precision, so he estimated that for every one they see, they've missed at least a few, maybe as many as 10 but it can't be much more than 10 they've missed.

So, they have to potentially correct up their 3.3 percent by a factor of 10.

Maybe as much as 10, 12 or so but it could well be less than that. It's very uncertain given that they've only got, like, three of these things.

But, fortunately, we have microlensing which doesn't have that selection bias.

It's much better at doing it, we just don't have as many objects.

So, what do we get if we compare the two results? Well, let's compare this and we find that here the data on the radial velocity surveys is mostly close in, so this is the number of these big planets as a function of distance, and here's a snow line, and the radial velocity is mostly telling you about the ones closer in and it's going up as we went down as we said earlier.

So, it's very uncertain when you get out here.

Because we're extrapolating the data where you've only got a very small number of the things out here, and that's the microlensing data. They're probably consistent, given the the large uncertainties on both of these things.

Okay, so they are consistent, although the microlensing is saying maybe there's even more than suggested by the radial velocities.

It looks like the number of planets really does keep on climbing as you get out here.

But we're really looking at 20, 30, 40 percent so 30, 40 percent seem to have Jupiter analogues.

It can't be much more than that because of the radial velocity there we've just been talking about.

If we try and work out the overall exoplanet populations, this is very rubbery.

We've got the classic hot Jupiters, the ones that were discovered first, and then maybe half a percent, one percent, depending quite on where you draw the boundaries around them.

(So, they really are an aberration.) Yes, they were seen first because they're easy because they're so big and so close in, but they're not a large fraction.

The eccentric giants are about seven percent, but then we've got the close-in Super-Earths seen by Kepler which is maybe 30 percent.

So, those are very common and we didn't know at all about them a few years ago.

Yes, and of course these ones are often the same stars as this one, for example, Epsilon and Andromeda has one of these and one of those.

Now, we're seeing the Jupiter analogues that are also maybe no more than 40 percent, but probably at least 10 to 20 percent so maybe 30 percent is a good guess we're getting.

Numbers are very rubbery at the moment.

But these objects, let's just be clear, can these objects occur in these solar systems as well and we just wouldn't know about them simultaneously? It could be because, bear in mind, these are most typically seen by Kepler whereas these are being seen mostly by galactic bulge micro-lenses, not at the same stars, we can't look at the same stars and see both of these things.

It would be lovely if you could do microlensing in the Kepler field or point Kepler at the galactic bulge or something like that, but that's not happened so it could be that these 30 percent are the same as this 30 percent or it could be different.

Maybe 30 percent here are 30 percent like that and they don't overlap.

Yes, the fact that microlensing only happens to one in a million stars means that even if you looked at Kepler, the chances of getting luckier is almost zero, so...

But maybe, with future big telescopes, we could look for one of these events and then wait until the foreground dwarf stars drifted away from the background star and then try and nail it for radial velocity and see if you can work out what else is there, so we'd do transit observations.

So, there are ways forward, but we are getting, I think, a kind of an interesting picture here, where solar systems seem to come in a variety of flavours and it may well be that they are mixed, but certainly our own solar system does not appear to be grossly atypical.

Though it's not dominant.

(Yes.) V5.7 So, Paul, I have to admit, I'm just overwhelmed.

You know, even 10 years ago, I thought we wouldn't know anything like this about planets.

This is amazing and it just seems to me that it's going to be hard to improve much on this.

Yes, and in fact, this is a gift that keeps giving, there's another surprise as well.

Remember, we were talking about what a planet would look like if it was all by itself.

You get a magnification pattern like that and as the Earth drifts across the image plane, you will get some pathetic little quick spike like this.

Now, this is much less amplification than you get if the planet is near a star, because then you start getting all the caustics, it's a much bigger signal, many more things you can measure.

The other benefit of a planet near a star is that you see the increase of brightness because of the star lensing event and therefore can trigger all the follow-up.

But none of this, in principle, you might be able to see something from planets that are a very long way out.

Well, you'd have to be pretty lucky to find one, yes.

Yes, I mean, it would only be possible if there were a lot of them out there and, curiously enough, they have been found.

Not very many of them but sort of less than 10 but here's a couple of examples.

Less than 10, I mean, if there's 10 of these, these seem like they're almost phenomenally almost impossible to imagine they'd happen.

Let's see, let's explain this first one. See if you can convince me.

So, we've got data, this is the data of many years from both the MOA and the OGLE surveys.

The MOA gets more data with bigger error bars and the OGLE gets the tighter error bars but less data points and what you can see is a lensing event, but it's a very small magnification, only about 40 percent.

It takes a couple of days to go across, that's quite short.

But look at this one, another one over here.

Look at that, nothing, nothing, nothing WOAH! Nothing, nothing, nothing, nothing, nothing.

Up by a factor of 30! But only for, this is one day there, so this is only happening over hours.

Wow, that almost seems impossible to fit.

Are we absolutely sure that's microlensing? Well, I mean, the star doesn't do a lot else, does it, over many years and it fits the microlensing shape.

They had, luckily this was up when New Zealand was observing because it went up and down during the night. That's a remarkable event, and this one is doesn't look like there's any way to get around it because everyone's seen it, perfect shape, wow! So, we have 10 events seen with these short little periods which means they have to be little tiny things, so what does that mean? What it means is that you need an awful lot of planets that are not near a star.

Because these are so hard to see because the image plane around it is actually so small, you have to get very lucky for the Earths track to go near it.

So, seeing even seven or eight of these things that we actually see, it's telling us that there must be huge numbers of these things out there.

Probably about 1.8 for every star, so these things outnumber stars.

Everything else, you're talking about maybe 30 percent of stars have these things, these are more than one per star.

They have to be not near the star, they have to be sort of out at Saturn's orbit or probably further out, maybe 30 or 40 astronomical units out, otherwise we start seeing all of these caustic things.

Okay, so how are we going to make these things? It strikes me as being slightly problematic from what I know of stars.

Yes, I mean, one possibility is that these are outer planets, Neptunes or something like that.

But that far out, you might actually be able to see them by direct imaging.

We're going to talk about that in the next lesson, but we don't see those things in enough numbers.

Odds are that these things really are free-floating planets.

These are not, even at a distant orbit around a star, they actually are drifting around the galaxy all by themselves.

Okay, so if we go to a place where we're going to make stars and planets, for example, the Orion Nebula, one could imagine making a bunch of little tiny things that are smaller than what we call a brown dwarf, so there's this limit of about eight hundredths of the mass of the sun, where you make a star and a star is defined as something that is able to fuse deuterium into helium and has an energy source.

But, below that, we have brown dwarfs and thanks to infrared surveys of the sky, we now know more or less how many brown dwarfs there are out there.

There are a lot of brown dwarfs but there are not that many brown dwarfs.

Yes, so there's only one possibility.

These things are basically the small failed stars.

They form the same way a star forms, we've talked about giant molecular clouds collapsing like this one in Orion, and we know that there are stars down to maybe times less than the sun, which we call these brown dwarfs, and maybe there are ones that are smaller still formed in the same way.

But, as you said, the numbers don't quite seem to work out.

Yes, we count how many stars there are, we seem to actually be going and, as you get smaller and smaller, you get fewer and fewer of them. So, you're going to have to have some little mechanism, something made of a bunch of little ones.

Yes, so if we extrapolate from the bigger ones, we can see that there wont be enough of these things. So we need another mechanism.

Another possibility is, in fact, these aren't failed baby stars, but in fact they are escaped planets.

So, you remember this planetary Billiards simulation, which we've shown many times, as a way to get the elliptical giants and to get the hot Jupiters, and maybe to get the stars going backwards we saw from the Rossiter-McLaughlin effect.

But if you look at the simulation, you see that every now and then you lose things.

Yes, so we actually lose quite a lot if we form lots of planets like this early on.

Yes, so it could be that this Billiards explains both the eccentric giants and it explains these few floating ones.

In most solar systems you had a lot of planets, then you lost a few.

They got flung out and they're now wandering the galaxy poor and lonely, whereas other ones stayed in and got warped into these orbits closer in.

Well, you don't just lose a few, it sounds like we need to have a couple of these things per star.

There's big ones, because already these are like Jupiter and there may be a bunch of smaller ones as well.

Who knows how many little things are out running around.

V5.8 So, Paul, this is all vaguely reminiscent of a TV show I remember watching when I was a kid. Space 1999.

It's sort of been relegated to the dust bin of TV sci-fi, but the idea was that there was the moon, for complicated reasons, got knocked out of the orbit of Earth and the solar system and traversed the galaxy with Martin Landau and Barbara Bain on it trying to deal with the trials and tribulations of going across the galaxy.

I always was struggling with this because it seemed to me that the moon would be pretty cold in a lonely place, a hard place to live if it were traversing the galaxy without a star.

Yes, you might think that these planets, if they got knocked out, would become very cold and unpleasant places and that's probably true, but some people have speculated that, in fact, these planets might be a good place for life.

Given how many of them are out there, they could actually be the dominant place where you'd find life in our own Milky Way galaxy.

So, you're telling me that these crazy stars that are free-floating might potentially be habitable places? These planets that have flung out? Well, let's look at the energy budget.

So, here's where the Earth's surface gets its energy from. On average, over day and night and the poles and the equator and after allowing for things scattering off, you get about 200 watts per square metre from the sun on the Earth.

So, that's because, although we get 0 watts per square metre, that's at noon on the equator when the sun is glaring down.

Above the atmosphere with no clouds and so on, and so if you average over it all the way it's about that.

That's going to go away if you're flung out into deep space.

You're going to get almost nothing from that.

So, where else? You get some geothermal energy. The middle of the Earth is hot with all that lava, and it actually stays hot.

It would have cooled down long since if it hadn't been for all of the radioactive elements in the middle of the Earth to actually keep it warm, even now 4.6 billion years after it formed.

So, it's not a lot of energy, but it's some.

Yes, I mean, it's pretty pathetic. People are using it for energy sources but it's not very much.

You also get some energy from meteorites that's falling on the surface.

I mean, it's quite big when one goes BANG! But that's a rare event.

When Tunguska happens, we get a lot in a very short period of time.

Yes, but most of the time it's just sort of a gentle drift of dust that's come down from space that makes almost nothing.

The solar wind would also go away if you're out, but there's a little bit of energy being dumped from solar particles and again, that's pretty small.

On Earth, humans actually generate about the same amount of energy as geothermal heat, just sort of all that burning fossil fuels and nuclear reactors and so on and so forth.

For an alien, this is about all you're going to get.

So, at first glance, it looks impossible.

You've gone from 200 watts per square metre to 0.03 watts per square metre, surely that means you're going to absolutely freeze.

It does seem that way to me.

But I suppose, in principle, you could have a really thick blanket.

So, maybe you have an atmosphere that's so thick that the heat can't get out, and certainly the top of that is going to be very cool, but if it's a really, really good blanket, maybe it could be warm at the bottom.

Very dark, you'd be living in perpetual blackness under a thick, thick atmosphere, or it could be that there's a really thick sheet of ice and so, at the bottom, the geothermal heats enough to warm it up.

You actually see that in Antarctica with things like Lake Vostok underneath four kilometres of ice, which is liquid. Maybe this can happen in space. Let's actually calculate how thick the ice would need to be to get something like this.

Okay, so let's imagine we have, in here's the rocky part of some planet and you've got your thermal heat of about 0.03 watts per metre squared leaking through there, and then we want a layer of water and then we have a very thick layer of ice.

Assume that this is very symmetrical all the way around the planet.

Now, a lot of conservation of energy tell us that the heat coming through here must also be the heat conducting through here and must also be the heat radiating out into space. That's also 0.03 watts.

We want this to be at a temperature above zero.

This presumably is going to be very cold out here.

So, what physics do we need? There's going to be a little radiation here, we've used that many times so we know that the amount of heat radiated, the power, is given by the Stefan Boltzmann equation, which is the area, let's assume we're dealing with one square metre here, so the A is just one, which is just sigma T to the fourth and that's got to be equal to 0.03 watts.

That means that T of the surface is going to be the fourth root of 0.03 over sigma, the Stefan Boltzmann constant, which comes out as about 27 kelvin. Oh, yep, that's pretty cold.

Now we are going to maintain a difference between 27 kelvin here, we need this to be 273 kelvin here.

Well, for conduction, we need Fourier's Equation; which tells us that the heat flow is equal to thermal conductivity at the surface area times the difference in temperature across whatever it is all over the thickness.

This is actually the definition of thermal conductivity, so it's telling you that the thicker something is, the less heat gets through it, the more conductive the more heat goes through, the more area means more heat and the bigger temperature gap.

Now, we know Q, 0.03, we want to find how thick it has to be.

We know the temperature difference you want, so we know Delta T equals 273 minus 27 which is 246 kelvin, area is one.

Now, the thermal conductivity for ice you can look up, it varies with temperature, but it's roughly about three watts per metre per kelvin.

So, we get S equals KA Delta T over Q, which comes out as about 25,000 metres of ice, so about 25 kilometres; which is a lot but actually not that unreasonable.

In the Earth, the deepest parts of the trench would have nearly 20 kilometres of water which could freeze, and it's easy to imagine planets with more water than the Earth.

Also, this conductivity here is assuming pure ice, whereas realistic ice is going to have cracks and impurities which is going to make it have less conductivity.

Also, if the water is very salty, which it may well be, then the point in which it freezes will be significantly depressed. So, we need about 25 kilometres of ice, maybe less if you allow for salt and impurities in the ice, which is a bit more than the Earth manages but not a lot, so it's not totally unfeasible.

V5.9 So, we go out and we monitor all of these stars for gravitational microlensing and when we do that, we see that a lot of stars actually have a planet about the right mass as what our solar system has in the form of Jupiter or Saturn. This is great news.

Yes, we're clearly finding things like our own, it's not the majority of stars, but maybe one sixth or one third or something, so comparable in numbers to those which have these close-in Super-Earths.

Right, but do we actually know these things for sure? Our Jupiter, I mean, we know that there's a mass out there, but what else do we know about them? Well, that's the trouble, we don't know what orbit they're in.

Given that closer-in ones are often in highly eccentric orbits, it could be that these things aren't the right separation to be Jupiters but actually in orbits that carry them in very far in or very far out.

So, we're not totally sure we've found solar system analogues.

I don't know how we're going to find that out.

We'd have to monitor these things for 20 years. But, of course, you can't go back and re-observe a microlensing star.

Yes, you're never going to be able to find it, but we can use the radial velocity technique, for example, if we're patient.

We just have to wait a couple of decades and say "yep, that's what's going on." At least time is on our side.

Now, one of the other things that we've discovered in here was a bit of a surprise.

We keep on finding these little short little blips that can really only be explained by there being these free-floating planets out there.

That seems hard to imagine.

I guess it's evidence for the Billiards theory we were talking about earlier about how we got these planets into these eccentric orbits and going backwards and close-in.

The same process of planets bouncing off other planets might actually produce something scattered out of the solar system, which could produce these free-floating planets.

Right, and so what do you think about the notion of these things harbouring life? I mean, some people seem, to me, to get a little carried away with this life thing.

Why would we think there would be life in these things? Well, I suppose there could be some little areas beneath some thick blanket that are warm enough and if life got going really early on before they got scattered out, which would be pretty hard because there are going to be meteorite collisions all the time that early on, then maybe life can keep going out there, but it seems pretty farfetched to me. Yes, I don't think I'll be betting on it.

V6.1 So Paul, we've been looking at how to find planets around other solar systems or in other solar systems.

But it strikes me that in our own solar system we have lots of stuff.

We have lots of little things, like comets and asteroids and things we don't call planets anymore like Pluto Wouldn't it be possible if there's lots and lots of those things to maybe see those around other solar systems, or in other solar systems? That's what we're going to talk about in this lesson. Is it actually possible to see the small stuff and it turns out they were actually discovered before the big things which is a bit weird, you'd think big things would be easier to see than small things, but all will be explained.

It all started back in the early 1980s with the IRAS satellite, which is a joint venture between NASA, the Netherlands and the UK. A little tiny satellite by modern standards.

So basically, to work at infrared wavelengths you have to have the telescope very very cool.

So this thing is basically a great big what we call a Dewar flask full of liquid helium which kept the whole thing at an incredibly cool temperature and it surveyed the entire sky.

Yeah, so it was really the first of a generation, of its generation to be able to go through and map the entire sky, and it quite revolutionised our ability to do astronomy at these wavelengths because from Earth you can see through the atmosphere but it's so bright, because the whole of everything that's warm glows at infrared, so it was able to get around those problems.

Yes, it actually triggered off a whole great conspiracy theory, partly by mistake.

Just like when we talked about quasars when they discovered the first big radio sources in the sky.

They didn't know what they were.

It turned out to be the quasars.

When we now have the first infrared map of the sky, they discovered a number of incredibly bright infrared sources, and they couldn't see where they were coming from. So one theory, they put out a press release back in the early 80s was that in fact that it might be a second star in distant orbit around our own that came near every now and then, and devastated things.

Oh, a sort of nemesis or something? Yes, and they put out a press release about that.

Then about a month later they discovered that in fact these were distant galaxies, what we now call ULIRGs, ultra-luminous infrared galaxies. A galaxy which is forming stars at an incredible rate with huge amounts of dust. And so they said "sorry, we made a mistake." But of course, the original press release got all the coverage and the retraction got nothing and to this day at least until 2012 people believed in this killer star and that IRAS had proven that it was all part of a conspiracy to hush it all up.

So I take it IRAS found more than just ULIRGs. Yes, and there was one thing that we knew already existed but that they didn't expect to see which was Vega, one of the brightest stars in the sky.

And one of my favourites, as it turns out.

And Vega is a hot star, so it should emit light at visible wavelengths which is this dashed line here.

And it does emit light at visible wavelengths. You can go out to the night sky and see it for yourself.

What they expected was lots of brightness at the visible wavelengths, then dropping off to essentially nothing into the infrared.

What they actually discovered was dropping off into "woop!" it went up and actually was extremely luminous in the infrared.

This is a bit of a problem because the reason this is one of my favourite stars is because it's one that I go through and use to tell me how bright all the other stars in the sky are and now you're telling me it's got all this extra stuff we don't understand makes me wonder whether or not we have these numbers right as well.

Yeah. It turns out about, it's not a very large fraction but it's luminosity in the infrared is about 2.5 by 10 to the minus five times the luminosity in the optical.

Ok. So you're using kind of funny units here. So although this looks a lot smaller than that, this really is a lot more energy.

Yeah, this is strange radio astronomer units where they emphasise things along wavelengths.

So, I mean what could be going on here? I mean the obvious idea would be that maybe there was something nearby Vega, so close we're not separating it out with a telescope and the IRAS satellite had a very poor resolution so anything vaguely nearby could be part of it.

Maybe something like a planet and the light from Vega is heating up the planet and making the planet glow in the infrared. We've already talked about these things glowing at the infrared, so maybe what you're seeing is Vega here and a planet because your 2.5 by 10 to the minus five doesn't sound like much.

Well that sounds like an easy calculation to do.

Ok, so let's work out if it would actually feasibly work by having a planet nearby.

V6.2 Ok. So how big would a planet need to be to produce the infrared excess that we're actually seeing in Vega? Now our working hypothesis here, so we have Vega and it's putting out radiation and some of that radiation hits a planet and the planet therefore becomes warm and radiates infrared radiation from its surface.

What we know is its infrared radiation here is 2.5 by 10 to the minus five times the optical radiation from here.

We also know that the infrared radiation has a spectrum that peaks at about sixty micrometres. That's going to be crucial. Ok. How are we going to solve this? So our first step is to work out the distance here, D, how far out the planet is.

And we can work that out by looking at the spectrum. The fact that it peaks at sixty microns is telling us something about the temperature of the planet. You may have heard of Wien's Displacement Law which says that the peak wavelength times the temperature equals a constant b where b is two point nine by 10 to the minus three metres Kelvin. So in this case we know that lambda peak is sixty micrometres sixty times 10 to the minus six metres, therefore T is b over lambda, so T equals about fifty Kelvin.

So to produce the spectrum peaking at sixty microns, we need quite a cold planet.

Now that presumably indicates that it's quite a long way away from the star.

In the first course we were talking about life in space, we worked out how hot a planet should be at different distances, and we've repeated that since.

And we find that the temperature of a planet is equal to the fourth root of the luminosity divided by sixteen Pi Sigma D squared where sigma is the Stefan-Boltzmann constant. This is not perfectly accurate, it's assuming that everything is a black body, but it will do as a first approximation. Now the luminosity of Vega is forty times the luminosity of the sun, and the luminosity of the sun if you remember is three point eight by 10 to the twenty six Watts. So rearranging this, we get that D equals root of luminosity, which is one point five by 10 to the twenty eight Watts, all over sixteen Pi Sigma T to the fourth. Which comes out as about two point nine by 10 to the thirteen metres, which is about two hundred astronomical units. So that's our first clue.

For a planet to be this cool it has to be a long way out. Given that it's that far out, we can now work out how big it would need to be. So our idea is that we have Vega putting out its luminosity, and the fraction that actually hits the planet is going to be given by the cross-section there on the planet, divided by the surface area of a sphere of the same radius D. So the cross-sectional area is going to be Pi r squared, where r is the radius of the planet. We have to divide it by the area of the entire sphere, which is four Pi D squared. And that's got to be the fraction of power that is intercepted by the planet, and assuming that the amount radiated is the amount in so it's a steady state, that has also got to be the ratio of infrared to optical emission. So that's going to be our two point five by 10 to the minus five. So therefore we find that radius of the planet equals the square root of or the Pi's cancel, take the four D squared up here, that's the square root of everything, so it's going to be two point five by 10 to the minus five, times four D squared which comes out as two point nine by 10 to the eleven metres. Which is enormous, that's more than an astronomical unit. This means the planet would have to go all the way from the Earth to the sun if it were in our own solar system.

Absolutely staggeringly big planet. The radius of Jupiter by comparison is a pathetic seven by 10 to the seven metres. So we're talking about something that's more than a thousand times bigger than Jupiter, way more. As it's a thousand times bigger in radius, that means that's a thousand squared times an area, so we're talking over a million Jupiter-sized things orbiting around at a sort of distance to give us that sort of infrared excess. So not looking plausible. We'd need either a ridiculously stupendously large planet bigger than any star let alone any planet we know, or millions of Jupiters either of which seems pretty unlikely.

V6.3 So, what are we going to do? If we put a planet near Vega it will indeed radiate the infrared but the surface area will need to get enough infrared out is staggeringly big. We'd need millions of Jupiter- sized planets to make it work which seems a bit ridiculous.

So how could we get enough surface area without having to require a ridiculous amount of mass? Well there is a possibility which is to use the Square-Cube Law. The basic idea is this.

You take a sphere like this one, as it gets bigger its surface area is proportional to r squared whereas its volume and its mass is proportional to r cubed. What that means is for a given mass small things have more surface area.

This is used in the natural world, for example mice can drop from great heights because they're very small therefore they have a lot of surface area for their mass, which means wind resistance allows them to drop safely from great distances.

If you're a massive thing like an elephant, you won't fall very well from a ten storey building whereas a mice can survive quite fine. Likewise elephants have a very small surface area per unit mass, so they need their big ears to keep themselves cool which mice don't have to worry about. So can it work for expanding infrared excesses, in space as well? Well let's have a look. Here we've got one mass and you can see it's surface area is quite small it's only a tiny fraction of your screen. But now let's go to break it up into ten pieces. Each with one tenth the volume and you see it's covering rather more of the screen. Let's break it up into a hundred pieces, so we're getting smaller pieces but more of them and it's covering even more of the screen.

And if you go to a thousand lumps ten thousand lumps, a hundred thousand lumps now you're seeing that the same mass spreading these small bits is covering most lines of sight through the screen. Let's look at the maths of this.

So let's say we have a certain amount of matter, say a mass m, and you want to break it up into spherical lumps, each a radius r. And there'll be n of these lumps. Now of course if r is bigger that means each of these lumps weighs more so we we get fewer of them and it will be smaller. And I want to see if there's some density here, Rho, as well as this matter and let's imagine that this whole cloud of lumps is exposed to some radiation and the amount of radiation absorbed will be proportional to the surface area of these things and that will also be the amount that is emitted because energy in equals energy out. So what we want to know is how does the surface area go as a function of r? Ok. So, how do we go about solving that? Well we can start off by saying what the mass of an individual... so let's call this a big M here. The mass of an individual lump is going to be its volume times the density.

Volume of a sphere is four thirds Pi r cubed times the density Rho. So that's the mass.

How many of these things do you get? Well, n is going to be the number, it's simply going to be the total mass you have to distribute divided by the mass of the individual objects.

So that's going to be three big M over four Pi r cubed Rho. Now that's told us how many of these things we're going to get, now we'll have to work out the surface area of each.

Now if the radiation is coming from one direction the surface area is actually the cross-sectional area so you replace that with a disk facing towards the incoming radiation of the same radius so it's Pi r squared. If the radiation was coming from all directions equally then light might fall on this bit or that bit in which case you might have to surface area of a sphere which is four Pi r squared. But let's use Pi r squared for the moment.

What we're really after is the concept of proportionality.

So in that case the surface area of all the lumps is going to be the number of the lumps times Pi r squared. Now this is assuming that these lumps are sufficiently fewer and far between that they're not shadowing each other.

When the number becomes very large you might get your one lump here shadowing one lump there and so then it won't be quite as big.

But this is what is called the optically thin case.

So the surface area equals n Pi r squared, let's substitute this value of n into that. So that's three M over four Pi r cubed Rho times Pi r squared. So we can cancel the Pi's, we can cancel the r squared with just bringing it down to r, and so what we find is that A is proportional to one over r. So take Jupiter and break it up into pieces a million times smaller, whilst down by a factor of a million see your surface area is up by a factor of a million, breaking into bits that are a billion times smaller and your surface area is up by a billion. So that suggests a way to get the incredibly large infrared excess that we're getting from Vega.

What you need to do is have some stuff out there but have that stuff broken up into small lumps. Small values of r will give you a big value of the surface area. If it's in the form of big lumps like Jupiter then you're in much more trouble.

V6.4 So Paul, I'm pretty convinced that there doesn't appear to be a planet going around Vega that explains that infrared excess. But you know, when we look at a lot of stars in the nearby neighbourhood of the sun what we saw on Vega seems to be something we see around a lot of stars. For example Fomalhaut, one of my favourites Epsilon Eridani, and Beta Pictoris and they seem to have this excess of infrared light.

And in a few of these cases where the stars are nearest you can actually look and see where it's coming from.

So here for example is what's called a coronagraph image from the Hubble space telescope.

They've blocked out the light from the star behind the little round disk here, and what you can see is it's coming from what is like a line on both sides.

Ok, wow. So it's really, really a very thin amount of material. It's not a big circle around it.

Yeah. I mean it could be, you know like a pencil sticking out both ends a bit but more likely it's an edge on disk around here.

Ok, so this is Beta Pictoris. What about some of the other stars that I was mentioning, what do they look like? Well here's a bunch of other ones. What we're seeing here is the age of the star, and you see these things in stars between ten and a thousand million years old and there's some more that look a bit edge on like Beta Pictoris, there's Beta Pictorus again. And there are some Vega you can't really see but it's a bit spread out, and some that look a bit more elongated. So it looks like it really is a disk.

So it's a disk and we just see it at different angles and it's not just young stars and old stars it seems to be a range of different ages.

So could this be for example the protoplanetary disk, the disk that planets form out of? Well if you remember we expect planets to form from a spinning disk of dust and gas.

However this disk first of all is mostly gas whereas these disks seem to be only dust by and large very maybe trace amounts of dust and gas in a few of them. So it's not the right composition.

And secondly the has usually gone away by about here in the first five, two or three million years very often at most ten million years. Whereas if you look at these you start seeing them, they seem to be very very common about 20 million years, well after. And then they become less dominant but they're still out there very long times.

So it doesn't look like it's a protoplanetary disk.

It's a different thing. It's what we call a .

Ok, so it's sort of the leftover from making the planets and stuff. It's sort of a debris disk leftover from the formation of the system.

Well, maybe. But there's a problem with that. Ok.

So there is a problem. The problem is that the dust won't stay put.

So Paul, we know that the protoplanetary disks after they've formed their planets are essentially swept out by radiation pressure where the actual photons of the star literally impart their momentum and blow the stuff out. And then we have the wind the solar wind where high speed particles also input, you know their momentum into stuff and we can clear out a disk. Doesn't that affect the dust around these stars? Well indeed it does. I mean it won't affect anything big, but a really small grain whatever has got rid of the... we actually get rid of those as well.

Not to mention having all the gas stripped away would drag them with it.

So it's very hard to imagine that this dust is actually just leftovers, although perhaps not completely impossible.

There's also another mechanism which gets rid of dust very effectively at least in our own solar system which is called the Poynting-Robertson Effect.

It turns out there's a lot of dust in the inner part of our own solar system that produces what we call the zodiacal light which is a sort of a glow you can see on moonless nights. And this is actually from collisions in the asteroids which produces small amounts of dust, and this causes it to rain down towards the sun.

So this works in the reverse of solar wind, it actually moves stuff in.

How it works, let's say you've got a dust ring going around an orbit around the sun.

To cause it to fall in, we need to slow down its velocity in this direction.

Adding velocity in that direction isn't going to make anything happen, it has to actually be slowed down. And let's look it from the grains point of view. The laws of physics should work in any possible frame of reference, so let's imagine we're sitting and having a ride on a micron sized dust-grain.

Now from your point of view, the solar wind is no longer coming straight out. You've got a bit of a headwind.

So this is like going through a rain storm or something with an umbrella and you're getting things coming at it at an angle from it.

Yes. Even if the rain is coming down straight, if you're running forward at a high enough speed it'll appear to be coming from in front of you. So that's going to apply a backward force which will slow you down and cause you to spiral in.

Alright. So, you know changing frames of reference is a little bit of smoke and mirrors.

So if we go back to the reference frame of the star of the sun, then it strikes me that I'm a little confused.

These lines are coming out at essentially right angles to the orbit, and so in that case, how does this work? We should be getting the same answer and it seems here we're really just trying to push it straight out.

Yes, like anything it should work in any frame of reference. And in this case as you say, the solar radiation pressure is not going to slow it down.

However if you remember back when we were talking about gamma ray bursts, if something is emitting radiation in all directions but is moving at the same time, that radiation is beamed forward.

Now is this emitting? Yes it is. Because sunlight's hitting it and heating it up, and because it's a warm dust grain it's going to emit infrared radiation. And that should be just the same amount of energy out as energy in.

So it's going to be radiating, but because it's moving, that radiation will appear to be beamed in a forward direction.

Ah, I see. So that's the difference. If I look in the perspective of the grain, I emit in all directions evenly but in the frame of reference of the sun or the star, then I don't.

But either way, you get exactly the same backward force.

In this case it's like a retrorocket.

It's firing radiation forwards so that slows it down. In its own frame of reference it's the headwind of particles that's causing it to slow down. Either way, it spirals in.

So this is going to clean the dust-grains out rather effectively. So we've got a problem.

We need small dust-grains to be able to intercept enough of the light of the star to produce these infrared excesses that we see, which are enormous.

But if the grains are small enough to do this without some totally ridiculous amount of mass then they're also small enough to be cleared out on very short time scales.

So we've got these three effects. We've got radiation pressure, we have the wind, and we have the Poynting-Robertson Effect. Which is the most important? In or own solar system Poynting-Robertson dominates and moves stuff inwards.

In these solars systems they've got A-stars which are very bright powerful stars, so in fact it turns out radiation pressure and solar wind are dominant and it would actually sweep the dust out, typically.

So, but any way you look at it, if there's dust there it's either going to go out or in, it ain't going to stay where it is right now.

Absolutely. So, why is it there?

V6.5 So Paul, it strikes me that if we keep on getting rid of all the dust one way or another the only way I could think to keep that dust to be in these stars we see, is to keep creating new dust.

Yep. So where does dust normally come from? Well, obviously the star was, you know, had dust when it was formed out of the cloud it was formed out of.

And then red giant stars make a lot of dust and supernovae make dust.

But this isn't a red giant or a supernova.

Alright, so that's not going to work. Now, I know you like comets.

They have some dust in them, don't they? They sure do. Here's a picture of a comet I took in the Gemini telescope.

This is what most comets look like. They're little tiny fuzzy things that move, and you can see just a little bit of a tail coming out which is actually dust-grains.

I think we'd probably better explain what's going on. That's actually a star, right? Where we've tracked on the comet and so the star is being dragged along in the image.

Yes, the telescope is following the comet as it moves. This is over about 20 minutes or so and the stars are moving across the background.

Alright. So that's one little comet. What about the big comets? It's actually a big comet, but it's a long way out. This is out at about Saturn's orbit However, most comets never get any closer than that, but occasionally comets like this one, Comet Hale-Bopp, does come close.

That's a picture I took about a day after it had been discovered, and it came closer and brighter still. And all these times what you're seeing here is dust being blown away.

What's actually happening is in the middle of the comet, these are some spacecraft images of the nuclei of two comets, there's this rather small thing maybe about in this case 16 kilometres long which is probably a dirty snowball.

And that's Halley's Comet, right? (Yes) So one of the grandaddy of comets.

And the radiation from the sun is coming in and melting it, and it's a mixture of gas and dust being blown out and the big tale that we see is in fact primarily a tail of dust. Here's a little simulation showing this.

So the red dot is the nucleus and the blue dot is dust-grains, and you can see as it comes near the sun... Wow. So, a comet when it comes by, really spews out dust in all directions. So this is what we need.

Yes.

Now unfortunately in our own solar system this is not going to work too well.

I mean, there aren't very many.

That's true. I waited for 15 years of my childhood to get to see a decent comet. I was expecting Comet Kohoutek to be everything, and it was terrible and I had to wait all the way to Comet Halley, and even it wasn't very interesting.

Yes, so comets are far too infrequent in our own solar system to produce anything like the dust even in our own solar system, let alone these debris disks which have millions of times more.

However, it turns out that at least one of these other solar systems has a lot more comets, or at least comet-like things. This is a spectrum of Beta Pictoris the star in the middle of Beta Pictoris. And you can see absorption lines due to gas and what you can see this is the main absorption line due to the gas, which is at rest relative to the star.

But you can see this little funny shape here.

What's happened is this is the spectrum taken earlier and that's the spectrum taken later, and the spectrum has dropped. and likewise here, and likewise over there.

Ok, so it's like there was something made out of a substance that absorbed light at these particular wavelengths and it was there, and then it wasn't.

Yes. So it turns out that for most of the lines you see in the star you have another line redshifted by between 10 and 100 kilometres a second so that means the gas is moving away from us more than Beta Pictoris is.

I see.

And it comes and goes on timescales of days. You see this absorption appear a couple of days, then gone again.

So you could imagine if it was a comet coming in it will of course have a high velocity because it's coming in on a highly eccentric or even a parabolic orbit. It's moving fast it's made out of stuff, and so we know if it were directly at the same speed as the star it would be here. It's coming in, it has a velocity relative to the star and we can pick it up that way.

That's right. So it looks like what's happening is the star's being hit by probably about a thousand comets a year, raining down.

Which is much more our own sun which is... a comet this size might hit the sun maybe once every a few hundred years.

So that would be a fun place to be an observer. You get you get to see all sorts of comets there.

Yes. But it turns out even here where you've got hundreds of comets a thousand maybe a year coming in, dumping their dust it's still nothing like enough to produce the amount of dust you require to give us the infrared excess. Ah, so we're still looking for another explanation.

V6.6 So comets seem to be out. How about if we just take two big objects 100 kilometres across, and smash them together. That's surely going to make a lot of dust.

Well, this is how dust comes about in our own solar system. You smash asteroids together typically and that produces dust. So this seems like a good idea. We just take some big rocks bang them together, and we keep supplying dust.

But we're going to have to keep doing this, because whenever we make dust, it doesn't stick around for very long.

So that means we're going to have to crash together a lot of rocks.

That's true.

But one rock can have a lot of mass, and it won't show up in the infrared because it's not blocking very much of the light. So, in fact we could have a situation where most of the mass is in a few big things. A few being like, a few billion.

And they're very rare collisions, but each collision of two things that are ten kilometres across will produce absolutely enormous amounts of dust. See, you probably could get away with these things going on for, hang on, hundreds of millions of years, slowly grinding down the big collection where most of the mass is to produce a constant supply of small dust things that then get blown away.

But I thought this is how we ended up making planets in our own solar system where they come together and form big things.

Yeah, that's the problem. I mean we just talked about how you had lots of rocks going around, but instead of smashing them to make small things, we joined them to make big things.

Why doesn't that happen? Why don't the astroids fuse together to form planets? (Yes.) That's what we believed to produce the Earth, after all.

Well if all the objects were moving around in nice circular orbits all the same then their relative speeds would be very slow.

So that means their gravity probably could push them gently together, until they merge and form big things. As they did collide, it'd be a very gentle collision, just like two pillows gently merging together and so it would make something bigger. So obviously we can't have something like this. We need them to be having more chaotic crazy motions so they bang into one another.

So we don't want them to get organised. We need it to be anarchy, so that when they come together they smaaash! we get all the dust. And so we really need to keep anarchy going, and don't allow this sort of organisation where we have none of those collisions.

(Yep.) We want just the right amount of anarchy. If we have too much anarchy, all the big things will smash together and produce a huuuuge! amount of dust that gets blown away and that's the end of it. (Ok.) So we want sort of mild anarchy.

Ok. And how do we do that? Well we need to stir these up as you say and the obvious way to do that is just what happens in our own asteroid belt which is to have a planet nearby. Our own asteroid belt hasn't coalesced to form a planet because there's Jupiter just outside it, and Jupiter keeps it stirred up enough that it can't all coalesce.

So maybe that's what we need. And there's a bit of evidence there are planets near these things. For example, if you look at this image of Beta Pictoris and the disk around it, if you look closely you see it looks like it's a sort of a bit of a slanty bit coming out down there. (Oh, yeah, there's a little flare there.) So that's saying maybe there's a little planet stirring things up.

Yep. So this is a warp. So maybe there's a planet on an inclined orbit that's pulling it up on this side down other there, or something like that.

Ok. Do we see anything like this on other systems that we can see better? Well here's Fomalhaut, and in this case you can see when you image it once again there's a coronagraph blocking out the light from the middle.

This is again a Hubble space telescope image. You can see the dust is actually in the form of a ring.

(Ok.) Which is a bit wierd.

You'd imagine it to be all the way in and out.

So it could be that there's in fact a planet inside the ring which is clearing out the dust in the inner bit, and keeping the ring stirred up.

Ok. So that is a potential way to solve our problem.

And there's a third, Epsilon Eridani, your favourite star. And in this case we actually now there's a planet there because of the radial velocity approach.

It's a little bit controversial, but it seems from radial velocity that there is a planet which has an orbit just inside this ring of dust that we can see.

Ok. So this is an image taken in essentially sub-millimetre in that, you know, some ways between radio and infrared and there's a little hole in the centre where the planet seems to be clearing things out directly.

So, again it seems to be holding together that these debris disks are something a little different than what we have in our own solar system, or maybe they're a much bigger analogy to what we see, where things collide, come together, it's very violent, and we can keep on making dust which reflects, and we can see here on Earth.

V6.7 So before we get too complacent and think we actually understand what's going on here lets show a couple of recent oddball results that seem to cast some doubt on this theory.

These may go away or they might fatally flaw everything I've just told you. Here is a very weird case of a very recent paper, this is a star, here's its optical light, this is what you'd expect its spectrum to look like if there was no dust around it. But, when it was observed between 2006-2008 the spectrum climbed up so that it looked like it had a debris disc around it so you'll see the infra-red wave lengths energy is much higher than you'd predict.

However, they went back and re-observed it a couple of years later, 2011, and the points had jumped from here all the way down to there.

- Right, so, you're telling me in the case of two or three years that somehow this star completely cleared its debris disc? I thought the processes we were talking about were going to take tens of thousands of years at least.

-It's pretty weird, it seems to have had a debris disc that went away as you said you can't clear the dust out by any of the methods we've talked about that fast - alright so, what do you thinks going on here? - well I'm damned if I know... people think that maybe the infra-red excess is due to something other than a debris disc to begin with maybe a solar flare, solar flares don't usually produce a spectrum like that...

-wow OK, so the solar flare would be up there or the solar flare would have destroyed the debris disc or something? who know? So you used the plural when you said "Oddballs" so this is one oddball...

-OK, well this is another family of oddballs I guess, this is the European Space Agency's Herschel space mission which is a bit like IRAS we talked about in the beginning an infra-red telescope sitting inside a dewar flask to keep it very very cool but this one worked at much lower temperatures and much longer wavelengths where it was incredibly sensitive.

And what they discovered was that normal debris discs, the spectrum's climbing up over here out at around maybe 10 microns. This one's only gently climbing at several hundred microns so what that's telling you is that you've got a very cold debris disc. because remember that the wave length at which something peaks depends on its temperature, a hot thing peaks over here cool things peak further into the infra-red this'd be a temperature of only 38 kelvin, so an incredibly cold debris disc.

-Paul, that's all well and good but this is a debris disc we think, of dust and I note that we're making measurements here at a thousand microns, that's a millimetere, and you can't emit light that is longer in wavelength than your length and so that would seem to indicate to me at least that we're not...dust isn't a millimetre that's like sand so somethings not right here.

- Yes so the dust we've been talking about is a micrometer in size a thousand times as small so a micrometer can produce things out here, maybe ten microns but a thousand microns you need to have sand the trouble is if you have something the size of sand first of all you need a lot more mass because you have much less surface area per unit weight so the disc has to be much heavier and its colder and further out but also if you have an orbiting disc of dust and we produce it the same way where we smash big things together what would normally happen, you smash big things and they make slightly smaller things they get smashed to make smaller things still until you end up with things so small they get blown away so most of the area should end up in the smallest things that can survive without being blown away.

And we're talking about very cold a long way out so even very very small grains should be able to survive out there so most of the radiation should always be from the smallest grains that can survive being blown out which would be a micron or even less than a micron in this case. - Alright so it does seem not to add up for some reason there is literally a sand box around the outside of this star, or, something else other than what we think is causing this emission.

V6.8 So it seems there really are small things, asteroids and the like in these extra solar systems.

We don't see them directly, but they smash into one another and generate all this dust.

So, given that our solar system formed probably in a way not dissimilar from those we must expect to find the remnant in our own solar system of something like these debris disks.

Yes, I guess we've got the asteroid belt in our own solar system which certainly generates dust, and the zodiacal light that we can see at night.

However the amount of dust generated by the asteroid belt is vastly smaller than the amount of dust generated by these extra solar debris disks.

And also, the ones we're seeing around other solar systems are much further out.

Typically seeing things maybe 40, 50, maybe 100 astronomical units out which is beyond the orbit of Neptune in our own solar system.

So they're really not asteroid belts so much as ice-dust belts.

Ok. But there is a bunch of stuff out there beyond Pluto, which we call the .

So the Kuiper belt is this impressive collection of rocks and debris that's out there and we sort of inferred the fact that Pluto was there and we think that Pluto was created from, you know, the conglomeration of all these rocks and pieces, and for a lot of time we figured there wasn't much stuff out there because Pluto was thought to be much larger than it really is. Now we realise it's actually quite a puny little instead of a full-sized real planet like the Earth is, and indeed it's actually even smaller than Eris, a new object that we've seen.

So the Kuiper belt is full of this stuff we need of these icy bits of junk occasionally conglomerating into planets, and it strikes me that that may well be what you're talking about. A debris disk.

Yes. It turns out we've got two asteroid belts in our solar system. We've got the rocky one between Mars and Jupiter, and we've got the icy one beyond Neptune of which Pluto and Eris and Sedna and all these other things are the biggest items. And in fact, presumably they collide together occasionally and produce dust. We can't see it here, but that is actually an analogue of the outer icy disk. The Kuiper belt is what we're actually seeing in other solar systems.

So how how big is our Kuiper belt? I mean, I know about the Kuiper belt but how big is it relative to the ones that we're seeing around these other systems? Well the amount of dust that we predict that should be generated in the Kuiper belt is maybe ten times smaller than anything we're seeing elsewhere.

Alright. But would we be able to see our Kuiper belt elsewhere? No, we wouldn't.

Ah. So maybe it is the remnant. That sounds like a good match.

So Paul, how common are these debris disks like our own Kuiper belt, around other stars? Well the latest data from the Herschel space telescope indicates that if you look at the spectrum of a star... so it goes up and comes down, and what they do is they look for whether the light at the infrared is higher than what you'd predict from the spectrum.

And in about 20 percent of stars it is significantly higher. So that they can say with confidence that there's some sort of debris disk out there.

Ok, so what you're saying is that 20 percent of stars have debris disks, and 80 percent don't? Well, what we can say is that we can detect debris disks in about 20 percent.

However given the sensitivity of current space telescopes the debris disk has to be about 10 times more massive, 10 times more dust than on our own Kuiper belt. So we're only picking up mega Kuiper belts if you like, and we couldn't see our own Kuiper belt. So it could be that 20 percent have these mega debris disks out 40 astronomical units or beyond and the other 80 percent have nothing, but more likely perhaps 20 percent of these mega ones and the other, some fraction of the rest, maybe half maybe all of them, have smaller debris disks more like our own solar system might have.

So we're really going to need... I mean, Herschel is a brand new really powerful telescope and it's sadly run out of coolant, so it's sort of ending its lifetime, and we don't really have anything until the next generation of huge ground-based telescopes are going to be able to do anything like this and they're not even that sensitive, where Herschel was.

Yeah so it might be that's going to be the story for a long time to come.

Alright. So these debris disks, they're out at large distances. But we know that there's going to be dust there, and that that dust will disappear over time, so we need to keep on replenishing it and we need to have some way to stir things up or else we just end up with the dust going away.

So in our own solar system that's Neptune.

What's going on in these other ones? Yes, so if the... as we said earlier, if these objects are just moving in nice circular orbits they won't smash into one another, and if they do they'll merge rather than blowing themselves to pieces.

So we need something to put them into eccentric orbits. As you said Neptune does this in our own solar system, it stirs up the Kuiper belt.

So what this is telling us is not only do we need large mega belts of these things out there, but we need probably some planets out there to stir it up. So we're looking for big planets a long way out.

So every time, and those 20 percent of the objects that have these mega Kuiper belt objects, we probably have something like Neptune or even bigger out there stirring things up.

So, indirect evidence for planets.

Yeah, but it'd be nice to actually see them directly to make sure our theories are correct here. The trouble is both the radial velocity approach and the transit approaches are only spotting things further in. They're not going to see anything out at Neptune-type distances. Microlensing something that far out will show up as a free-floating planet, and we know they saw some free-floating planets, but we don't know if they really were miles out or whether they're actually out at Neptune-like orbits.

Right. So we need a new technique, a technique that allows us to get a long way out from the planets, because all our other ones really are biased towards things close in. That's what we're going to talk about next time.

Oh, very good.

V7.1 So far we've talked about exoplanets a lot, but we've never actually seen them.

We've seen the effect they have on their star, we've seen them blocking out the light of the background star.

We may have picked up the light from them merged in with the light of the background star.

But it'd be really nice to actually see the damn things.

Well that's really the holy grail, Paul. To actually see the things.

Yes, I mean just apart from, you know, do you really believe they're there until you've seen them? If we see them, we might be able to find the far away ones.

All our techniques so far have been really good at finding things pretty close in even the gravitational lensing only works out to about Jupiter or Saturn's orbit.

Anything further out we're not going to pick up by any other method.

And if we see them, we're going to be able to know what colour they are and if we can take a spectrograph put a spectrograph onto them... we'll actually be able to see what they're made out of, and we might be able to see if they're made out of water and stuff. But we have a problem.

If we recall, the difficulty is Christine here taking over the world so we can't see anything.

So it is, you have a star shining... it completely obliterates everything else that we could possibly see.

Yes. So the difference we're talking about here between a candle and full-beam headlights is about a factor of a thousand.

Let's calculate what the difference in brightness between a star and a planet is.

Ok. So let's imagine we're looking at a star and a nearby planet.

And you want to know how much fainter the planet is than the star.

Now let's assume that this planet is only shining by reflected light, which is the case at optical wavelength in our own solar system. So we've got to ask about all the light coming out at all directions from the star, and some fraction of it will hit the planet and then bounce back off in all different directions, and some fraction of that will come to us.

So the first question is what fraction of all the light from the star will hit the planet? We'll assume that the light from the star is spread uniformly over a sphere. Let's call that radius D that's the distance from the planet to the star.

So the flux out at the sphere is just the luminosity of the star over 4 Pi D squared. Now the radiation actually hitting the planet is going to be its cross-sectional area, Pi r squared, where r is the radius of the planet times the flux. So, flux hitting the planet is going to be Pi r squared equals a quarter r over D squared times the luminosity of the star.

So that means, we'll now assume that all the radiation that hits the planet, reflects off.

And we'll also assume it reflects at all angles. In practice the amount bouncing off in different directions will be different. There'll be less going this way than that way. But let's just assume on average it's all in the same direction.

In that case, the luminosity of the planet is going to be this. So the ratio of the luminosity of the star to the planet is going to be L over that. So it's going to be 4 D on r squared the ratio. If we plug in some numbers, let's say, take for example Jupiter. So for Jupiter its radius is about seven by 10 to the seven metres. Its distance from the sun is five astronomical units, so for Jupiter that comes out as about five by 10 to the eight.

So nearly a billion times difference.

And that's assuming that all the light that hits the planet bounces off.

In practice only a small fraction is going to be. So in reality the ratio of star brightness to planet brightness for something like Jupiter is going to be about 10 to the nine.

About a factor of a billion.

V7.2 BRIAN SCHMIDT: So, that is-- it's a much, much worse problem than even what I see as being a pretty scary movie already.

PAUL FRANCIS: Yeah.

So we really have to understand what it is that makes it so hard to see faint things near bright things, so we can do something about it.

So I mean, here is the camera I used to take that scary movie.

BRIAN SCHMIDT: I'm a Nikon man, myself, Paul.

PAUL FRANCIS: And basically, this consists of a lens and a detector.

Any Canon engineers in the audience will lynch me for that.

There are a few more things in the middle here, but want can simplify it as this.

What you could imagine is, you've got light rays coming from different angles here, like the red and the white, and they'll be brought to focus at different points on the detector.

BRIAN SCHMIDT: So the different angles map onto a different place of the detector, and we should see things.

So that doesn't really explain what's going wrong.

PAUL FRANCIS: Yup. So here's a still frame from the scary movie.

And you can see, this is when the light was not too bright, you can see the candle over here, and you can see the light.

And indeed, the headlight is there.

The candle is there.

They're landed on quite separate parts of the detector, so all is good.

BRIAN SCHMIDT: Yes.

PAUL FRANCIS: But now when you increase the light by a bit more, still, that light's coming from here and that's coming from there, but you'll begin to see that not all the light's coming in there.

For example, look up there.

No light's there in either situation, but if you go back, it's quite dark.

There, it's quite bright.

BRIAN SCHMIDT: And that's presumably not because the light is being misdirected now.

It's just that there's so much light that we're seeing light where it was not so obvious before.

PAUL FRANCIS: Yeah.

And if you go later still, you can see that the light from over here, and from over there is, you know, like up there.

Go back a bit, there was no light up there.

Where's that come from? And even more, later on, still.

Now it's impossible to see anything else.

BRIAN SCHMIDT: So, Paul.

People always like when I'm out showing them the skies, talk about the magnification of our telescopes.

And so you might be tempted to think you can solve this problem just by raising the magnification from your Canon to a big telescope.

PAUL FRANCIS: Yeah.

Well, let's go through and look at exactly where the light's coming, which will explain why the magnification isn't going to help you.

So here's our image when it's not too bright, and we can turn that into a map of the brightness on the pixels.

So here's a map of that.

So you can see there's a lot of counts coming in these pixels over here.

That's the main headlight. There's the lower headlight.

Over there is the candle.

And they're well, separate, but you can see there's not a sharp edge here.

You're getting the light from the headlight, but it doesn't drop to 0 suddenly at the edge of the headlight.

It sort of slants off gradually.

As you ramp up the brightness a bit higher, you can now see it's slanting off very gradually.

BRIAN SCHMIDT: So the candle's just barely visible now.

PAUL FRANCIS: Yeah.

So the light, and if you make it brighter, still.

BRIAN SCHMIDT: So if we magnify in on that, we're just going to see the same thing everywhere.

PAUL FRANCIS: Yeah.

So the problem is, the light's not going where it's supposed to go.

So instead of the light going like this, some fraction of the light's going elsewhere.

Not a very big fraction, but if this red light was incredibly bright, even if 1 part in 100, or 1 part in 1,000, or 1 part in a million that's going the wrong direction, it's still going to swamp the rest of the stuff.

And if you magnify that-- let's take an image here, and you magnify it, you're going to get a fainter, but equally blurry image.

You're not going to see anymore.

You're just going to make the same misdirected light spread over more pixels.

That's not going to help you.

BRIAN SCHMIDT: OK.

So we need to think about how to get around this.

We have technology on our side.

Presumably, we can use that technology to solve this problem

V7.3 PAUL: So it turns out there are a number of different reasons which cause the light to go not where we want it to go.

The first one, and the one that actually dominates in the case of my Canon camera, and probably your Nikon as well, is just scattering.

The idea is that there a minute imperfections in the lens, or grains of dust on it, or light bounces off a surface of the detector and bounces back and forth inside the camera a few times. BRIAN: So Paul, that strikes me that our first piece of technology could just be a microfiber cloth, and you could clean your lens up a bit.

Is that going to solve our problem here? PAUL: It certainly solves it a lot.

I know I've often taken a camera out in cold weather it mists over but you get really bad scattered light.

So this is a problem.

It tends not to dominate for professional telescopes.

The mirrors on the professional telescopes-- here's the main mirror on the Gemini telescopes-- are extremely good.

You really need everything to be accurate to 1/10 of the wavelength of light.

BRIAN: Right.

So the Gemini mirror is 8.2 meters across, and it's accurate to 1/10 of the wavelength of light.

And the wavelength of light is less than a micron, so you're talking-- you've got everything better than 10 millionth of a meter across this 8.2 meters.

Well that's impression.

The technology is amazing.

PAUL: It's impressive, but it's something we actually can do.

You wouldn't have guessed ahead of time, but optical engineers are very smart people and they'll do it.

BRIAN: So problem solved.

We're done.

PAUL: They even have high tech dust cloth.

In this case, they actually put carbon dioxide snow over the surface to clear it off.

You don't really want to go scrubbing cloth on something with this level of accuracy.

BRIAN: Oh, you'll probably scratch it up.

OK.

So we've got it solved, we're done.

PAUL: Or so you might think.

Unfortunately, we have this problem.

Again, we've seen this before, atmospheric seeing.

And this turns out to be what limits you for ground-based telescopes.

So how does this work? The image is blurry like this one. Why is it blurry? Well you've got to imagine all your rays coming down for space, and then you've got to imagine the atmosphere is not uniform.

Some bits of it are hot and some bits are cold.

So let's say we've got a cold bubble of air in front here.

What's it going to do? Well-- BRIAN: So that cold bubble is going to have a higher index of refraction, so it's actually going to act like a lens in the way and cause the light to converge in the same way that if you shine it through a convex lens it's going to convergence.

That's going to mess the image that you think you're seeing.

PAUL: Yes.

Or you might have a bubble of hot air going in front, in which case this acts as a diverging lens and spread the whole light out.

And it won't be very good lens odds are, and this is going to be drifting across the telescope at enormous speed, and they're not going to be my simple shapes like I've shown here.

So whenever you've got thermals, bubbles of hot and cold air, you can have trouble.

BRIAN: All right.

And this is, maybe, one of the problems we have when we go up to Siding Spring Observatory here.

I routinely go up there, and it's hot, and there you can literally see the stars twinkling above you, we can have a pretty stirred up atmosphere that hasn't had a chance to settle as it has traveled 2,000 kilometers across the Australia continent before it gets to us.

PAUL: Yes.

You can usually see large numbers of wedge-tailed eagles circling around the mountain, which tells you there are definitely thermals coming off the side of the mountain to keep them aloft.

There are better place on Earth than Siding Spring Observatory for this.

For example, Mauna Kea in Hawaii.

Somewhere else we've both spent a lot time, I imagine.

BRIAN: Yes.

PAUL: And here you see we're much higher up.

There are gumtrees anymore.

You're suffering from altitude sickness at this location.

And here, there's a much smoother air flow, much fewer thermals.

So for example, here's an image I took of a particular region in the sky at Siding Spring Observatory, and here's an image of the same part of the sky I took using-- BRIAN: Oh, go back.

So this little bit, you really see. So one object is smeared together here, and then if we go up to Hawaii it suddenly breaks into three objects.

Now Paul, why on Earth were you looking for something changing? Why were you taking pictures of the same part of the sky from Hawaii and Australia? 100 PAUL: Well it turns out this part of the sky contains one of the 100 brightest radio sources in the entire sky, which is actually about there.

And we took this picture and didn't see anything, so went and took a deeper picture.

And if you look just about very faintly over here, you can see a little red smudge which, actually, we believe is a 12 billion light year away radio galaxy, which is producing the equivalent to a radio naked eye star.

BRIAN: OK.

So with a clear sky, or a non-turbulent sky, from Hawaii, we can see further and see more clearly.

But I note that these stars still aren't infinitely small, so we haven't quite solved our problem, perhaps.

PAUL: Yes.

I mean, the reason Mauna Kea is so good is because of-- there's a temperature inversion on the big island of Hawaii.

You think of Hawaii, you think of hula hula girls, and rain forest, and things like that.

People always look askance at me when I arrived at the airport with my thick coat, and woolly hats, and mittens when they've got their surfboards.

But of course, up at the summit it's freezing cold.

You can see in this time lapse, taken from Gemini, that most of the clouds are locked below the summit by this temperature inversion, so up at the summit it's actually very, very clear, the thermals are locked below the temperature inversions.

BRIAN: So it's nice, and smooth, and steady and all the turbulence and problems that we have in Australia are kept low below you.

PAUL: Yes.

So a pool site, like where I grew up in London, you might be talking 10 arcseconds seeing.

Siding Spring Observatory's pretty good by that standard, maybe about 1 arcsecond seeing.

BRIAN: So when you say that, you mean that the angle that a star subtends in the sky is on order of 10 arcseconds.

So that's 1/360 of a degree.

So that's pretty small.

PAUL: Yes.

A human eye can only see about 100 arcseconds.

So that's why magnification works for things like binoculars because the human eye is not capable of seeing even very poor seeing. When you get above a certain amount of magnification, about 100 or so, that doesn't help you anymore because it's being blurred by this.

So what this means is if you get a light ray, it's bent by about that amount, and for Siding Spring is about 1 arcsecond.

That would be a good observing site from the 1970's.

Similar for Mount Palomar and places like that.

Mauna Kea, or one of the other good sites like the Atacama desert in Chile, we might be talking about maybe 0.6 of an arcsecond at visible wavelengths.

And that's still not going to be good enough, because that's about all that separates a star from a planet.

BRIAN: OK.

So it strikes me that the best thing to do is get above the atmosphere and be done with it.

Like the Hubble Space Telescope, our $2 billion telescope in the sky, and so viola.

Problem solved.

V7.4 Now Brian, you suggested that if you put a telescope in space, your problems are solved and you get infinitely sharp images. But I mean I've seen images from the Hubble Space Telescope.

They're pretty sharp but not infinitely sharp. So what's going wrong there? Yeah, maybe I was being a little optimistic there, and I think to really understand why the Hubble Space Telescope doesn't produce infinitely sharp images, we need to understand (to first order?) why light goes and travels in straight lines.

Yes, so you have to bear in mind that light is a wave. And let's look at some other waves.

Here are water waves on Lake Burley Griffin here in Canberra, and they're moving.

This is a windy day, and there are waters moving from left to right, or the waves are moving from left to right.

So it kind of looks like all the water is going this direction and eventually we should have a whole mountain of water on your side of the lake.

And a dry lake bed on this side.

Exactly.

But of course it doesn't work. The waves are moving but the water isn't. Let's zoom in on it a bit.

Almost getting sea sick here.

Yes, and it sure looks like the waves are moving this way with the water, but the water isn't.

The water is actually just doing little circles. (going up and down, right?) At any given point the water is going up and down, maybe a little bit side to side and around. So that's water waves. What's happening is the waves are moving but the water isn't. And presumably light, which is a wave, is quite a similar process where in this case you have essentially a wave of electromagnetism going up and down so you have the field going up and down, and it's not so much that it's moving, it's just that that field's moving up and down.

Yes, the electric field isn't moving, it's just oscillating at each location.

So if nothing's moving, why do waves have a direction? So let's imagine we had a flat surface of water and we heaped it up in a pile. So maybe we've dumped another bucket of water on the top here and then pulled it off. So we start off with the water higher in the middle.

What's going to happen? Well presumably it's going to move out in all directions.

Yes, you'll get a wave going out in all directions.

So that doesn't sound like a straight line.

No, not at all.

Exactly the same thing happens with electromagnetic waves.

If you have an electric field and you make it oscillate at one point what will happen is waves will go out in all directions. That's exactly how radio and TV transmitters work. So how do we get a straight line? Well, let's imagine instead of having a single mound of water we've got a whole bunch of ridges of water.

Ok, so a bunch of plain waves essentially going out.

Yes, and we just freeze it and release it and set it all going at this time?.

What's going to happen is the water here, say is high, so it's spreading all directions from there.

The water here is also high, so it's spreading in all directions.

So what we're going to have is from every location where the water is high, things are spreading out in circles.

Ok. So we have all this superposition of circles. (Mhm) And so that superposition how does that end up giving us movement in a straight line? What you can see is, let's say that every different location has had enough time to move to this radius, is that they all line up over here.

Ah.

So from every point ever here, we're getting a wave of water at this location. With any other location like here, sure, it's on the wave location of this circle, but it's halfway between on that one. So for any point that's not on this line... on this line you're getting lining up of the waves coming out from in circles in every location. But anywhere else you're going to get plus from some, minus from others, and it all cancels out.

You get the peaks the troughs cancelling out to give you nothing.

Alright. So we end up with these places where everything lines up in phase and that is effectively where the light is travelling.

So that's right. This is why light travels in a straight line. It's just the only place where everything lines up, and this is called Huygens Principle. Basically the idea is that the waves do not travel in a straight line. So they spread out in circles from every location or spheres in 3D. But it turns out that if you have a plain parallel wave, and you have a sphere coming up from every point on that, the only place all those spheres will add up in phase, where all the peaks line up with the peaks and not cancel with the troughs, is going straight ahead. So that's why light travels in a straight line because the width of the beam is much bigger than the wavelength. And so the only place that adds up in phase is to go straight forward.

Right.

And in fact this is why other things go in straight lines. Because if I throw a ball at you, it turns out it's actually a wider ball by Newton's first law. Because in quantum mechanics the atoms in the ball are actually waves. (Right) And once again they only add up in phase if they're going all in a straight line.

So it turns out this actually explains Newton's first law of motion that objects continue in a state of uniform motion in a straight line unless acted upon by an external force.

Alright. So, we now have Huygens Principle the idea that we can explain how light moving out is really a series of waves added together, and that explains how things are moving in straight lines, and we can now use this to go through and figure out why we're going to end up with a blurry vision with the Hubble Space Telescope.

So Paul, we're going to have a wave being the superposition of a bunch of little circles going out. They all add up in phase, and so as we allow time to move forward, our wave is going to move out and move forward in this nice straight line. But this is a very ideal case where things go on forever that way and forever that way.

Life isn't like that. Often things are constrained, they're finite.

Yes, what happens if the wave instead of going on forever has a definite edge? In that case you're still adding up circles from every high point but you've not got an infinite number of circles, you've only got a few.

So you see you're getting a bit more of a complex shape. They still add up in phase over here, but what's going on around the edge? Yeah.

Well you can calculate that, and you start getting patterns a bit like this.

(Ok, so...) What we've got here is plain waves coming in and we've got a barrier with a slit to only let waves through in the middle.

And so you've drawn a circle starting in principle from every point in the system. In this case it's been approximated as six of them.

Right, and so here we can go through and we can see things add up very clearly to that same nice solution. But then here on the edge, we get this complex pattern which looks different, and so it does end up affecting the shape of the waves that pass through.

So here's a simulation courtesy of Wikipedia showing 100 a fairly big slit with plain parallel waves coming in, and you can see that the light does continue straight on. But some fraction of it is going off in other directions.

Right, and so in a perfect world, this part looks ok, but then around here things are getting mucked up. So... And that's actually quite a big slit. If you make it a narrower slit like this, you're getting a much worse situation.

So now we've taken something that's nice and flat and perfect and we've made it into this big effectively curved surface, and so if I were looking at what I thought was this, it's going to be modified quite substantially.

Yep. So in this case you're trying to measure how bright things are. You've got to pick up light all the way along here. Maybe a bit more in the middle, but it's going to be very spread out. And in fact this happens in reality.

Here you can see a photograph of water where they've got a barrier here with a little hole.

Plain waves are coming in here, and you can actually just about see circles coming out the other side.

So it really does seem to work at least for water waves.

Ok, so imagine we have the Hubble Space Telescope, and we have light coming in from almost a long way away. So the light is coming in in nice little straight lines, and it gets to the Hubble Space Telescope which is like a slit.

So suddenly we have something funny going on. How does this end up affecting what we see with the Hubble Space Telescope? Well let's calculate that.

V7.5 So let's work out what fuzziness, what blurriness diffraction applies for a telescope.

So let's say we have the mirror or lens or aperture of a telescope here, of diameter D.

And assuming the telescope is correctly built, if you get light coming in here, it will all be brought to a focus at some particular point. Now if it was an ideal telescope the light from any other position would not contribute to what you're picking up here on that particular pixel.

So if the light was coming from any other angle at all, it would land somewhere else on the detector. So now let's consider light coming from a different angle, the light you would like to go somewhere else. So we'll say this angle here is theta.

And you want none of that light to get to that point. Now, if the light can be straight, all the waves add up in phase, for example if it's a peak here, it'll be a peak all the way here if it's a trough, then a trough all the way to here, and your optics is designed so all those peaks will add up, and if you in- phase it on here. So that's coming from an angle, though.

The waves are going to be coming in something like this. And you see that... let's say these are the peaks. When there's a peak here, it's not a peak over there. It's a little bit different from a peak. So let's say for example that, that length there that we're going to call L.

Now if L was a wavelength, then when it's a peak here, it'll also be a peak there but a different peak. So it might be like the peak of this one and the peak of that wave.

So in the middle it'll be a trough. So, peak trough, middle peak. If it was lambda over two, then when it's a peak here, it'll be a trough there and sort of halfway between a peak and a trough in the middle, and so on. What that means is, if you had all peaks along here, it all adds up in phase over there.

If it's got a peak and a trough and a peak then it absolutely won't add up in phase over there. It'll cancel out. So generally speaking if L, this distance here, if L is about a wavelength, then the things are not going to add up in phase there. If L is much smaller than a wavelength, like a tenth of a wavelength you're still going to get maybe not quite all peaks, but fairly close. So you'll see you'll still get some light over there. So that's our requirement.

If the path difference from one end to the other is about a wavelength, then you're not going to get light from this angle contributing over here. Which means for example if this is light from the star and that was the planet, you could separate them nice and clearly. If L is much less than a wavelength of light, then there's going to be some contamination. Some of the light from both will contribute, and so it will be very hard to tell the planet apart from the star.

Ok. So what we need to do is work out what L is. So let's zoom in now.

So we've got the parallel waves. We've got the waves coming in at an angle, theta, and we'll do a right angle wavefront there, and what we're going to work out is what L is. We know the diameter D of the telescope mirror. Now if this is theta, that's a right angle, so this must be 90 minus theta. So that must be theta.

So from trigonometry, this is a right-angle triangle, so the opposite is L and the hypotenuse is D. So sine theta equals opposite over hypotenuse over D. But now we can play a trick. If you remember the small angle approximation for theta less than about 10(or tan?) degrees.

Sine theta is very close to tan theta, and it's very close to theta. They're all about the same thing. Only works for very small angles, but in this case the different between a planet and a star is going to be a tiny fraction of an arcsecond or maybe an arcsecond or two, so it's a very small angle. So it's a good approximation here. So instead of writing sine theta we can just write theta.

As long as we just measure it in radians. So what we actually have is theta equals L over D.

But if you remember, the requirement to get the light not contributing was, L is about the wavelength, so that's going to be the wavelength over D. That in fact is the equation for diffraction limit. Roughly speaking if the angle is in radians equal to the wavelength divided by the diameter, you're ok. If the angle is much smaller than that, you're in trouble, you're not going to see things very clearly. Technically speaking for a perfectly circular (???) you could add up your peak, slightly off a peak, slightly more of a peak all the way down to trough all the way over there, and it turns out it comes out as one point two lambda over D. But just straight lambda over D will work fine for the purposes of this course.

So what is that for the Hubble Space Telescope? For the Hubble Space Telescope it works at optical wavelengths, so lambda is about say, naught point five micrometres.

Diameter of the Hubble Space Telescope is two point four metres, so the diffraction limit, the angular limit is going to be naught point five times 10 to the minus six to convert from micrometres into metres, over two point four, which is two by 10 to the minus seven radians which is naught point oh four arcseconds.

Pretty good, considering from the ground you might get ten times worse than that even in the best sites. But still not perfectly sharp.

V7.6 So Paul, you've shown that we can use the Hubble Space Telescope to get down to about a tenth of an arcsecond in resolution. Which is great, compared to what we get at Siding Spring. But we're going to have to probably do better, and it strikes me that we have here on Earth ten metre telescopes. But we're going to have to fix the problem of the atmosphere to move forward.

Yeah, we're kind of stuck in a bind. If we're on the ground, we have big telescopes so that the diffraction limit is very small, but we're mucked up by the atmosphere.

If we're in space... you can't put ten metre telescopes in space the nose cones of rockets aren't big enough. So you're stuck with a diffraction limit.

So wouldn't it be nice if there was some way to cancel out the effects of the atmospheric seeing.

And of course there is... kind of. This is a diffraction limit pattern with a laser as you'd get from a space mission.

Right. So that's what you would see if you don't have an atmosphere, and we want to be able to try to get that pattern in through our big telescopes here on Earth.

Yep. So to understand this we have to go from the ray picture of a telescope to a wave picture. So here's a ray picture of how a telescope works.

You get the light coming in here, the rays. They bounce off the primary mirror (And they're coming in from infinity so they're parallel) Yes.

They hit the surface of our mirror.

Yep.

And then they're focussed on the secondary mirror.

Not quite focussed, but they're directed there.

And then that secondary mirror curves them and puts them down through the hole in the back of our telescope, and so this is what we call a cassegrain telescope, so that we can have our imager here and take a picture.

Yes.

Now let's think of it from a wave point of view.

We've at once got these infinite parallel waves coming in, and some of them enter the telescope and some just miss. And they come down here and they hit the primary mirror and the primary mirror is shaped so that the path for every wave coming from infinity should bring it in phase to the focal plane at the same place. So the outer parts have further to travel so they get intercepted first. So you get a series of more circular waves coming down to the secondary, and that turns into curving slightly the other way they come down here and come perfectly into focus. (Ok) So if all is well it should turn a perfectly plain parallel wave here into...

...into a perfectly plain parallel wave again. All focussed and brought to a... every point from here to here should have exactly the same path length to add up to exactly one point over there.

Yep.

That's the principle.

What does atmospheric seeing do? Well if it's cold air, the higher refractive index slows light down.

Right.

Relative to the speed in normal temperature air. So that means the wavefronts are going to be lagging behind here. Whereas hot air, the air will go a bit faster than on average, and so it will move forward. So you've now got a distorted wavefront coming into the telescope, and so we add that all up in phase, it'll give you... if Brian steps over a bit, you get a sort of pattern like this that we talked about before (it gives us a mess, is what it gives us) A mess. Yes, speaking technically.

So what can we do? Well, here's a movie from Gemini showing the concept of adaptive optics how you correct this. So you get the light coming in off the primary up to the secondary and down through here and on the back of the telescope you have the instrument support structure which can rotate to cancel out the movement of the sky as seen from the telescope, and one arm of that is the adaptive optics system. It's called ALTAIR on Gemini.

So again the light coming in from the top...

So the light enters our instrument through the telescope, it comes through the hole in the back of the mirror (Here comes the light) and it's brought into this instrument.

It bounces off a mirror, and this is a dichroic. We talked about them a bit before.

This sends the infrared light this way where it gives us an image, a rather blurry image because of the atmospheric seeing, whereas the blue light goes over there.

So that could be transferred here, and so that light here is... we could look at it in detail.

So here come the wavefronts, and as you can see they're distorted because of atmospheric seeing. So they're not flat pancakes... this is the march of the pancakes, and they're pretty horrible looking pancakes. What we have down here is a wavefront sensor that measures the exact distortion, and then makes this mirror bend an equal opposite way.

Ah. So now, the pancakes are flattened and we can make sure we keep on keeping those pancakes flattened, so when those nice wavefronts which are all lined up hit our detector our star doesn't look blurry, it looks like that wonderful pattern.

Of course you have to change the shape of this mirror hundreds of times a second because the atmosphere is always moving, and that's one of the big challenges of this.

You have to be able to measure with exquisite precision the distortions and measure it a hundred times a second.

And so that means that you can't just do this on some faint galaxy.

You're going to have a lot of information in the form of a lot of light to actually see what the atmosphere is doing. When trying to directly image exoplanets you're normally lucky, because you typically have a very bright star right there, next to your planet. But in general it's a problem because what you need is a bright star nearby, just so much like that even after you've diced it up in all the different ways, you can still measure the distortion with great precision.

So what a number of telescopes now do is actually create an artificial bright star just where they want it. And the way they do this is what's called a Laser Guide Star System and once again here's the example at Gemini North.

So there's the laser bolted onto the side of the telescope.

And this is a sodium laser, and a sodium laser is kind of interesting because our atmosphere has sodium in it. It has a little layer way up in the sky that has sodium atoms in it, and you can excite those atoms and literally make a beacon in the sky with this system.

Yes, we'll see that here. So the light goes up, so it's transferred to the top of the telescope and then bounced off into the sky from the top.

You'll see that in a second, here.

So we point up to the sky... (There we go, as the light goes up) We take a laser beam, and it goes very dramatically into space.

And it comes up 50 kilometres, 70 kilometres... and we now hit a sodium layer. This is actually deposited by meteorites primarily. You get meteorites and meteorite dust that lands in the upper atmosphere and they deposit this layer of sodium. Its altitude varies but maybe about 90 kilometres up, and we look at that from the ground, so we change our orientation it looks like a glowing orange dot. This is the same colour as sodium street lights, low pressure sodium street lights. And that's giving us a bright artificial star exactly where we want.

So as the light comes back down through the atmosphere and back down to our telescope we can get the light coming in and we can also look at that sodium artificial star and use that to measure the distortion and correct for it.

Kind of interesting. It gets twice the effect, it goes up and down. So it sort of magnifies the effect and presumably that has to be corrected for but can make it a bit easier to figure out what's going on with the atmosphere.

So you get the dual of the lightsabers here at Mauna Kea you can see the laser coming from Gemini and also from the cape(?) telescopes in the background.

100 And presumably it's curved, not... only because of the optics of our picture that we're taking.

Yeah, I think this was taken with a fish-eye lens. It's quite difficult to operate these things.

They have to be absolutely clear that there are no aircraft around. So they have lots of students up there whose job it is to look at one quarter of the sky and have a big red button to say "turn it off now, there's an aeroplane coming over!" They also have to notify US space command ahead of time.

We're going to look at these targets at these times...

please tell us if we shouldn't.

We wouldn't want to blind a downward looking device. So that's adaptive optics.

V7.7 There's a large amount of research in adaptive optics here at ANU, and it's a great pleasure to welcome Céline D'Orgeville and Francois Rigaut who are some of our local experts.

Céline works on the lasers that are used in adaptive optics, and Francois works on the adaptive optic systems themselves.

So Francois, you are, I guess despite your young age one of the grandfathers of the field of adaptive optics.

From my memory, you were part of the first program to put adaptive optics on a telescope which we are allowed to know about.

I believe there were ones that the military did before, but what was it like working back in 1989 on that first system? Oh, it was very very exciting.

I was actually lucky enough to do my PhD, and it was the beginning of the second PhD ever on adaptive optics for astronomy so, on the first adaptive optics system for astronomy, ever. So it started in 1989, it was in Europe in France actually.

At the time we also had a collaboration with ESO, and at the time we didn't know if it was going to work of course. So we assembled everything in the lab, and then we went to the telescope in Haute- Provence in the south of France at the 1.5 metre. And then we turn the system on and it was working and we could use it, you know. The image size from maybe typically one arcsecond or one point five arcseconds, down to like point four, which was the diffraction minutes.

So how were those systems different than the ones we use today? They were much simpler. They were the same if you want... essentially it's the same, and in this system what you do is that you analyse the deformation of light, then you correct it with some kind of device.

But nowadays the systems are like a hundred times more potent. Because there are many more of these little actuators that you use to correct the light, and they will also install on telescopes that are typically eight to ten metres instead of the one point five metre at the time.

So back in 1989, did you have powerful lasers to make your own little beacons (No) or did you just use stars? Yes, exactly. At the very beginning we used stars because it was already, you know... wonderful. And then quickly we realised that even though the technique was very powerful, it was out of our limits in its capabilities. Just because you needed such a bright star to analyse the waveforms. So in 1985 actually the first civilians, ah, astronomers actually a researcher, came up with the concept of shooting your own laser to actually create an artificial guide star in the upper atmosphere at about a hundred kilometres. And since then people have been working on integrating these lasers with adaptive optic systems to make them all encompassing if you want. We can now find them everywhere, and get nice images.

So you can put a star anywhere in the sky and that's a huge advantage we have (exactly) nowadays.

Yep, so Céline, the lasers are often the technically hardest part of the thing to get right. At least they seem to be broken most of the time and every time I hear a telescope bulletin saying "delay" it's usually because of the lasers rather than anything else. What are the challenges? Why is it so hard to get a laser to make a star like this? Well, to get started there isn't that many people interested in producing powerful lasers at that kind of wavelength.

If we're talking five eighty nine nanometre, that's the sodium line, it's bright orange and we want typically ten watt per... laser guide stars. So one is a guide star watt five as a guide star is fifty watt... this kind of laser power you don't get off the shelf.

Actually there's no... there was a company until maybe two years ago that could deliver such a system.

So I guess most lasers are used for fibre optic communications and they work in the infrared, not at these wavelengths.

Well there's lasers working all over the spectrum from the UV to the infrared really, but at this particular wavelength typically it's been used for spectroscopy experiments in the lab and they use just a few milliwatts for that.

So, for astronomy we need, you know, watts. And tens of watts.

(Yeah, so ten watts is a really big laser) It's a pretty powerful laser that one, and so you have to develop technology to get there, and there's been several generations of sodium lasers. So the first lasers were liquid lasers, they used liquid dye as the laser medium, and they've done a good job but you know, they were cumbersome to use and a bit unsafe in that they run with alcohol and so there was a flammable issue with those.

So eventually people went to solid state types of lasers, and that's what... for instance, runs on the Gemini North and Gemini South telescopes in Hawaii and Chile. And the next generation ones are going to be fibre lasers.

So, the technology is definitely improving.

I would say at this point, the lasers run well.

We know how to operate them, they're not the issue. The problem is with the logistics of propagating a powerful laser beam into the sky. So typically you have to deal with aircraft going over the observatory and you don't want to hit those. So you need some sort of, either spotters watching the night sky, or some automated system based on cameras to make sure that you're going to terminate the beam propagation when an aircraft is flying over.

That means turn them off when any aircraft's coming over, yes? Yeah, you just close the shutter (I see, ok) and you know, shutter the beam. But the rest of the system is still operating normally.

Yep.

The other thing you have to take care of at least for observatories that have the US as a partner, is to make sure that they're not going to fire the laser into a satellite and damage it. So they have to work with US space command to get, you know approval to propagate the laser at any given time.

And they don't just tell you "here are the orbits of satellites to avoid" you have to tell them where you're going to look basically, to say yes or no.

Exactly you can't know where the satellite is, because it's usually NSA they don't really want to reveal. But you send them the list of what you want to observe through the night, and they send you a list back saying "Ok from that time to that time, you can't propagate." V7.8 Ok, so Céline, what are you working on here at the moment? So this is an adaptive optics experiment.

It's not meant to be used for astronomy, but it's going to be used for another project dealing with space debris tracking and de-orbiting.

So we're actually going to use lasers to get rid of space debris? Yes, they use a powerful infrared laser that they shine at debris and they do imaging and they can determine based on the time of flight of the light to the debris and back, what's the orbit and its actual location.

Now the key part of any adaptive optics system is a deformable mirror.

I believe this is your deformable mirror here.

(Yes) How does this work? So this mirror deforms in real time. It's got some actuators in the back that can push and pull and deform the front surface here and it runs about a kilohertz. So a thousand times a second, you'd change the shape of the mirror.

So the other crucial part of an adaptive optic system is a wavefront sensor. You have to know what the distortion of the waves are before you can correct them. Where's that? So this is this camera here. It's a very powerful camera that can detect single photons and it's got a lenslet array right here in front of it and that's where you actually do the image analysis.

So what's a lenslet array? It's a tiny piece of optic that is like an array of miniature lenses.

One adjacent to the other and you can analyse what the shape of the waveform is based on that.

Right. Thankyou.

So, Francois and Céline... you guys helped developed what is the most advanced adaptive optics system in the world right now which is the GeMS system which uses five lasers at a time. Maybe you can explain a little bit how that works. And Francois, why don't you start out about the adaptive optics and then you can tell us about the lasers.

Yes, well one of the limitations of classical adaptive optics is that it corrects for the atmosphere aberration but in one direction.

So if you look away from this direction, if you move off, it's going to be a little bit more blurry.

So that's clearly a limitation because people, you know, are interested in imaging and correcting the whole... the largest field possible. So there is this new technique that appeared at the end of the 1990s, that is basically using tomography techniques like when you're imaging the brain, for instance.

So you are taking information from different angles and then from this information which is 2D information, two dimensional information because it's taken from different angles you can actually restore the 3D contents of your information.

And therefore, if you have three dimensional information about the atmospheric turbulence you can also correct it in a 3D fashion and therefore you correct it in any direction. So what it does is that effectively it enlarges the field which is accessible with the adaptive optics improving its quality.

Ok. And that instrument is now working, I believe.

Yes, it’s been very very challenging because as you say it has five lasers it has three deformable mirrors and five waveform sensors.

So there's physically classical adaptive optics, multiplied by five and the complexity also went up with maybe not by a factor of five, but at least a factor of two or three. So, it's a very complex system.

And it took some time and effort to make it work, but eventually it was working, and delivering, you know, very very nice results.

And Céline, that laser system... I remember seeing, trying to get the laser system there. But once you get the laser system working in California, how do you get it working on top of a telescope in the middle of Chile, night after night? And how does it work, in detail? Well, you need to have a team to support operations, so typically there is a dedicated laser engineer who is in charge of making sure everything's going to run smoothly, and he works with two laser technicians so that before a laser run, typically it runs our schedule in periods of, say, seven to ten nights in a row. So before the laser run, they'll start the laser realign it if it doesn't perform as well as it should, and then during the run they're going to be there operating the laser system and making sure, you know, everything goes smoothly.

Ok. I'd like to finish off by asking, where do you think the future of adaptive optics is going to go? What's going to happen in the next few years? Is it going to get drastically better, or are we already close to the limits? Oh, no no. There's still room for improvement.

One of the next very very interesting adaptive optics systems that's coming online is actually a GPI, which is coming online in a few weeks at Gemini South, so at the same telescope as MCAO installed right now. And GPI is an adaptive optics of a different kind. Instead of correcting a wide field well, it does an extremely narrow field, but extremely well. So it means that there will be, it will correct 99% of the atmospheric turbulence, leaving only a very very small residual. And this is for planet detection. GPI stands for .

A lot of people are actually extremely anxious and impatient to see what this system is going to deliver.

So we'll know in a few weeks.

Great. Thank you very much.

You're welcome.

(Thankyou)

V7.9 So Paul, this is absolutely amazing. It's like something out of Star Wars.

You go through, you have these huge telescopes, and then you put these little contact lenses in the forms of a mirror, which you vibrate around at fifteen hundred times a second. To go through and take the ripples out of the atmosphere, to make stars go from twinkling masses and blobs to being sharp as pins. I mean honestly, 20 years ago when I was student, I remember people talking about this and I was like "that's crazy, and it's never going to happen." It's now got applications outside of astronomy. In fact originally a lot of it came out of military research.

If you remember the... talking about Star Wars, there was the Star Wars program back in Ronald Raegan's time which was supposed to use lasers to shoot down incoming ballistic missiles. The trouble with that is, you're trying to fire a laser up through the atmosphere to hit a missile, which means you're pumping your kilowatts or megawatts of power through the atmosphere, and the atmosphere of course has dust grains and things which will get hot from the laser beam going through it. So you get a nice column of extremely hot air just where you're looking, and of course hot air has a lower refractive index and acts as a diverging lens. (Ah) So the missle comes in and you focus your powerful laser at it but instead of getting a missile melted, you get it slightly warmed up by a defocussed lens.

So they did a lot of the early research.

They had to be able to bend their mirrors to counteract that, and then it was declassified.

I was actually at one of the talks when it was first declassified, and astronomers have now used it. But it's now getting applications elsewhere.

Just last week a former student of mine who did this class about adaptive optics in astronomy, and is now doing research on using it for medical imaging.

The idea being to actually look inside cells in the body or through tissues, and of course the tissues are all different refractive indices, but you can once again bend your mirror to cancel that out, and get sharp images looking inside cells and through body tissues.

So once again, you know, the little things we do here in astronomy to push the boundaries end up being useful. So that's a good story.

But you know, it's not a complete panacea.

We do have some issues where we can't use this under all circumstances.

Yes, I guess one big issue is at the moment we can only make this work at infrared wavelengths not at visible wavelengths. The trouble is that... well the benefit of infrared is that hot and cold air has only a very small amount of difference in a refractive index at these wavelengths.

So you're not trying to create very big effects.

And also the changes are relatively slow only a hundred times a second or so. Whereas if you want to work at visible light wavelengths you're looking for much bigger shifts. You have to boot move the mirror by far more and it has to be much faster, thousands of times a second.

At the moment we can't do it at optical wavelengths.

Right, so it's not impossible to do it but it's a little, it's technologically beyond the scope of what we can do right now.

And don't we have a problem that the atmosphere unfortunately the little puddles of turbulence in the atmosphere are like that big, and our telescopes are that big, and so we can only, that means correct a tiny little piece of sky? Yes, of course we're looking through one part of the sky at our target, and we can correct what's happening there. But let's say we wanted to take a picture of a big part of the sky. Light going to a different angle will be looking through different parts of the atmosphere. And so it's really hard to correct... you can correct near our guide star on a laser, but trying to correct somewhere else... so we tend to get a very sharp image of a very small part of the sky. That's fine for looking for new planets, but if for example you wanted to map galaxies with this, it's such a small part we can't even map a whole galaxy.

But here at Mount Stromlo where they built an imager for the Gemini telescope which has five lasers, and I know the whole point of that system is so that we can look at a much bigger field of view. So even technology can help that out as well.

Yes, so the idea is by bouncing five lasers up, you can actually have a three dimensional map of the atmosphere not just the one long line of sight, but a whole bunch and actually see when these blobs are there moving back and forth across it.

So it's called multiple conjugate adaptive optics, a bit of a mouthful.

But it's now working and getting some spectacular results over wide fields.

And I've seen some of the images that we're using. They're getting to essentially, I think, 90% of the way of what's theoretically possible where you have quantum wave effects, which end up limiting you. So we're really close to really getting all the way there, this way.

Yes. I mean another traditional problem with adaptive optics is you've got the light spread out, and you want to gather it altogether, and most adaptive optic systems gather some of the light together, but leave us a halo of light that's very spread out.

So what's called the Strehl ratio, it's telling you what fraction of the light is gathered in the middle and what fraction is further out. And to do better at this you need to deformable mirrors with more actuators. The early ones might only have a few actuators so they could take out the big blobs of hot and cold air but they can't take out the small ones.

But they're getting better and better all the time. They're now talking about ones that have millions of actuators, so they can really start taking out all the really fine variations in the atmosphere. The trouble with this is, to be able to take them out you have to be able to measure them.

Right.

So you need to be able to measure say two thousand, three thousand components of distortion, and for that you need a really bright star.

Or a really bright laser, presumably.

So the other thing they're doing is getting more and more powerful lasers.

So they can just pump so much light out there, that when it comes down they can measure the really fine details of the distortion.

Right. Ok, and I've seen some of the new deformable mirrors aren't little ones in the lab. They're these giant ones which are actually the secondary mirror of the telescope itself. I mean, they're this big and they're huge and tiny little wafer thin pieces of glass with all these little magnets behind them, and that go at fifteen hundred times a second.

A truly remarkable piece of equipment. And advancing very fast. (Yep) But I guess the real question is, can we see anything with these things? So what we're going to talk about next time is what have we learned so far from all these adaptive optic systems? Can we actually directly see planets around other stars?

V8.1 So, we've got these fantastic new toys; Giant, ground-based telescopes with Adaptive Optics Systems, that allow you to de-blur the atmosphere.

Now surely the time has come to directly image Exoplanets. We can actually see these things at last, rather than inferring their presence in these indirect ways.

- So Paul, why don't you show us what one of these curves looks like for an Adaptive Optics System. So, what we're plotting here is; you look at a star and you plot how bright a planet you could see or essentially how much fainter than the star you could see, as a function of separation. And so we plotted these things in the lovely units of Hipparcos, called magnitudes. And essentially a magnitude is that when you have 5 magnitudes you have a factor of 100. Ten magnitudes, a factor of 100 times 100, or 10,000, and so on. So, it's a logarithmic scale. So, I note here that we're sort of 'bottoming out' at about a factor of... that's 100... so, a factor of a couple hundred, 300 and-- so, you're saying we can see things at this separation. So, that's half an arc second and that's one arc second.

So, when something is half an arc second away, we can only see it if it's no more than maybe two or three hundred times fainter than the star.

- Right, and we know we need to do a lot better than that. We're talking: we need factors of a billion or something, right? So, we're not even close yet.

- Yeah, in fact we'd even have trouble seeing the candle and the high headlights. Of course, they're much further than a half an arc second apart from each other, but the contrast ratio will give them trouble. So, are we stuck here? Well, it's clearly time to start cheating, I think. So, one way we can cheat would be to look at the infrared. The normal calculation is you get a star and it's emitting visible light that comes out and reflects off the planet and bounces to us. But, in infrared, if a planet is glowing by itself because the planet is hot, then the star won't be emitting very much light and the planet will be emitting quite a lot... we talked about this before... and that might give us a bit of an edge.

- So, we just have to choose hot planets.

Now, planets in our own solar system are...

I wouldn't call them hot... so, we'll have to think a bit about that. I mean, here's Saturn. And it is glowing. It is warm inside due to when it was born it had all that heat.

And it is still glowing. And I guess we can... maybe we should go and figure out exactly how that process occurs.

- Yeah so, the idea is... as you can see this infrared, these things are glowing a little bit, these giant curves and that's because of left over heat from formation. So, let's see how hot we'd expect these things to be when they're newly formed.

V8.2 Okay. So, how hot are young planets? Well, the basic idea is you're forming a planet.

So, a little bit of it’s formed and then you get more matter falling in from infinity.

And because it's falling in from infinity, the gravity makes it go faster and faster until it hits the middle where all it's kinetic energy is turned into heat.

And then, so, you know you've got a slightly bigger planet in the middle then even more matter falls in and gets faster and faster; ends up making the planet a little bit bigger and dumping yet more heat.

Now, if each individual lump that comes in we can work out how much energy it has once it reaches the surface from potential energy.

Let's say it starts at infinity The potential energy of the surface is G, mass of whatever's in the middle, mass of the lump that's falling in over r, where r is the radius at that time.

So, in principal what we could do is just go through with this.

So, steadily add bit by bit and for each bit we work out this.

As each bit is added, the r gets bigger, so the energy per lump goes down, but also the M gets bigger, so the energy per unit mass goes up.

In fact, that's the biggest effect because mass is proportional to r cubed.

So, generally speaking; the last lumps come and dump more energy than the early ones.

To do this properly you would therefore actually integrate.

You would take this equation and sum it over all the lumps coming in and gradually build it up.

However, for today’s purpose we are just going to estimate the value roughly to within an order of a magnitude or so.

And the way we are going to do that is assume that half the mass of the gas giant magically appears there by itself and then we drop the other half in from infinity and we can work out how much energy half falling on to half would do.

So, what is that energy? Well, that is going to be this energy here.

So, the potential energy is going to be: gravitational constant, the mass of the lump in the middle, which is half the final mass times the in falling mass, another half the final mass all over, let's say bring it into the radius of the final planet.

It'll actually be a bit less than that.

So, this is an underestimate of how much energy you're going to get.

So, that equals G m squared over 4 r.

Now if we substitute in the mass of jupiter, which is 2 times 10 to the 27 kilograms, gravitational constant 6.67 times 10 to the minus 11, and we substitute in the radius of jupiter, which is 7 times 10 to the 7 metres.

We end up with an energy of about 10 to the 36 joules. Probably an underestimate as we said. So, it's probably a little bigger, but it gives us the rough magnitude.

Now, that's a big number, but of course Astronomy is full of big numbers.

How can we estimate whether that's going to make things hot enough? Is that enough to make something the mass of jupiter hot? Well, we said the mass of jupiter is 2 by 10 to the 27 kilograms.

How much energy does it need to increase something of that mass by 1 degree? We have to multiply that by the specific heat capacity, which is exactly the number of joules you need to raise 1 kilogram by a degree.

I don't actually know what the exact heat capacity of Jupiter is.

Jupiter's mostly made of Hydrogen, Helium, and ice and things like that.

But let's say it's approximately that of water. So, about 4000 joules per kelvin per kilogram.

Now that's probably too high. Most substances, the gases, actually have lower specific heat capacities.

Water's one of the highest specific heat capacities around.

But that'll do roughly, because in order to get an approximate calculation we need to get a rough order of magnitude.

So, the energy needed to change the temperature by one degree is 4000 times that, so, a thousand 10 to the 3, everything 10 to the 30, 2 times 4, so it's about roughly 10 to the 31 joules to raise the temperature by one kelvin.

So, this means, if we compare it with this, that we have enough energy to raise everything by 10 to the 36 over 10 to the 31 by about 10 to the 5 degrees.

So, even if you started at absolute zero, it's going be 100,000 degrees by the time we'd finished.

So, oodles of energy. Plenty of energy by any estimation to make a planet very very hot.

It won't get that hot, because as the stuff is falling in, a lot of the heat will be radiated away.

But, there's clearly plenty of heat to go round and you'd expect new born giant planets to be extremely hot.

V8.3 Ok. So a young planet is very hot. But how long does it stay hot? Even if it only stays hot for a few minutes, we're not going to see any planets in that form.

It has to stay hotter for a fair while for us to have any realistic hope of seeing them while they're still hot.

So let's imagine we've got something with the mass of Jupiter, and by the time it's settled down and formed it's at a temperature of about a thousand Kelvin.

That's cooler than the a hundred thousand we calculated in the last video, but a lot of that heat would we dissipated during formation, so a thousand might be a not totally unreasonable guess to what it is once it's actually settled down to look like a planet. Probably a bit of an underestimate, but anyway. How long is it going to take it to cool down? Well it's got to cool down by radiating. There's no other way it can get rid of energy, really.

We know the radiation is given by the Stefan-Boltzmann equation, A sigma T to the fourth to the power radiated. Where A is a surface area, sigma is the Stefan-Boltzmann constant and T is the temperature. Now once again it's going to be a rather complicated system.

If you look at the temperature against time, to begin with it's going to be very hot a thousand degrees. That means this is going to be very large, it's losing energy at a fast rate so the temperature will start dropping rapidly. But as it gets cooler, T gets less so the rate at which water goes away decreases, and it'll slow down something like that.

But let's just assume that it cools down steadily to its initial rate, and we can estimate how long it will take to get rid of the energy that we calculated that we'd have to begin with.

So it had about, energy of about 10 to the 36 joules. How long will it take to get rid of that if it's at a temperature of a thousand Kelvin? So all we simply do is take this energy and divide it by A sigma T to the fourth, A is four Pi r squared.

Once again we'll assume that our planet is Jupiter-like as an exemplar of a big planet. So we'll put in the radius of Jupiter here, multiplied by sigma, and T to the fourth, and it turns out we get a time of about three by 10 to the 14 seconds. That's because the A sigma T to the fourth comes out as about three by 10 to the 21 watts, and divide this by that and you get about three by 10 to the 14, roughly speaking. Once again a meaninglessly big number but we can convert that into something that makes more sense like years. So divide by 60 to get seconds to minutes, divide by another 60 to get to hours, divide by 24 to get to days, divide by 365 to get to years, and that comes out as about 10 million years.

So this is telling us that the planet will stay hot for several million years, and we've made lots of approximations here so, like assuming it started at a thousand whereas it probably started hotter than that.

But roughly speaking we're talking tens of millions of years. Much less than the four billion years than our own sun is old. So it's telling us that most of the heat that was originally in Jupiter is gone, but certainly not in a few seconds. So quite long enough for us to have a reasonable chance of finding glowing planets if we look around stars that have only just formed.

V8.4 Alright Paul, you've convinced me. Saturn must've been hot when it was young.

And so I can see a way of cheating here. We could look in the infrared at stars that are young.

So around the youngest stars they will have young planets, and so their planets will be hot still they would've faded and cooled like our planets. And then we can do one other obvious thing, which is, why pick intrinsically bright stars? Let's pick the faintest stars intrinsically so that we maximise our chance of seeing one of these young bright planets.

Yes, so this is how we'll cheat, and indeed this is how the first direct imaging happened back in 2004. We're looking actually at brown dwarf stars, a star which is so low mass it doesn't even have nuclear fusion in the middle. It itself is just cooling down like a very big planet.

And we observe in the infrared, and here we see something near it, point 8 arcseconds away that's 55 astronomical units away. So that's actually considerably further out than Pluto is from the sun in our own solar system.

This thing, from its brightness and its age, is probably about five times the mass of Jupiter. So this is a big object.

Yep.

And it's very young which is why we can see it. But the star itself is actually not that much bigger.

This is only 25 times the mass of Jupiter.

So that's almost not a star itself. So, I mean to me, we're getting into semantics about what's a star and what's a planet.

I lost a vote on what planets were a few years ago, because Pluto was demoted against my wishes.

But to me, I always think of a star as being something that fuses nuclear, you know, like deuterium in its core. But this star, it's not even clear it did that. So, I think maybe I can accept that that's a planet.

So it could be a binary planet. Some people would say that the boundary is nuclear fusion, in which case brown dwarfs are big planets.

Some people would say that the boundary is 13 Jupiter masses. I don't know why, but that's often bandied about in literature, 13 is the boundary.

But that seems completely arbitrary to me.

Some people have said that it's something to do with formation. If something forms like a star does from the collapse of a giant molecular cloud, it's a star.

If it forms in a disk around a star, then it's a planet. (Ok) So what's the case? In this case, this is almost like a binary planet or a binary star or something.

They probably... there's no way this could have formed by a disk, it's just too massive.

There's only a ratio of five in mass here whereas Jupiter is a thousand times less massive than the sun.

So it sort of begs the question of whether or not we might have lots of objects like that and maybe these things don't even need one of these to form if they really are that star form. (That's the ultimate way of cheating) And we want the star to be as faint as possible, how about not there at all? That's pretty faint. I wonder if we can see any of these things floating by themselves? And to do this we're going to need an infrared survey telescope.

Finding objects like these was one of the prime goals of NASA's recent mission the Wide-Field Infrared Survey Explorer.

This movie from NASA explains what it found.

Astronomers are interested not only in the bright stars in our neighbourhood which are easily seen here around the sun but also the small dim objects we can't readily see. Finding these is one of the prime objectives of NASA's Wide-Field Infrared Survey Explorer, or WISE.

As we move further away from the sun we focus only on our neighbours within 26 light years.

Within that volume, we increase the brightness of the faintest reddest stars to make them more easily visible.

These objects, known as M-dwarfs, are the most common type of star in the solar neighbourhood.

Now, viewing from a distance of 30 light years, we circle all of the known brown dwarfs faint objects with too little mass to shine stably as stars do.

The blue circles show all the previously known brown dwarfs while the red circles show the ones that WISE has identified for the very first time.

This updated census of our solar neighbourhood now shows that brown dwarfs are much rarer than stars there being roughly six stars for every known brown dwarf.

So WISE has found a large number of these.

Some of these brown dwarfs are very, very cool and they're what we call Y-dwarfs. Here's how you spot these things.

This is an image of the same part of the sky at a bunch of different wavelengths, starting in the optical and going out into the infrared observed by WISE. And what you see from one of these things is nothing, nothing, nothing, nothing, boomp!, nothing.

Ok, so the idea is that these are in the infrared and there's water and methane out there which tends to block all the light coming out at certain spots, like here and here. And so all the light is able to leak out through this one little window (that's one way of looking at it) where there isn't this stuff. This window, a wavelength. And then out here they're simply so cool they don't put out any energy at all in the optical and... the infrared.

Yes, we're talking of temperatures of only between like 300 and 500 Kelvin.

That's still hotter than Jupiter, but comparable to the Earth and masses of between say five and twenty times the mass of Jupiter.

Ok. So these objects are sort of, they're big objects. They're almost like planets but they're not exactly the same as the free-floating planets we seem to have found through microlensing.

Those are a fair bit smaller than these.

Yes, and also less common. These are far less common than stars whereas the microlensing planets, there's like one point eight of them per star.

So maybe these are the top of the population.

You've got lots of small things which we can't see with direct imaging, but we can see with microlensing, and a few of these big things.

Or maybe they form quite differently, maybe the free-floating planets are expelled planets and these form like small stars.

And these are pretty common, right? The nearest ones are as close as 10 light years in distance. (There's one within 10 light years of us) Although that's common, it makes them a fair bit less frequent than stars. There's many more stars than one, within 10 light years, beyond our own sun. And those free-floating planets are supposed to be as common as stars themselves. So maybe we are just missing something and there are whole parts of space full of these free-floating planets, we just can't see them.

Yes. So by our cheating techniques, looking at the infrared, we are picking up large numbers of either free-floating or binary things, that whether you call them planets or whether you call them small stars is a bit of a grey area. I mean we couldn't live on them, they're much bigger than Jupiter, but they might be quite spectacular things to look at.

What we'd really like to know is, are there or can there be imaged things that look more like normal planets.

V8.5 - So if we want to see more normal planets rather than cheating we're going to need to do better. At the moment we're only finding contrasts of a few hundred anything more than that and we lost it in the glare of the star and that really doesn't seem very good I mean we could probably do better than that with a normal camera, surely our telescopes can do better so what's limiting us why can'y we do better than...why can't we see anything that's fainter than two or three hundred times fainter the star? - Well let's look up close and personal around a star that you might see and so, this is, a picture that one of these giant telescopes would look at when you block out the central star and you see all this junk shining around and that junk is actually sort of the dust and stuff the imperfections of the telescope itself.

And so the problem is that a telescope just isn't sitting there in a vacuum in a place that's not changing, it has to move and follow the sky, the temperature changes, it bends and warps a little bit so this pattern changes over time. If it was fixed we could just see what it is and remove it. But it's changing and it changes fast enough that it's very hard to get, you know, a real fix on so it always kind of leaves you with this contrast of a few hundred where you're stuck with.

- So, people were thinking how can we deal with this and they came up with a cunning technique called Angular Differential Imaging.

Here's the basic idea, as modern telescopes are built like gun sights here's a time-lapse of the Gemini telescope inside it's dome and you can see it's moving around and up and down. Now as you track something across the sky like it's doing here let's say something's rising over there...as it goes across the sky it might move something like this but our telescope isn't, our telescope is always upright. So here's the upright of our telescope and here's the thing what it appears as it moves across the sky is the object rotates with the respect to our telescope.

Now, all these aberrations, these distortion patterns are due to the telescope and so they won't rotate. They'll just stay fixed in the frame of the telescope. But where the planet is with respect to the star will rotate and you can calculate precisely how it will do.

So what you can do is take a whole bunch of images as something moves around the sky and then rotate them, so that if the planet is there it should always be in the same place. But that means all the aberrations will not be in the same place there'll be different angles and they will largely cancel out.

And so you should be able to get a nice clean image only of things that are rotating with the sky and not rotating with the telescope.

- So it can average out over some of these things in a clever way.

- Yeah, and here's the difference it makes, here's the image we saw before and here's one using this angular averaging technique.

You can see it's done a lot better.

- So it's done much much better, yes.

- So we've not got rid of everything but we've gotten ridden of a lot of the stuff.

- And this is tried and in 2008 they hit paydirt.

They were looking at the star HD8799 this is kind of the opposite of the star we've been talking about so far, instead of looking around a really faint little red dwarf this is actually an A star, a massive, luminous star but despite the incredible brightness of the star you can see the pattern here but you can also see faint dots marked A B and C.. Not A,B and C...B, C and D, don't know what happened to A, off to the side and this seemed to be planets.

- Wow so there's...this object has four planets? - Well they found three here and they went back and re-observed, in another paper a year later and found another one a bit closer in.

- OK WOW! - Now these planets are pretty bright, to be this bright given how old the star is would mean they'd have to be somewhere between maybe five and fifteen Jupiter masses so these are still very big, just below brown dwarf planets.

They had to be sure they actually were planets orbiting here and not some sort of background object the way they worked that out is of course the Sun is moving and these stars are moving and so our point of view on the star is constantly moving so the star would appear to move across the sky what's called a promotion and if the planets in orbit around it were actually moving with it you won't see them do their orbits over that year or so but they will be moving along with the star.

- They should have the same speed as the star and not be stuck with the background stars.

- But if they're background stars much further away the stars should move and leave them behind .

So they had to go back and re-observe years later to see these things are all moving together and it seems they actually are and they've been seen by multiple people so it looks like these things really are planets.

The closest in is fourteen point five astronomical units out which is a little bit further out than Saturn is in our own solar system they're the ones going considerably further out. So we are looking at something that we haven't been able to see before, really massive things a long way out.

- A good beginning.

- It is. And if you remember we talked about debris discs this star has a debris disc around it and it's one of those debris discs which...in a gap, an inner gap which is just outside where the planets are. - So these planets have gone in and cleared out the inner part of the debris disc, - And they could be responsible for stirring up the big lumps of rock further out that make them crash into each other to produce this debris disc. So that all seem sto work very nicely.

Also the stars are of a curious class which is very low in some elements that form solid grains, it's got heavy elements that don't form solid grains like gasses but things like iron, silicon that form rocks it's very low on.

So it could be that all these heavy elements got stuck in the extrusion disc and turned into these massive planets instead of feeding into the star.

- Alright so then this would be under that account maybe this star is a little unusual because the star is missing some of these key elements that are in most stars and that would be maybe a signature to go out and look for other stars that might have such planets.

- That's Right. And it gets rid of the holy grail because we can actually measure the spectrum...kind of...of this planets and this is one of them I forget which and these circles are the data points and the lines are models, we'll talk about that in a second and what you can see is an optical wavelength that's not emitting very much and it climbs up to the infra red then it goes down and then it goes up then it goes down.

- So it's not much of a spectrum it's really a bunch of data points rather than a true spectrum.

- True, but that's still a lot more than we've had for any other extrasolar planet we have a whole bunch of points at different infra red wavelengths and the fact that it's going up and going down is probably telling us something about what's going on in the atmosphere.

So what we need to do is compare these sort of data with a model of the atmosphere of one of these planets so that's what we're going to talk about next.

V8.6 - So, we need to be able to model a and model its atmosphere so we can see what it's going to appear when we look at it from Earth so Paul, what are the steps that we need to do to do that? - Well, we're going to have to start off by working out what the planet is made out of.

So we could just guess it's the same as Jupiter or we could look at the composition of the star that it orbits around assume it's going to be the same as that only with probably a bit less hydrogen and helium that didn't get trapped or something like that.

- And we can change that around, obviously start with what a planet looks like in our solar system and change it accordingly.

- We know very accurately what Jupiter is made of because the Galileo's dropped a probe into it and actually measured it in situ.

These thing will probably be different but not too different so that bit's fairly easy, at least until we get some hideous surprise.

- And then we have to think about how the gas is situated around the star, so Paul, if I have a cubic metre of gas here in this room - Which we do - And then we ask ourselves that cubic meter of gas weighs roughly, a kilogram. Why doesn't it fall to the ground like if I was holding a ball and I dropped that? - here's something else that weighs a kilogram - So that's a kilogram, that, when I drop, falls and the gas in this room that weighs the same amount doesn't. Maybe you can explain that? - yeah I mean, because gas, air weighs a lot so why isn't it falling down? Well there must be downward gravitational force on the gas there must some equal and opposite force upwards to keep it balanced and stop it falling down.

Now we have air pressure, there's air pressure at the bottom and there's air pressure at the sides and air pressure at the top you might think that would all cancel out. But if it did cancel out it would all fall to the bottom.

- Right, because gravity would pull it down - yeah so there has to be more pressure at the bottom of this cube than at the top. And indeed that's what's happened the air is thicker, lower and as you go higher, you don't notice it in this room but if you climb a mountain you'll notice it very much but even in this room the air at the top is going to be a bit lower pressure than the air at the bottom.

So it's higher pressure air at the bottom gives more upward force than the downward force at the top and that's what keeps this air from falling to the ground.

- OK.

- And so exactly the same thing happens in a planet. So let's say we take this planet, let's do an imaginary sphere.

Now this sphere is being sucked by gravity towards the middle so why doesn't it fall down? - Presumably because the pressure here is able to balance out ah the pressure gradient's able to balance out the gravity.

- Right so that gives us the first equation, I put it in words here, so basically, for each shell there must be more pressure on the inside out than there is on the outside in and the difference between those two gives you the gravitational pull on this which will be the mass times whatever the gravity is there.

- And so this is, we're assuming the star or the planet is in equilibrium it's not, you know, getting bigger or smaller or vibrating? - yes we're assuming it's just sitting there.

- So that means we can make sure that those things are equal to each other.

- So this is the first equation for planet structure and it's also used for studying the structure of stars and other things like that.

So that's one thing and that's going to be helpful because it tells us what the density and the pressure must be at each level.

Next thing will be to look at heat. In this case the heat is presumably leaking out, so you've got all the heat from when it first formed and that's being radiated away from the surface. So once again we look at any given shell, this shell or any other shell at any other distance and there'll be heat coming in which could be coming by radiation or by convection or conduction, the normal ways that heat can go from one place to another.

And there'll be heat leaving at the outer surface here, and the difference between the two is going to give us the change in the thermal energy of that ring. It's a bit like the specific heat capacity times the temperature or something like this.

- Yep. - That's our second equation.

So if we know the densities we can then work out how the pressure must vary because it must be able to balance them. If we know the temperatures, the temperature flow we must be able to work out the temperature at different points because it must be balancing it.

Then we need the chemistry so at any given level, we'll know the temperature and the pressure and we can work out what chemical reactions happen. So, we do all the normal rate equations, how your hydrogen forms with this and forms with that and balance them all out, get them in equilibrium and you get sort of plots like this.

- And so basically, different chemical compounds can only exist at certain temperatures and densities is what it comes down to and this diagram sort of tells you the temperature at least where these things can form.

- for one particular pressure.

- Yep - So for example you're not getting water, H2O, when it's too low because it's all frozen this is only in the gas form, so then it boils up here, then you get methane, ammonia you get things like titanium dioxide, vanadium oxide...

- Vanadium oxide, now there's something you're not gonna find around Earth very easily.

- Yes, considering it only starts becoming a gas at above seventeen hundred Kelvin that's not that hot on the Earth generally speaking.

So you can solve these equations and that will tell you if you know the temperature and the pressure what you should expect to get in the chemistry.

So that all sounds pretty straight forward. however there is a problem. What this is all giving us is if....if we know the temperature and the pressure we can calculate the chemical composition so it's a one way reaction however unfortunately it also goes the other way around.

It turns out that the composition also affects the temperature.

- Presumably because we saw that things like Methane blocks lots of light coming out and so it will sort of control how much of heat can travel through the star for example.

- That's right.

V8.7 BRIAN: So Paul, let's talk about how molecules interact with light.

PAUL: OK.

Well here's a simulation of this.

So behind Brian we've got an oscillating electric field.

BRIAN: That's this one.

PAUL: That's what light is, electric field that goes one way and then the other way. And here we've got, in this case, CO2.

So carbon in the middle and two , so typical molecule, and they're bound together with chemical bonds, which are represented as springs in this highly sophisticated simulation.

In this case, it's covalent bond.

So there's net charge in these things.

As the field goes up, it pulls the oxygen one way, and the carbon the other way, and vice versa.

BRIAN: So we're moving just a little bit here with this oscillating charge right now.

PAUL: So it's not doing very much.

So this would correspond to a frequency that doesn't have much effect.

But let's increase the frequency a little bit and we can see what happens now.

BRIAN: So now we've excited it a lot more.

It's almost like a trampoline now.

PAUL: Yes.

So what we've done is we've resonant frequency, a frequency that matches the natural frequency of this particular oscillation.

So this is sort of up and down oscillation of the carbon dioxide and so what this means is if you get light at this particular frequency it will a very strong effect on carbon dioxide and it would generally be absorbed.

The photon will come past and make the carbon dioxide excited and be absorbed so it won't penetrate.

And it turns out this particular oscillation like this is the one responsible for global warming on Earth because this particular frequency of light has that normally escape from the Earth just being blocked when you have carbon dioxide in atmosphere for all out pollution.

BRIAN: So this is an infrared.

PAUL: Yeah.

So this particular frequency, this particular transition, has toppled several governments here in Australia.

So politicians don't like this particular oscillation.

This would make the frequency even higher still-- not much happening now.

BRIAN: When you go out of the resonance again, so.

PAUL: It no longer matches that particular oscillation.

But if you make it higher still, you start getting something different.

BRIAN: You tune it in and there'll be some other residents.

This one's a little different though. It's not going up and down, it's going back and forth.

PAUL: Yes.

So it's going back and forth in opposite way to-- I call it like an Egyptian dance.

They're going something like this.

And so this actually turns out less important on Earth because this frequency is not where the Earth is radiating.

It turns out that for carbon dioxide there are basically three.

You have wavelengths of the sort-- there's one which corresponds to this, one like this, and also one that goes a bit like this which I haven't shown here.

And you have high frequency, still nothing again out of the resonance.

The residents.

So what you expect is for a molecule as you go through the spectrum, you'll see some where it absorbs and somewhere it doesn't and that will depend on what molecules are present.

BRIAN: Very good.

So CO2 is one molecule.

Does this work for all molecules? PAUL: Yes.

CO2 is a relatively simple one.

Something like N2 or O2 nitrogen nitrogen or oxygen, they're not polar.

So they have no net charge, so they don't have much effect, but you get something which has a polar molecule and where it's not in a line.

It can do lots of things.

So let's take, for example, water and this is going to do a lot more.

First of all because most of the mass is in the middle, so it's got less moment of inertia-- BRIAN: Right.

Water's sort of shaped like Mickey Mouse with two little ears, the two off the oxygen.

PAUL: --and so something like this, they can do all sorts of stuff.

They got many, many more ways they can oscillate.

And similarly for other things that are not in a line, like methane or-- water is quite spectacular.

You see it's doing all sorts of things.

It's going like this, and going around like that, and back and forth, and all sorts of things.

So this will cause it to absorb all over the place.

And indeed you could do the calculation, and what you can find is here we're plotting across the infrared what wavelengths different things absorb. So you've got water, and you see it absorbs, and doesn't absorb, and absorb, and doesn't.

It goes up and down like crazy because there's so many different absorptions because of all the different sorts of oscillation it can do.

And similarly for ammonia in H3 and methane, CH4, and they've 100 all got rather complicated patterns.

BRIAN: Right.

And a very distinct pattern which obviously is this part.

The energy's not going to be able to leak out in this part because it's all being blocked if it has these elements in it.

So you really do need to worry about this if you're going to calculate what one of these planets looks like.

PAUL: So it's good because we can see which wavelengths are leaking out and therefore work out what's present.

It's bad because it clearly means the chemistry is going to really strongly affect the flow of heat.

So the heat affects what chemistry you get and the chemistry affects the heat.

BRIAN: Well it sounds like that's some mathematics we need to take care of, but the good thing is that I want to know what these things are made out of.

This does give us the opportunity to figure that out.

PAUL: Here are our ingredients.

We know the lab measurements and theoretical predictions of molecular capacities.

So we can guesstimate if you have so much methane at this temperature and this pressure what it will do.

BRIAN: And so when you say opacities, that's how much of the light it absorbs as it's trying to go through the material.

PAUL: And that depends very much on the wavelength.

You've got the chemistry rate equations, which, again, we kind of know.

We have some very clever chemists around.

We've got pressure balance.

We know that the pressure must be such that the top of the planet doesn't collapse down or expand out.

BRIAN: Yeah.

PAUL: We have energy balance, law of conservation of energy, the heat leaking out must change the internal energy.

And we have radiation transfer, so we're looking at radiation going from one place to another and it depends on what molecules you've got what gets through. BRIAN: Right.

So this depends on that, but also what exists here.

So you really got to do the whole thing simultaneously.

PAUL: Yes.

This is one way to solve it.

You might guess the temperature and density profile.

So how our temperature density varies as you go out.

Once we've given that, we can use that to calculate the chemistry at each level.

Once you've got the chemistry, we can compute the heat flow because we then know what wavelengths are blocked and by how much.

Once you've got the heat flow, we can compute the temperature.

Once you've got the temperatures, we can calculate temperatures and pressures, and then go back to the chemistry.

What we find as we go around the loop it probably won't match.

BRIAN: Yeah.

PAUL: First one probably didn't work, and we end up with an answer here that doesn't make sense.

So what we might do is tweak this and then try again, and go around and around-- BRIAN: Until we make the whole thing consistent, internally, with all five pieces of information.

PAUL: This is what's called iteration, from the Latin word "to go".

You just don't get to the solution right away, you have to walk around and around in circles getting better and better, and slowly approaching perfection, and in the end you might finally get there.

[SIGHING] It's been a long haul.

When we finally get there, we get our models.

We've got the green and red models-- sorry for your color blindness again.

BRIAN: Yes, I'm color blind so they look the same to me.

PAUL: --which are for two different temperatures, and you can see they do a not too bad job in fitting the spectrum of this particular planet.

BRIAN: So one is hotter and one is colder? PAUL: Yes.

BRIAN: And in this case they both, more or less, fit the data.

PAUL: However, it turns out they had to fudge it in this case.

If you just naively expect a planet at this temperature to have no clouds-- if it had no clouds, you don't get a good feel at all. So what they had to do was put in clouds, and clouds are things we do not understand, well, anywhere.

We can't even model them on the Earth.

We have some ad hoc laws, if the temperature and pressure is like this we'll get clouds, but they're really to hard to model and so we had to put them in almost by hand here to make it fit.

So these things seem to be cloudier than brown dwarfs at the same temperature, maybe because of their smaller and have lower gravity.

So that's one surprise.

BRIAN: OK.

Well that is interesting, and a mystery to figure out why they would have clouds.

PAUL: But apart from that, it seems to actually kind of work.

And this is what allows us to get an estimate of the age and the temperature of these things.

In this case, about 1,000 Kelvin

V8.8 So, Paul, we've managed to image our first planetary system around a nearby star, is that the only one we've seen so far? -Well, this is a fast moving field and probably everything we tell you here will be out of date before we've said it, but there are a few more being discovered. And the next one is actually, in some ways, kind of similar.

It's another bright star, Fomalhaut, another star with a debris disc. So, very similar to HD-8799. And when it was looked at with the Hubble space telescope you can see very clearly this debris disc and you can also see this little dot just beside the debris disc, that seems to be moving.

-Oh right. And so, the Hubble space telescope normally looks in optical and infrared wavelengths, or near infrared wavelengths, so that's a little different than the previous one which was looked at in the mid infrared, where these things could glow if they weren't... didn't have to be very hot.

-Yes. So, it's a bit weird. I mean, here's what you'd expect a spectrum to look like; these dotted or dashed lines over here, which is nothing in the optical wavelength, and then climbing in some sort of complicated zigzaggy way up. And these are the infrared attempts and you can see no one has yet succeeded in seeing this is infrared. They're not very hard with the number of big ground based telescopes.

How about we look at the Hubble space telescope in the optical. It's booming in. So, somehow it's producing optic light, but not infrared light.

-Right. And that optical light looks an awful lot like an A star, that is a 10,000 degrees star, which is of course what Fomalhaut really is.

-So, either this planet is actually at 10,000 degrees, which doesn't sound like a planet to me-- --Well, doesn't seem bright enough.

-Or, what we're actually seeing here is not the glow from the planet, but a reflection of the light Fomalhaut had off the planet. -Okay.

-Okay. So, by looking at how bright this is we should be able to tell how much light is reflected off it and hence get the size.

-So, we're going to see if it's a disco ball in the sky, reflecting it's stars glory off into space.

-Yeah, so let's see how big it is.

So, How big is this thing orbiting Fomalhaut? Fomalhaut B. Well, if its spectrum in the visible, then it probably means it's scattering the light from the star. So, you've got the star, Fomalhaut, emitting its light in all directions. And out here is planet of radius r and it's intercepting some fraction of the light, which is being re-scattered. This is a calculation we've done many times before.

So, what we want... what we know is that the distance here is Astronomical units. This planet's a long way out. And we also know that Fomalhaut B is about 25th magnitude and Fomalhaut itself is about 1st magnitude. So, there's a 24 magnitude difference in brightness.

The magnitude scale is a strange and barbaric thing left over from prehistoric times. Each magnitude is a factor of 2.5. So, that means difference in brightness is a ratio.

So the brightness of Fomalhaut over the brightness of the planet is roughly a vector of 4 by 10 to the 9. So, a very big difference in brightness between the 2. So, given that, how big is this thing here? We need it to intercept this fraction, 1 over that, of the light. So, the cross-sectional area here is just pi r squared. The total sphere of which the light has spread has got an area, 4 pi D squared.So, we want 4 pi D squared over pi r squared, to equal 4 by 10 to the 9. So, it's light of D planet. 1 over total area.

This is assuming the planet scatters all the light, so it's a mirror planet, which is unlikely.

But let's run with that at the moment. Cancel that. Cancel the 4s. And we end up with r is approximately equal to 6 by 10 to the 8 metres. And if you bear in mind that jupiter has a radius of 7 by 10 to the 7 metres, that means this thing is 10 times bigger than jupiter.

That is to say its radius is 10 times bigger.

That means its volume is 10 cubed, i.e. a thousand times bigger, so presumably its mass, if we assume a fairly constant density, is a thousand times that of jupiter, which makes it a star, not a planet. So that's awfully big if it was a star. Even a brown dwarf would be very much brighter than this and would have a rather different spectrum.

So, something odd is going on here. It's very big.

-So, Paul, that is one mighty big disco ball.

That doesn't seem remotely plausible that that could possibly be a planet.

-So, what could it be? I mean, maybe it's some alien civilisation that's built huge sails or something like that.

-Oooo, I like the sound of that.

-But, most likely it's what we've already talked about; it's dust. So, what we need is a big ball of dust. Lots of small things that can reflect lots of light like debris discs can. -Yeah okay, but Paul, we saw that when you have balls of dust going around stars, the dust gets stripped off and dragged away and it shouldn't last very long.

-This ball's actually moving from place to place. If it's orbiting around-- -Should leave a comet-ry tail or something, right? -Yeah, and also the inner bits will be closer to Fomalhaut than the outer bits, so it should orbit faster, so it should get stripped out.

So, there's no way it can stay as a coherent lump over several years. So, what's going on here? Maybe if it's a ball of dust or a disc of dust or something, there must be something holding it together. So, the current best guess; there really is a planet here. We're not seeing the planet. What we're seeing is, somehow the planet is surrounded by a cloud or a disc of dust, and it's that disc of dust that's been held together by thats planets gravity that we're seeing. It could even be what we're looking at here is the formation of the moons of a planet. So, you've got a planet which is got like Saturn's rings only much, much bigger, which is eventually going to coalesce and form moons. This is how we believe the Galilean satellites of Jupiter were formed. There was a disc around Jupiter that sucked it in. So, maybe that's what we're seeing here. Or maybe it's just some cloud of collision... something that's bound, and trapped and, doing some sort of weird orbit around this planet.

-So, this object really could, I guess, be like a giant version of saturn. Saturn's rings are very good at reflecting light. So, you could imagine a super Saturn out there. That would be cool to see.

-It would indeed.

V8.9 And that wasn't the only star with a debris disc that's to be found around planets. We get to everybody's favourite debris disc star Beta Pictoris and this one, once again, same technique-- - It really does stand out there doesn't it, impressive - So it looks like this one's got a planet--; this one's much closer in, this is only about as far out as Jupiter is, or actually more like Saturn's distance out.

- So Paul we remember that Beta Pictoris is the object that had that amazing disc that was edge on that had a little flare that we thought might be due to a planet or something.

How is this situated to explain that? - It looks like it's more or less inside of this disc and it might well have the right sort of orbit to be able to cause this flare so it seems to kind of work. It also could be stirring up the debris disc to cause the big rocks to collide and make all the dust that we see - So Beta Pictoris has it all it's got this debris disc, it's got a planet, it has comets by the score.

- Here's an artists impression of Beta Pictoris actually taken before these discoveries, so this actually shows multiple planets with collisions and giant comets and discs and you name it. Though in fact this planet that you see is very massive, we're talking maybe about ten times the mass of Jupiter, that's assuming it started really hot, the age of Beta Pictoris is a bit controversial so it could be even- -; it might be a brown dwarf rather than a planet.

But it does look like this is a solar system which has it all.

- So if we look at that plane and see what it's spectrum looks like though, it has these features which again suggest clouds.

- It's the blue points of actual data for beta pictoris...these different coloured lines are spectra of brown dwarves. And what you can see is they don't actually do a very good job of fitting it so, once again what you need here are some clouds to bring this up here and up there to give it a flatter spectrum so we seem to be seeing a trend that these things are cloudier than we'd expect from their temperature.

-So it kind of looks like we've got a pattern here, we've found planets, big planets, 5 to 10 times the mass of Jupiter or thereabouts but they've all been around very massive, very hot stars, A-Stars, and they all have debris discs.

- right so that seems to indicate that you may not want to go look for super Earths around these right in their centres but if you want to go find big planets a long ways out, A-Stars with debris discs look like the place to go and see them.

-Or so people thought....

V8.10 PAUL FRANCIS: So in the last few years, a number more have been discovered.

In fact, several have come out just in the months while I've been writing this course.

And so this is a fast-moving field, and these things are massive, and far out, and typical borderline brown dwarf planets, depending on, you know, exact age, and modeling.

BRIAN SCHMIDT: But we only have a handful, Paul.

And, you know, you don't learn much from a handful.

If you've got to go poll to find out who the next prime minister is, you don't ask five people. you need to ask a lot of people.

So strikes me, we need a survey, a big survey, to go out and really see what's going on.

PAUL FRANCIS: And we want to look systematically at the whole range of stars and see, how common are these things, what sort of stars they found around.

BRIAN SCHMIDT: Right.

PAUL FRANCIS: And the technology's getting much better.

We have a whole bunch of new instruments coming along, which both use this angular differential imaging and some new tricks.

For example, what you can do is, you can observe simultaneously at two different wavelengths.

One wavelength where you expect these planets to be bright, and one where you expect it to be faint.

BRIAN SCHMIDT: So you'd look at them where the methane isn't causing you problems, and where it is, presumably.

PAUL FRANCIS: Yeah.

And all the interference from the star should be the same at both wavelengths, whereas the signal from a planet should only be at 1. So you can use that to discriminate between the two, subtract off the contamination, and just see what's left over.

BRIAN SCHMIDT: So this kind of shows that we're doing pretty well, because remember, this is our magnitude difference.

So this is talking about the ratio of how faint we can see relative to the star, and that's 15 magnitude.

So that's 5 plus 5 plus 5.

So that's 100, 100, 100, 1 million.

So we're getting down into very, very close to where we want to be.

We're down below a million now, so that's getting where we need to be able to see these planets.

PAUL FRANCIS: Yeah.

So maybe a million.

Maybe even 10 million.

Still not a billion.

We've still got another 100 to go, but, so that's a vast improvement.

So there is a problem with this, which is, typically, whenever you take a picture of a star with this, you'll indeed see lots of little dots, and you'll think, yay.

We've got planets! But then you actually discover that they're not planets.

They're just background stars.

BRIAN SCHMIDT: Because there's a lot of stars out in sky, fortunately.

PAUL FRANCIS: So what you have to do is go back and take a picture a year later and see if all these dots have moved with your bright, nearby star.

And if they haven't, they were background things that were left behind.

But if you do all that, you find nothing.

BRIAN SCHMIDT: Nothing? So the first ones, we see these things, and then we go and look at 57 objects and find nothing.

PAUL FRANCIS: Yeah.

So some recent results, there have been a number of big surveys done, and they seem to be finding very little.

Maybe one object, maybe nothing.

This is a particular survey done at Gemini, and they looked at 57 all of these debris disk stars.

These big, bright stars, exactly the places where we've seen all these things so far.

And nothing. Nothing.

If these things really did start hot, and were therefore very, very bright when they're young, this allows us to put an upper limit.

You can't have something more than 40 astronomical units out, so beyond the orbit of Pluto, that weighs more than 3 Jupiter masses, in more than 21% of them from this survey.

And other surveys are coming to similar sort of things.

BRIAN SCHMIDT: So they're not everywhere, although that isn't completely constraining.

But it's saying that we may have gotten lucky in these first few things, that Beta Pic, and Formalhaut, et cetera.

PAUL FRANCIS: HR8799 seems to be unusual.

It's in that 20%, and not the rest.

They've done more surveys.

For example, they've got other hot stars ones which don't have debris disks.

In these cases, they get fewer than 10% of these analogues.

That could also look about, maybe, not these very massive stars, but more normal stars.

So there aren't that many stars that are both nearby and so young that their planets are still glowing like crazy, but those that are, fewer than 10% have something that weighs between 1 and 20 Jupiter masses, between 10 and astronomical units out.

BRIAN SCHMIDT: All right.

So we're, I guess, getting a good look at the nearby universe.

But then this has to be reconciled, I guess, with all these free-floating planets, and the planet rates that we're seeing from microlensing.

So microlensing not just tells us about free-floating planets.

It also tells us about planets a fair ways out around normal stars.

100 Yeah.

Remember.

With microlensing, we saw a little tiny glimpse, just from our planets, and all we knew from that glimpse was that it had to more than about 10 astronomical units from the planet.

So it could've been a planet a long way out, or a free-floating one.

But there was an average, something like 1.8 of these tiny things per star, where, what we're telling us here, is that fewer than 10% of stars have planets out there.

This is the other half of the argument for why they must be free-floating.

Because if they really were in orbit around the planets, this would be more like 200%, not 10%. So it looks like they really are free-floating planets, and these massive things a long way out do exist, but they're not common.

V8.11 - so Paul this is a kind of a different story than what we saw with planets discovered with radio velocity and transits where you know we had some really exciting results first up and then it's been kind of disappointing we haven't seen so much as opposed to long hard slog and then suddenly a flood of events.

- Yeah, it's been a bit weird but with radio velocities if you peg the first discoveries and then a whole flood did surveys determine for transits ah but here first result's exciting and then the surveys that found nothing. But actually this is a very common occurrence in science you get a really exciting first result and then everyone storms into the field and does surveys and the like and don't find anything. I guess it's because whenever you make an observation there's an element of chance it could end up being looking easy...it might be more exciting than you expect or less exciting just from chance. So for example but if a particular phenomenon is rare you might get lucky and see it the first time, or, you might.... even though it's common for them you might get unlucky and not see it but the trouble is it's those rare occasions when things look more exciting than they really are that gets published in the top journal, everyone gets very excited and goes and replicates it. Whereas if it looked less exciting then everyone doesn't bother following it all up.

- Yeah so there is this natural selection effect so, I guess it doesn't always happen but it can happen where you really just get lucky and find the really exciting bit first up and you're actually chasing....we're chasing something that's not as good as you think it's gonna be.

- Yes I mean from my own experience I was once trying to pioneer a new technique to discover very distant galaxies and we went for the very first observing one and we saw the spectacular thing what's now called a Lyman Alpha Blob and so we thought yay this is exciting we went back and got lots more telescope time and looked again and again and saw nothing.

- Yep - Eventually, decades later people have got much more sensitive telescopes and are now seeing these things everywhere, but we just got really lucky the first time. but if we had been really unlucky we wouldn't have been bothered following it all up.

- yeah you wouldn't have gotten the telescope time and so in some sense that chance was both good and bad for you.

- So where to from now we've got sort of mixed results, a few very interesting discoveries but we're only seeing very massive, very hot, very young things is there any hope of seeing smaller, more normal planets? - Well, I think we're really going to have to defer to new technology but there's alot of scope for technology , so right now we're in the process of building new adaptive optic systems for the largest telescopes on the planet Earth and these are quite clever so instead of using one deformable mirror, they use multiple ones so you can make, you can take out the little scale stuff, you can take out the large scale stuff or you can actually take out different bits and pieces of what's going on in the atmosphere, and you can do it faster and faster. So that's one area we can improve.

- yeah and one of the mirrors could be used to take out the errors in the telescope itself which is causing the big problem for these things and they also use spectroscopies so they actually measure a spectrum at every point rather than just an image with the idea that the spectra of the exoplanet would look different from everything else but the distortions will be the same. So they should be able to get exquisite precision, these will be coming online in the next few years.

- And the other cool thing they can do is to use the wave nature of light to set up a system where the starlight cancels each other out so you actually setup you lknow those slits using Huygens principle so that the light from the stars cancels itself out in a very clever configuration of how the light comes through the telescope so that you minimise again that scattered stuff, that's the problem behind all these observations.

- So hopefully when the instruments come online we should see a flood of planet direct imaging discovery so then the....

- 'cos we're almost sure it's there, we see all these debris discs the only way that makes sense to me is to have something like Neptune stirring things up so we're pretty sure there's stuff there it's just a matter of getting technology to the point where we can see them.

- And then everything will turn to actually characterize all these things, looking at the spectra, what would really be interesting if you could start finding smaller planets by this technique maybe even Earth like ones and just looking for bio markers and signs that it could be inhabited for example the Earth has an oxygen atmosphere if you can see oxygen spectra because the oxygen on Earth isn't natural , it's produced by living things , i guess that means it is natural but....if there wasn't any life on Earth there wouldn't be any oxygen in our atmosphere.

_ Or maybe there's something like us making CFC's or uranium through a nuclear explosion\, who knows the possibilities are endless.

- So that's where it gets really exciting but it's going to need another generation of telescopes, we're not going to be doing that with our current telescopes.

- We really need big ones, so....

- Very big adaptive optics and very big telescopes.

- But, it's all possible.And the future it's not five years away but it's not a hundred years away necessarily either.

V9.1 Okay, so in this lesson, we're going to finish off talking about exoplanets.

We're going to start off by asking about exoplanets we really would like to see, which are potentially habitable ones.

Not all of these giant, frigid pulsar, whatever it might be, but actually a planet that you could set a science fiction movie on or something like this.

Then we're going to talk about, if we could find habitable planets, all we're going to learn about them is their mass and their orbit with the current technology, but what would they actually be like? Would they have giant mountains? Would they have oceans? Would they have atmospheres? We'll talk about these sorts of things and then finally we're going to try and summarise everything we've learnt about exoplanets. So, I mean, we're talking about habitable planets, we're going to need to think a little bit about what habitable means.

Now, we know what is habitable here for life on Earth and so here on Earth we know that you ultimately need water to probably be liquid at some point, so that means that the temperature of the planet has to be between zero and a hundred degrees Celsius.

The habitable zone that we've talked about already, so that gives you a certain distance from the star, it's got to be in roughly, with things like greenhouse effects, many planets seem to cheat and be outside the zone.

Right, and so also the composition, I mean if the Earth was made out of solid rock and not have water and carbon at some level associated with it and oxygen which seem to be very important of course, to life here on Earth.

Then again, you would be problematic, so you can imagine there being worlds out there that are just simply not made out of the right stuff to have life as we know it.

Of course, most of the planets discovered so far are probably gas giants, which have no solid surface.

I suppose you might might imagine some blobby thing that floats around in the atmosphere at the right temperature, but it might be nice to actually have a solid surface.

Of course, these gassy things might have moons around them, which is I think what Pandora in the movie "Avatar" was.

They put it on a moon around one of these planets.

So, the one thing we don't know at the moment is whether any of these giant things actually have moons, because they might be a good place for life.

Well, we do have Europa in our own solar system which is thought possibly to have a water ocean underneath it.

But then we get to the big question I guess is "what is life?" I think at some point we sort of have to work with what we have here, we could speculate even further that there's life based on silicon and all sorts of other things, but I think we're going to try and keep our conversation around the stuff that we actually know.

Yes, I mean, it could be that life could exist on the surface of the sun, strange magnetic beings, who knows.

Maybe our definition of life is too narrow. But, let's think about life as we know it and whether we can see that.

Let's start off by talking about what we know so far about potentially habitable planets.

V9.2 So, we've found vast numbers if planets of incredible diversity, but what I really care about is planets that we could send space probes out to and put colonies on and meet aliens and have good science fiction movies on.

How do we find anything to Earth-like? Earth-like mass, liquid water in the habitable zone. Well, it really seems that everything is against us.

We have all of these techniques where we find big objects orbiting around these very nearby stars, then we have the ability to directly see things a long way out, you know, these big 10 size Jupiter mass things that are 100 times the distance from the Earth to the Sun out, orbiting A stars, but we don't seem to have that many objects in that sweet spot of Earth-size things at Earth distances.

The best way to find things of roughly Earth-like sizes has been the Kepler missions, so looking for transits.

Now, remember, what Kepler was doing was it was looking at one patch of the sky over and over and over again for three years, it's finished now, and so the typical stars and planets it sees are going to be about 1000 lightyears away.

Because of the exquisite precision, it can see very small dips.

You can only find things close in because that's where the odds are going to be edge on, but if you have a faint star, a red dwarf star, a close-in thing could still not be too hot.

If you put something in a 30 day orbit around our sun, it would be fried, far to than Mercury.

But, if you had a pathetic little red dwarf, provided it's a few percent as luminous as the sun, maybe these close-in things, if they are of Earth mass, could be right.

So, here is the closest analogue to Earth we've found so far.

Now, this is probably going to change by the time you view this, it might well be obsolete, but at the time we record this, this is accurate.

So, it's orbiting a small little star, one of the cockroaches of our Milky Way, as we like to say.

But those are kind of nice because they last for a long, long time.

None of this 10 billion year stuff like our sun.

Trillions of years for these things.

It goes around every 57 days. If it was a normal star like our own sun, it would be fried, but because this thing is so pathetic, this actually gives about the right temperature.

It's got a radius of 1.33 Earth radii.

So, it's a little bit more real estate than on Earth.

Yes, and we can see these small things most easier about these small stars because, if you remember, the size of the dip in the light tells you the ratio of the size of the planet and the star.

So, because the star is small, even the small planet can make quite a big dip.

But, we have a problem here, of course, it's because this thing isn't an intrinsically bright object and so it's pretty faint and the object is so faint that we can't really collect enough light to really see the orbital, the reflex motion, the motion of the planet.

Yes, so we can't do the radial velocity technique and find the mass of the stuff.

Even if the star was bright enough to do it, these planets are below the threshold of anything we could feasibly see at the moment. But it's over a thousand lightyears away, so it's not one we're going to be visiting with our space probes anytime soon. The temperature...

Minus 27 degrees Celsius, that doesn't seem very warm.

Why is this habitable? That sounds to me like it's frozen.

But, it turns out that the expectant temperature of the Earth, according to the same calculation, is also below zero.

The Earth is habitable because we have this greenhouse effect.

A natural greenhouse effect, not the human-produced add-on to it, mostly due to water vapour in our atmosphere and that brings out every temperature up enough that we have liquid water.

So, it wouldn't take much of a greenhouse effect to bring this up to habitability.

But it seems that we don't know anything about it apart from its radius and its orbit.

So, Kepler has found a lot of things, this isn't the only thing, this is probably the best place to maybe look for life.

Here's a spectacular one and probably the best studied one.

This is Kepler 62, which has actually five different sets of transit dips occurring.

Five little dips, okay. Let's see, we have a very close one in, presumably that wouldn't be a very nice place, even around a puny little star.

5.7 day period, about 1.3 Earth radii.

This one is a very small dip, so I'm not sure if we believe this one or not, but it's only 0.54 times the radius of the Earth on a 12 day period, then an 18 day period, about two Earth radii, day period and a 267 day period.

Right, so a real bevy of Earth-like things around here and even down to mars and similar types of things.

So, it turns out that in this case, it's probably the two furthest out that are in the habitable zone.

One is right at the close end of the habitable zone, which might make like Venus in our solar system, and ones in the outer edge might be a bit more like Mars.

They weigh 1.4 radius, that's 1.4 and 1.6 times the radius of the Earth which sounds like it could be a rocky planet, but we don't know the mass, we don't know the density.

We don't know the mass and the density and so we saw, when we able to measure some of these objects, that when they're down here, they seem to have that density of not too dissimilar to the Earth, but you do have to worry about, maybe these being gas mini-giants because we don't understand how these things form very well And so we really do need to try and get a sense of their density.

But, one again, this is a long way away, in this case about 0 lightyears away, so it's not something we're going to be sending colony ships to anytime soon.

V9.3 So, these Kepler potentially Earth-like planets are all well and good, but they are 1000 lightyears away, they're too far away for us to send space probes to write a science fiction novels in the near future.

What I'd like is some nice habitable ones close by so we can study them really well.

But, how are we going to find them? Kepler is not going to find anything that close.

Well, I think that in the short term, maybe what we can do is use the radial velocity technique.

But it only finds giant things, typically.

Well, it does if you look around big stars, but let's say we look around little stars, the smaller stars, and then the planet won’t have to have that much mass to make a measurable imprint on the velocity of the star.

So, we're back to red dwarf stars again and perhaps the most spectacular example is Gliese 667, which on the base of its radial velocity seems to seven planets around it. (Seven planets!) You need seven different sine waves superimposed, not all of these are completely sure, I mean, that's looking a bit marginal over there. Maybe this one.

But as they get more data, hopefully they will be able to nail this one down more accurately.

Alright, but any Earth ones in this one? Well, this is a really weird system in more ways than one.

We've got the red dwarf here, but it turns out that the red dwarf is actually at a distant orbit, around 300 astronomical units out, from a binary pair of brighter stars.

So, you've got the bright stars and then you've got the red dwarf orbiting much further out and the planets are all going around this red dwarf.

So, this is what the night sky, and it looks like two of these things, E and F, might be potentially in the habitable zone.

Here's an artist's impression of one of them and it's showing the red dwarf, it should look quite large, you're very close in, but because the red dwarf only puts out one and a half percent of the light of the sun, you've got a nice temperature, and you can see the other two stars in the background in this, so giving you the interesting triple-sunset.

Okay, it sort of looks like something from "Star Wars", that's nice. Nice lakes.

Of course, we have no idea if it's got lakes.

All we know is the mass, but it could be a black hole.

Okay, so this is planet E, does planet F look equally compelling? Well, this was discovered by telescopes of the European Southern Observatory and they've put together this simulation of what it might look on the next one out, and they're guessing that this one might be a bit like Mars.

Okay, so this is the first one we just saw with the lakes and this one is more Mars-like.

Unfortunately, we really are at science fiction here rather than science, but it's at least nice to speculate.

Yes, I mean, these things are very big. They're masses are, there's a lot of Earth masses out there and so we don't know anything about them really.

This is about 20 lightyears away.

Okay, so I know that there are a few, a handful of stars which really are close.

There's Alpha Centauri, there's Sirius, there's a few other stars that are within 10, 15 lightyears where we could imagine getting to within a few hundred thousand years in todays spacecraft.

One of them, Tau-Ceti, does seem to have potentially habitable planets.

It's actually probably the closest sun-like star, depending how widely you'd want a bracket of sun- like.

It's only 12 lightyears away, it's actually quite a dusty system, so traces of maybe a little bit of a debris disk and it's not a red dwarf, but nonetheless, because it's so nearby and so relatively bright, you can get very high precision of radial velocity measurements.

There's this claim, it's a controversial claim, that it maybe has four or five planets, two potentially within the habitable zone.

I actually know one of the Authors of this paper and I was asking him about it and he said "Yeah... maybe." It's hard work, it's really hard work.

We're talking mass Sini, remember that we don't know the inclination of these things, so this is a lower limit on the mass, of between 4.3 and 6.67 Earth masses.

So, it's either a lot of real estate or a giant balloon, that's not much use at all.

Yes, I mean, odds are that at these sort of radii, we're talking about a mini Neptune rather than a Super-Earth I would have thought.

Okay, but presumably, this star is so close that we have a chance in the future of maybe even looking at these planets directly from Earth with the new telescopes of the future.

This might be a good time for some direct imaging, I mean, it's much closer in what we're seeing so far with direct imaging and much older, but because it's so nearby, maybe we've got some sort of hope.

V9.4 So, Paul, we're beginning to find habitable style planets, well, potentially anyway, but they're not quite the same as Earth.

They tend to be Super-Earths.

They're big and that's potentially interesting if they're actually made out of rock.

(Or of real estate.) Yes, lots of real estate, good place to go.

But they're around these little, puny stars, red dwarfs we call them, and so that is a little different. The years are shorter, but I guess the question is "are these the places that are really going to host life like we know it?" Yes, I mean, on the face of it, it looks like red dwarfs could be the ideal place for life.

There are far more of them in the big stars, we know from the Kepler results that they tend to have more planets in close-in orbits and these are the places we're now finding potentially habitable planets.

This actually begs the question that if this is the ideal place for life and there are so many of them, why don't we live around a red dwarf? Is there something weird about us living around such a big star as our sun? So, you're sort of getting into that anthropic argument again where we say if we're a random chance, we would expect to be around the most common place where life would be formed in the universe and so if life is everywhere around these red dwarfs, we should be around a red dwarf, not around a sun-like star.

Yes, I mean, the statistics are not that compelling, because about 20 percent of stars are like our sun or bigger, so it's not as if they're ridiculously rare. 20 percent can I could live with.

But some people have speculated that maybe there's something wrong about red dwarfs.

One possibility is that a red dwarfs often flare on the surface in a much stronger way than the sun does.

Yes, that would be kind of a pain because when I'm out looking for supernovae, we occasionally get these stupid red dwarfs that flare up out of nothing and they get really, really bright for periods of time and if you were on a planet around there, you would not want to be around that star when that happens.

So, that is a common occurrence.

But it could be the opposite situation, these things normally put out very little ultraviolet.

Some people have speculated that actually, the ultraviolet that we get from the sun helped trigger some of the chemical reactions to get life going.

That's sort of the other argument, that these things are either too violent or not violent enough. Maybe it's a combination of both.

Most of the time they're not violent enough, they don't produce the ultraviolet to catalyse the chemical reactions, but some of the time they're too violent.

Yes, they sort of go through a phase because they tend to be quite active when they're young and fade away and, of course, these stars, not only are they, as I said, they're cockroaches, there are so many of them around the galaxy.

They live for a hundred trillion years, so they last forever compared to our sun which has a mere 10 billion years under its belt.

So, maybe life is going to form in the future, it just hasn't happened yet.

It could be. Anyway, let's now go on and talk about what these exoplanets might be made of.

We've seen the ones around red dwarfs, presumably there are more that we can't detect yet, maybe around normal sun-like stars. Are they going to be made of weird elements? Or are they going to be made of familiar elements? How weird are they going to be?

V9.5 The staple of science fiction is that planets around other stars might be made of strange and weird elements like 'kryptonite' or 'unobtainium' or something like this. So, is this at all plausible? Could we find new elements unknown to science throughout other stars? Well, Paul, the laws of nuclear physics are pretty well set in stone, and we know that, for example, our sun is made out of these elements all the way up to uranium, effectively, and it is pretty hard to imagine how things are going to be made out of things other than this.

There is just the tiniest possibility that there are elements heavier our here, but they would be in minute quantities, minute quantities and so I think we're stuck with these elements, nothing new.

We are probably also stuck with these sort of ratios, like lots of hydrogen, not much scandium and so on.

The patterns here are, once again, set by well-understood nuclear physics.

Not only set by well-understood nuclear physics, our sun is made up of the same stuff that all the other nearby stars are made out of, so we really are formed from sort of the same gene pool.

So, if the stars are going to be pretty similar, are we going to ask about the planets? Now, planets are not quite the same as stars, here's, for example, the crust of the Earth and what you can see, for example, is hydrogen is no longer the highest.

It needs to be off the scale, but not much hydrogen got trapped in the Earth. There's still some in the water.

It's actually oxygen and silicon that are most common in the crust of the Earth and indeed the Earth crust is made out of silicon oxides of various forms, also there's bits of aluminium in there as well and some iron and so on which are called 'rocks'.

We also have some elements that have fallen almost to the bottom of these plots. These ones are called 'siderophile'.

It turns out that when the Earth is molten, most of the iron sank to the centre and a catalogue of other elements, iron-loving siderophile elements down with it, so we lose some things.

But, by and large, this is about the same pattern as this, only with some well understood changes, the volatile of the gasses never got trapped and the siderophile stuff got sucked down to the bottom.

So, Paul, we have sort of an interesting issue actually, when we think about it, because my understanding is that the early solar system, the carbon and oxygen were bound together to form carbon monoxide.

You look here, carbon and oxygen are very similar.

You see that like carbon is a lot more common than silicon whereas carbon has really dropped off here. That's right, and so that maybe suggests that somehow the carbon monoxide was blown away, it didn't form the Earth and the fact that there was more oxygen than there was carbon meant that we got oxygen on Earth, which I'm rather fond of, in the form of the water and the air that I breathe.

Not to mention the rocks we're walking on, which most of it is. (That's true, yes.) Yes, so the idea would be that you had fair large amounts of carbon and oxygen, but a bit more oxygen than carbon and so when the solar system was forming, they will bind together to form carbon monoxide, which is a very easy thing to form at fairly high temperatures, and that would mop up all of the carbon and most of the oxygen.

Whatever oxygen was left over would then, at a lower temperature, combine with silicon to form rocks and everything would form.

But this might be one form of getting really... I want some weird alien planets. I want the aliens to be right different.

You see, the elements aren't always quite the same.

Here, for example, is the ratio of carbon to oxygen in stars around.

This is actually a little controversial, there's some paper saying that these points up here is actually wrong, they just failed to measure the things accurately, but nonetheless, there's a bit of a range here.

Likewise, with things like magnesium and silicon over there.

So, you can imagine that there will be some stars, and presumably their planets, where you have more carbon than oxygen and we would get a carbon dominated planet rather then an oxygen dominated one.

So, this time it's cooled down, once again you form carbon monoxide, but now all the oxygen will be mopped up and there will be some carbon left over.

Now, when there was oxygen left over before, you can't just form oxygen planets, it has to combine with something, but carbon actually can form graphite.

So, what you will get is planets made of graphite and the rest of the carbon might combine with silicon carbides and things and so you get a planet that's a mixture of graphite and silicon carbide, silicon carbides are refractory, it's used for industrial processes because it can tolerate heat very well.

Indeed, on planets like this, if you had a lot of graphite, when you go below a few kilometres, that's going to turn into diamond because of the pressure.

So you get planets with some sort of mixture of silicon carbide and graphite on the centre, but then you dig down a few kilometres, you might get solid sheets of diamond all the way around.

So, a diamond in the sky but no kryptonite.

(That seems to be the way it's going to be.) V9.6 So, Paul, I'm kind of relieved, but it looks like the average planet is not going to be that dissimilar from what the Earth is made out of, although there might occasionally be these kind of wild carbon worlds that might be different.

But the vast majority are going to look similar to us.

But there is a problem here. We've said that the Earth should be made of silicon oxides and things like that, ie: rock.

So, the idea being that the inner part of the protoplanetary disk, you have lumps of rock smashing together to form things like the Earth.

However, the Earth also has this rather nice thing like the atmosphere and the oceans; which would require water and gas.

But there shouldn't really be ice which form water, it should have evaporated.

We've said that these planets have depleted all the volatiles and the gassiest things because they can't form rocks and stick together.

So, how did the inner planets get their oceans and atmospheres? You can get ice, which can form water, but it's too hot close in where the Earth formed.

Well, okay but maybe the ice, there's not that much ice on Earth, it's just a little thin layer on the surface, so maybe it's that they were brought by your favourite objects, comets.

Comets are icy balls and in the early part of the solar system, there should have been a lot more comets going around and hitting the Earth and so you literally just threw snowballs at the Earth and you got a bunch of water that way.

Comets are actually a hard thing to produce because it turns out that they have the wrong ratio of hydrogen to deuterium.

Deuterium is hydrogen with an extra neutron, and it turns out that the ratio of the oceans on the Earth is different from the ratios in comets, they'd be measured in a handful of comets.

So, more likely icy asteroids that show, we've talked about this planetary Billiards early on, and this would have, as the planets moved around, did their funny stuff, it would have stirred up some icy from the outer solar system and they may have rained down on the Earth and given us the atmosphere and the oceans, or at least the oceans.

But there's also a puzzle here because this bombardment should have occurred on all the other planets, so it should have occurred on the moon, for example, and Venus, and Venus has a very thick atmosphere, but no ocean.

Earth has an ocean and a thinner atmosphere.

But why doesn't, for example, the moon or Mars have a thick atmosphere like the Earth does? Okay, so presumably the question is you can get this stuff, maybe they all got the same delivery of stuff from this bombardment, but of course, the moon and Mars are smaller than the Earth and Venus, so maybe it's something to do with their size. Yes, so let's calculate. Maybe their gravity isn't enough to hold these things. Let's see if we can calculate that.

Okay.

V9.7 So, what determines that a planet can keep its atmosphere? Let's imagine we have a planet and it's got an atmosphere.

Let's zoom in on that, so we'll zoom in somewhere over here and you can see al the molecules in the atmosphere, and they're all moving around because of the temperature, unless the atmosphere is at absolute zero, it'll be jiggling around.

Now, what would allow an atom to escape? Well, normally when they jiggle around, they don't get very far before they bang into another molecule.

So, that might bang into this one which might bang into that one and so on and so forth.

When we get up to them all at the top of the atmosphere, the atoms are getting few and far between.

So, for ones heading upwards, it might actually be able to escape.

But if it's going slowly, it will fly out and then arc around and come back down again.

What we need is atoms near the top of the atmosphere that are going so fast that they can actually escape into space.

So, what would determine the speed of an atom? We've got two questions. First of all, what determines how fast these atoms are going, and secondly, how does it compare to the escape velocity, the velocity to escape into space? Now, for the first one, we have to use a result from statistical thermodynamics.

You just have to take this on trust unless you're familiar with that subject.

Statistical thermodynamics, which was worked out in the 19th century, tells you that the average kinetic energy, half MV squared of a atom or molecule in some gas is equal to three halves the Boltzmann constant, which is 1.3 by 10 to the minus 23 times the temperature.

So, what that means is that the velocity is equal to the square root of three KT over the mass of the particle in question.

How fast is that? Well, you can see that it will depend on what atom in the same atmosphere, let's say the atmosphere contained oxygen and hydrogen, an oxygen atom weighs 16 times more than a hydrogen atom, and oxygen usually run in pairs over two, so in fact it's 32 times more.

So, the speed of oxygen in the atmosphere will be root 32 less than the speed of hydrogen in the same atmosphere.

But let's try this for the Earth.

The temperature is around 290 kelvin, about 17 centigrade, and let's take hydrogen. So, let's assume there's hydrogen in the Earth's atmosphere originally, then the mass of that is 1.66 times 10 to the minus 27 kilograms.

Boltzmann's constant is 1.3 by 10 to the minus 23, plug those all into here and we get a velocity of about 2.7 kilometres per second.

Very fast. A bullet might do one kilometre a second from a high velocity rifle.

If we plug in oxygen, say, or nitrogen, so oxygen has a total mass of 16, but if always goes around in the form of O2, so the mass is actually that of a molecule which is two times 16.

So, for hydrogen, that's velocity, for oxygen, that's going to be much lower and that comes out as about 0.5 kilometres per second.

It's still very fast, this is actually why air pressure is so strong.

You'll be constantly banged into your skin, molecules travelling at this speed, twice as fast as a bullet, and that's the cumulative effect of all those impacts as what causes air pressure.

Okay, so that's the first part. We now know roughly how fast the molecules are going, you can see that if the temperature is higher, they'll go fast, and the lighter molecules go faster than the heavy molecules.

How fast do you need to go to escape? Well, once again, let's take our planet, and we'll assume that the molecule is going straight up at some distance from the centre of the planet R, this is now a straightforward potential kinetic energy problem.

So, to begin with, it's kinetic energy is one half MV squared and that's got to be overcome the gravitational potential energy, so that's got to be more than G, mass of the planet, mass of the particle, over R, the gravitational potential energy.

So, if it's got this, it'll be able to escape.

So, let's rearrange, so we get that mass of the particle cancels this time.

Take the two over to this side so you end up with V squared equals two GM over R, take the square root of both sides, you end up with V equals root two G mass of the planet over R.

Now, let's try this for the Earth.

We'll use R over the top of the atmosphere, so the surface is about 6400 kilometres from the middle of the Earth, so R, this gives me about, let's bet about 100 kilometres up, so 6500 kilometres roughly speaking, doesn't make much difference.

The mass of the Earth is six by 10 to the 24 kilograms.

G is gravitational constant, 6.67 times 10 to the minus 11, plug that all in and so it comes out as about 7.8 kilometres per second.

So, that's an interesting number.

It's about three times the speed of the hydrogen atoms and more than 10 times as fast as oxygen molecules.

So, the face value that would seem to imply that neither hydrogen nor oxygen could escape from the Earth. So, we should have an atmosphere that's full of both hydrogen and oxygen.

Given that hydrogen is so super-abundant in the universe, that means that our atmosphere should be mostly hydrogen, just like Jupiter's atmosphere.

That would be a pretty inflammable combination.

However, you have to bear in mind that not all atoms and molecules move at the average speed.

Worked out at the average speed of hydrogen was 2.7 kilometres per second, but some hydrogen atoms are moving much faster than the average and some will be going much slower, and it turns out that an appreciable fraction will be going at three times the speed of the average and they will therefore be able to escape.

So, over time, a tiny fraction of the hydrogen can escape and keep escaping over billions of years until there's none left.

But, with oxygen, it would have to be going more than 10 times as fast as the average and essentially no molecules are doing that, so the oxygen can stay.

So, it looks like this can explain why some planets have hydrogen atmospheres and some don't.

V9.8 PAUL: So one thing I'd like to know is do these planets have mountains.

I'm a sucker for these big fantasy novels with these huge mountainous landscapes in the front.

I'd love to have an exoplanet with enormous mountain ranges, 100 times bigger than anything on Earth.

BRIAN: Well, we know that the mountain ranges on Earth are formed by , where, for example, the Indian subcontinent goes into Asia and produces the Himalayas.

Or volcanoes, those can make big mountains here on Earth.

Or Olympus Mons, for example, on Mars.

PAUL: For all these things, we need a molten interior of the Earth.

And of course, the planets start off hot with lots of lava.

But as you'd imagine, as time went on, they'd cool down and solidify, as happened, to a large extent, on the moon.

What keeps the Earth molten inside is actually trace amounts of things like uranium inside it.

There's not very much of it mixed in with it, but there's enough that as decays, the nuclear fission generates heat and keeps the inside of the Earth very molten and therefore allows us to still be having volcanoes and plate tectonics 4.6 billion years after it formed.

BRIAN: Yeah, and so I think there's a pretty good reasons to believe that most planets will have some of that radioactivity. Because when we look across the Milky Way, most of the relatively young stars have similar abundances of things like uranium to our own sun.

And so that uranium is always going to be sort of part, and it tends to, through chemical processes, conglomerate in one spot, where we expect the Earth to be.

But there is the chance-- because we think the process, which is called the rapid process of neutronization, probably occurs at very funny mergers of neutron stars, like we talked about in one of the earlier courses.

And that process will produce large amounts of uranium sometimes.

So there's probably stars that have huge amounts of gold and uranium and all sorts of other interesting things.

So they would have a very liquid crust compared to ours, really hot, and stay hot for a long time.

PAUL: So the idea would be one of these particular supernovae might go off and, given time, the stuff it squirts out would get mixed thoroughly.

That's where we come from.

But maybe you could get a giant molecular cloud right near one of these things, get a really heavy dose of these heavy elements, and then the parents that formed out of that would be quite interesting.

BRIAN: Right.

And so one of the other interesting things to think about is that we talk about the idea of super- Earths.

These are bigger ones.

So you're going to have the same surface area, a slightly larger surface area, much bigger volume.

And so that radioactivity, which is keeping the thing hot, is going to work better in the super-Earths than the Earths.

So do you think that would be a place to go look for huge volcanoes and huge Himalayas? PAUL: Well, there's a problem with this.

It turns out that you actually can't make mountains much bigger than Mt.

Everest on Earth simply because rock isn't strong enough.

I mean, Mt.

Everest is what? Just under 10 kilometers high.

And if you tried to make it twice as big, the pressure of all that rock would actually liquefy the rock at the bottom and cause it to flow away.

So it turns out that on Earth, unless you start building mountains out of diamonds or something, you really can't make things much more than about 10 kilometers high, no matter what you do in the way of volcanoes. And so maybe on the super-Earths, the gravity is going to be much stronger, and so even though you've got huge amounts of volcanoes and lava and so on, maybe it can't do anything.

Let's actually calculate how limiting this effect of gravity is on the formation of mountains on different sorts of planets.

BRIAN: OK.

PAUL: OK.

So let's imagine we have a planet.

And there's a mountain.

And the planets pulls on the mountain with some force F.

And we know there's a limit to the force beyond which the mountain's going to blob away and become molten and disappear.

Now the force is going to be given by GM of the planet M of the mountain over r squared, where r is the distance from the center of the planet to the mountains.

That's the radius of the planet.

And we know that's going to give us a limited size.

So we can imagine that the height of the mountain is going to be proportional to 1 over this force.

So the bigger the force, the smaller the mountain.

So it's going to be proportional to r squared over the mass of the planet.

So that's telling us that a large planet should have bigger mountains.

In fact, if the planet goes twice as big, the mountains should go four times as large.

Does that work? Well, not really.

The big planets in our own solar system are likely to have no mountains at all.

It's the small planets like Mars that have big mountains.

So what's going wrong here? Well, it's probably this mass down here.

If you assume, for example, that all planets have 100 the same density-- so you're looking at, say, rocky planets-- then mass is going to be the volume 4/3 pi r cubed times the density.

So that's proportional to r cubed.

So that means that the height of a mountain is proportional to r squared over r cubed proportional to 1 over r.

So if you've got uniform density, it seems that, in fact, the small planets should have bigger mountains.

Does this work? Well, here is Olympus Mons on Mars.

Mars has got a radius 3 times smaller than the Earth. And indeed, the biggest mountain, Olympus Mons, is about three times higher than Mt.

Everest.

Even smaller things, like this asteroid, 433 Eros, have even bigger lumps on them.

In fact, you could almost say one definition of an asteroid is something small enough that the mountains could be the same size as the asteroid itself so they look significantly non-spherical.

V9.9 Alright, Paul. This is an amazing field that's changing rapidly and we've learned a lot of things. Some stuff that we really didn't expect.

So, let's think about and summarise what we've learned.

-Yep, so I guess the first planets were the ones discovered from around pulsars. And they're neat but weird. The first, what we describe as more normal planets, were discovered by the radial velocity technique and that started off by finding hot Jupiters, but now it's mostly discovering these eccentric giants.

And it looks like maybe 20 to 30 percent of solar systems have these things...

-And when you say eccentric, you don't mean weird, do you mean they're going in orbits that are elliptical as opposed to circles? -I mean, they might be weird. We don't know.

But they're in weird orbits. So, these are things with sort of gas giant masses, down to neptune masses or even super earths but in orbits... some of them are nice and circular, like jupiter, but most of them are in more eccentric orbits. Reasonably quite common.

-Right. And so, that's a place where having more and more time really allows you to improve things, but when we say more and more time, we mean lots of time. Like years or even decades.

-Yeah. So, the way the radial velocity field is going is they've now got the precision down to slightly below a metre per second.

And I don't think they'll do much better than that because the surface of the stars jitter around at that sort of level...

-Due to asteroseismology, and sun spots, and all sorts of other stuff.

-Yeah. So, in some sense, no matter how good your telescopes get, you're going to be limited by these jitter of the stars. Which means you're never going to be seeing really small planets, except around very small stars like we've just been talking about. So, where you're going to go is you're going to look at more stars and, in particular you're going to keep this metre per second precision and observe for longer. So, you can start seeing things with that accuracy further and further out.

At the moment they've been going for a mere 10 or so years and they're starting to see jupiter analogues. So, presumably they start getting 20 years, 30 years of data, especially with the sort of metre per second precision, they're going to start seeing more of these things further out.

-Okay. Very good. So, that's one way to go forth and it will continue to be an important part. Partially, because it's also a good way of just testing to make sure something else isn't happening when you discover them, for example: using transits. So, transits of course, are really blossoming now. But we tend to find things that are really close in preferentially.

-Yes, and just this morning there was a press release talking about a planet that's the closest match to the size of the earth and the density of the earth that had been seen.

But it was incredibly close in and so a temperature of thousands of degrees on the surface.

-But, it was kind of cool because it has exactly the same density, 5 thousand 5 hundred kilograms per metre cubed, which is the same as the earth. So, that is interesting there seems to be something similar.

-So, where's the future for transit surveys? -Well, it strikes me that, you know, with Keplar being in space now, its mission finished, it's going to be really hard to work at earth size planets from the ground. The atmosphere... even with adaptive optics, you really can't take out that variation of brightness well enough to compete with space. But there are plans, of course, for a new satellite called, Tess. Which is going to be like Keplar, except for it's going to look over the entire sky at all the bright stars.

-And the idea of looking at bright stars is if you do find something going around them, it's relatively easy to follow up by radial velocity and measuring the map.... measure the mass and also look at the secondary transits and start measuring what they're made of.

Wait till it goes in front and try look for dips in the spectrum.

-But there's another thing that's interesting about bright stars; is they preferentially are the nearby stars. And so that means we can also use these for targets for direct imaging, because that means the objects are going to be further out and easier to see and brighter than otherwise.

-And it could be that these are going to first things colonised by the human race when we develop interstellar travel, a thousand years from now.

-So, in some sense that's very exciting for the future. It's going to be probably the end of this... in 2020 before we start being able to do this and this will be worked with the new giant telescopes, which are better at direct imaging.

-Yep. So, what we're learning at the moment from the transit surveys is mostly; the super earths really close in. This new survey will find maybe even smaller things around nearer stars and maybe we might start seeing things further out. But no matter how we do it, the radial velocity technique is going to be biassed towards close in things. Tess is supposed to look at 500,000 stars and so you're going to get a few things further out, but the odds are really against you.

-So, the radial velocity technique is biassed to things close in. The transit technique, also biassed towards things close in. So, we're kind of stuffed in terms of getting a full view of what's gong on. And the other problem of course we have is when we're looking at these nearby stars, which are in some sense the most interesting, for the transits, which is good at finding small things which Tess will find, you really only have that 5 percent chance of the orbit been lined up. So, for every object we see we're missing probably 19.

-So, Tess should find a lot of interesting things but it could well be that the closest and most interesting ones are just going to be missed simply because they're not edge on enough and they're too small to sharpen the radial velocity approach. -So, if we get direct imaging right, that really doesn't have any of these biases. It's hard to see the close in ones, but it's pretty good at seeing the ones out and so, nearby stars, big telescopes, adaptive optics, we have the potential of moving in and really seeing everything that's interesting.

-Yes, and the direct imaging is one field where bucket loads of money are being thrown at it, in terms of bigger telescopes and better adaptive optics. So, this could be the one over the next 10 or 20 years that we're going to see the most progress and if they can actually start directly imaging smaller planets, closer in, that aren't so young, that could be very interesting. At the moment, of course, they can only pick up things that are gas giants a very long way out and very, very young.

So, it could be that the really neat, near planet is an earth like thing and might be around a star that's 4 billion years old, just like our sun. So, it's cooled down and not going to show up with these things. So, finding things like that is going to be a formidable challenge, even for the next generation of telescopes.

-So let's just briefly talk about the next generation of telescopes. We have, here in Australia we're part of the Giant Magellan telescope consortium. So, that's 7, 8.2 metre mirrors put together that makes, sort of a 25 metre telescope.

-Yes, and then there's the TMT 30 metre telescope, which is a consortium of California, Canada, Japan, which would have a more like Keck, with butted together segments.

-Yeah. A bunch of little hexagons that you put together and that's a thirty metre, given the name, very original, Thirty Metre Telescope, TMT. So, that's a thirty metre telescope that's planned to go in Hawii on top of Mauna Kea.

-And the Europeans are also looking at a telescope.

-Right, so that's the extremely large telescope, equally unique name, ELT, the European ELT, and that's really ambitious. That's like TMT with all these hexagons put together, but to be 39 metres across. So, that's the grand daddy of them all. But the main problem between now and these telescopes seems to be money, because they're very, very expensive. So, I think we're just going to have to wait to see how these things pan out and how big they really end up being, because big is expensive when it comes to telescopes.

-And perhaps the most interesting statistics for these things, about solar system like things, have come from microlensing. Where do you think that field is going to go? -Well again, I think that time is on our side.

We have these amazing survey telescopes, like our own Sky Mapper here, that have huge digital cameras that can monitor tens of millions, or even hundreds of millions of stars at a time. And really with these microlense kits, the more you can look at, the better you do and then it's just time, and we wait. Now, you're going to be biassed towards things around earth or maybe a little further out, but in that sense those are really interesting. The problem is, the objects you find are so far away, you can't do the direct imaging on it.

So, I think it's good to find out the statistics, but again, it's a complementary probe to everything else we're talking about.

-Well, what would be really nice though would be to actually have such a good telescope so we could look at the continents and the cloud patterns and do all that sort of stuff.

So, let's calculate what it would need to actually do something like that.

V9.10 Okay. So, what sort of telescope would we need to see continents on an exoplanet? The idea is that we have some exoplanet, let's say it's a very near star about 10 lightyears away, and it's got continents. And let's say the continents are about a thousand kilometres. And let's say the continents are about a thousand kilometres across.

That's sort of being a rough continent scale, at least on Earth. And we want to observe. And we want to observe them from the earth.

So, here's our telescope.

We won't be able to see is a continent here, there's an ocean over there. Now, there are two things that we'll need to be able to achieve that. Firstly, is that we have enough angular resolution to tell the difference between light coming from the continent and light coming from just off the side of the continent.

So, we need angular resolution. But, there's a second thing that we need. We need to actually be able to pick up enough light to be able to see the continent. The continent is reflecting some light and those photons are bouncing off. We need enough of the photons to arrive here to detect something. If it's only one photon in a hundred years, it's going to take a very long exposure time to see anything.

In fact, the continent would have rotated around, so you can't see it at all. So, we need enough photons to reach us.

So, let's look at that in turn. Let's start off with the angular resolution.

So, we need to achieve an angle theta, which is a thousand kilometres; 10 to the 6 metres here, and 10 lightyears; which is 10 to the 17 metres there. So, if you remember the small angle approximation theta in radians is just 10 to the 6, over 10 to the 17. So, that's 10 to the minus 11 radians. If you convert that into degrees by multiplying by 180 over pi, then to arc seconds by another 60 times 60, you find that it comes out at about 2 micro-arc seconds.

If you remember, a ground based telescope can achieve maybe 1 arc second or 0.6 of an arc second, space telescopes get down to about 0.05. So, this is way, way better than any telescope on space or the ground or with an optics search even at the moment.

So, how are we going to do it? Well, let's say we use a space telescope, so it's going to be very good at diffraction or it's going to have very good adaptive optics. We know that the limiting theta for diffraction is given by the wavelength over the diameter of the telescope. So, we know theta. So, let's say we're working at optical wavelengths. So, wavelengths... if you're working at smaller wavelengths, then you get a better resolution, but there's not much point working at x-ray wavelengths because continents don't normally emit x-rays. So, we're kind of stuck with the wavelengths that scatter light out, which means optical. So, let's assume we're working at about half a micron, which is sort of greenish light. So, 10 to the minus 6 metres. So, then the diameter of the telescope has to be equal to, we have D up there lambda, so; 5 by 10 to the minus 7, divided by the limiting angle; 10 to the minus 11, which comes out at about 50 kilometres.

So, we need a telescope that's 50 kilometres across. An optical telescope that's 50 kilometres across. The biggest in the world at the moment are of 10 metres. Biggest in the next generation will be maybe 40 metres. That's an awful long way beyond anything we can do at the moment. This is a problem radio astronomers had for a long time. They needed telescopes of enormous sizes.

What they'd do is, instead of having one telescope that was say 10 kilometres across, they'd have a small bunch of small telescopes spread over many kilometres. That's what's called an interferometer. And they combine signals from the different telescopes to synthesise much bigger ones. And in principle that can work in the optical as well. In fact, there are a number of test beds around the world, Optical interferometers that do this. So, in principle, 50 kilometre diameter telescope, one mirror 50 kilometres across with an accuracy of a 10th of a wavelength of light, sounds pretty scary, but in principal you could have a bunch of small telescopes scattered over 50 kilometres, maybe floating in space, beaming a light together where it's combined by some interferometer in the middle. So, maybe it's not totally ridiculous for a future free-floating space telescope. So, that's the angular resolution limit. But, that's going to do us no good if we're not picking up enough photons. So, how many photons are we going to pick up? So, you've got a continent and it's maybe got an area of 1000 by 1000 kilometres.

So, that's about 10 to the 6 squared...

10 to the 12 square metres. And it's reflecting sunlight. So, we've got the sunlight coming in. Let's assume it's got as much sunlight hitting it as we have on the earth, which is about 1 kilowatt per square metre, actually 1.3 kilowatts per metre is the solar constant.

So, that's about a thousand watts per square metre times 10 to the 12. So, that means the continent has a luminosity, assuming all light is reflected, of 10 to the 12, times 10 to the 3 which equals 10 to the 15 watts. It'll probably be less than that in practice because some light will be scattered off the atmosphere and it won't reflect everything. But maybe it would if it was an icecap. But that'll give us a rough figure. So, we can therefore work out the flux at the earth, which is given by the normal equation of luminosity over 4 pi distance squared. This D is not the diameter of the telescope, it's the distance to the planet, which we're receiving as 10 lightyears away. And that comes out as about 10 to the minus 20 watts per metre squared.

Which is very small. We're not going to power a light bulb with the solar electricity from that.

But how many photons is it? Photons, after all are pretty small themselves. Well, the energy of a photon is equal to h nu, where h is the plank constant and nu is a frequency.

Frequency is also wavelength divided by the speed of light... I'm sorry, speed of light divided by the wavelength.

This is because you've got a wave... the frequency tells you how many crests go past per unit time. They have a wavelength, lambda. So, lambda... number of waves... length of a wave times the number of waves per second, the frequency must equal the speed of light. Thus, frequency equals speed of light over the lambda, the light wavelength.

So, that comes out for optical light at an energy of about 4 by 10 to the minus 19 Joules per photon. Which is not that different from this. So, what that means is per square metre of telescope, you're going to be picking up a photon from this continent every two or three seconds, roughly speaking. Now you're going to need a hundred photons to say you've detected something. Possibly more if there's a background signal. But what this means is, the number of photons is not particularly limiting. Even with quite a small telescope with a few square metre area will pick up your hundreds of photons in less than an hour or so. So, enough photons isn't a problem.

Angular resolution is a problem. So, probably the best solution is a whole bunch of small telescopes spread over some big distance in space, 50 kilometres or maybe a bit bigger, combining the light in some sort of interferometer.

Telescopes individually don't have to be very big because you're getting enough photons in quite a short time. So, these might only be a few square metres. So, not doable now, but free-floating telescopes in space might be able to image this in the future.

V9.11 So, we've talked about a whole bunch of techniques here from: Radial velocities, Transits, micro- lenses, direct imaging. Could there be any new techniques, actually different techniques that we haven't tried yet? Another way to find these planets and other stars.

-Well there's one that's hanging around that hasn't quite materialised, which is .

That's looking at how somethings position changes over time. So, in the same way that a planet causes a stars velocity to wobble, of course, the star itself wobbles in the sky. And it may seem crazy but, with the incredible resolution that we can do, especially with interferometry or space space missions, we can get to the point to see that wobble and the wobble is nice, because if you have the wobble this way and the velocity this way, then you don't have that problem of the inclination, you do know it. So, you can get rid of that problem.

-Yes, and hopefully in a couple of months the European Space Agency are going to be launching the space probes. By the time you view this it should be up. Hopefully, it doesn't blow up on the launch pad. This space probe is designed to measure the positions of stars very accurately, but its primary goal is to measure the positions 6 months apart as it goes around the sun and therefore use parallax to measure distances. So, it should measure distances to hundreds of thousands of stars in our galaxy, and that's fundamental to standard astrophysics. But also it might well pick out these side ways wobbles of some fraction. And they're estimating they might be able to find a hundred planets with this technique.

-And these will be the really nearby planets, presumably. So, you'll really get a good snapshot of these nearby planets using this technique.

-The sort of planets it's going to find are the same sort of things the radial velocity approach finds, because once again you look at the reflex motion of the star. It's all the same bias that's happened. So, it's not going to a new population of planets... probably, though I'm very happy to be surprised. But it'll give us the full three dimensional motion of these things that you can follow up with radial velocities.

-So, that's exciting. Now, one could take this the next stop further and you could do a dedicated mission for planets where you would literally do the interferometry. So, you'd actually... probably can't afford to put a big enough telescope in space, but you could imagine putting separated mirrors in the same way that radio astronomers combine the radio waves from two telescopes and do the wave interference to figure out how big something is. You could imagine doing that in optical light in space and really getting these measurements to be incredibly fine. -Yes, indeed a number of proposals have been made for things. There was one mission called the SIM, for Space Interferometry Mission, which had multiple mirrors on a boom and it got quite a long way through the design phase before it was cancelled by NASA. And they're even more ambitious things like the finder or the '', which were actually free floating space telescopes that would... so you'd have a big telescope floating in space over here, then another one might be thousands of kilometres away and they would bounce lasers back and forth between them to measure their precise position and bounce the light they receive between them and combine to the middle to get this incredible accuracy.

Very megalomaniac telescopes -So, those are serious futuristic type facilities.

Maybe not going to happen in the next decade or two, but technologically it is possible.

So, one could imagine building these things to really get down and probe nearby solar systems and really see what they're made out of.

V9.12 So, let's wrap up this course. What lessons have we learned about the whole progress of science from it all? I guess to me, the most striking thing is how unexpected this all was. No one saw Exoplanets coming as a giant field. And it's just been one big surprise after another. In fact, it's very worrying making this course cause I'm pretty convinced that by the time it goes live 3 or 4 months from now, let alone when you view it in the second or third year we run it, huge chunks of what we've talked about are going to be obsolete.

-Yeah, that is a problem with a very exciting field like this. You know it's quite remarkable because you and I both trained as Cosmologists, and Cosmologist was cutting edge and pretty much anything you did was exciting, and there were these people 'beavering' away, making very careful measurement after measurement in what looked like... you know... doing it for the sake of doing it. They were being careful, they were working hard, but they had no expectation of making a discovery of planets. They had interesting things they wanted to ask. And yet, through that hard work, that diligence, they were able to make what is arguably the discovery of the century: Planets beyond our own Solar System and that is leading to this explosion of activity now.

So, sometimes it's good to be on the really exciting stuff; Cosmology, like it was for us, but on the other hand there's huge benefits because the unexpected excitement often comes from the least expected places. So, I think that's one of the lessons here.

-And it's a lesson that generally governments don't want to hear: that you can't predict where science is going to go. Governments always like to have ten year plans and "we're going to invest in this and that", but the whole history of science is full of big surprises, because of course if we knew the answer then it wouldn't be science, we wouldn't know what's going on. So, in some sense you have to do a whole bunch of stuff and a whole bunch of not very sexy stuff, because most of that not sexy will remain not sexy, but every now and then something that revolutionises the world is going to come out of it.

-That's right. So, you have a portfolio of stuff where you just sort of let things go and you work on whatever and then you have your ten year plans for the stuff... like, you know, we wouldn't want to just not be organised in what we're doing in planet discovery, now that we know what's going on. And now we are quite organised. But it's really important to keep that basic curiosity driven stuff going, even within something like Astronomy, which most people would say is curiosity driven, period. Even the planet stuff we do.

So, for me it's quite interesting because although trained as a Cosmologist, my Nobel Prize is in Cosmology, planetary astronomy is so exciting; going out and looking for these newer solar systems, that I'm putting considerable effort now in this area and in some sense so are you.

So, it really is, I think, one of the most exciting and promising areas for the coming decades for astronomy and for mankind to learn more about the universe we live in.

Conclusion [PAUL] So this whole story of exoplanets over the last fifteen years has been a pretty wild ride, an incredible flood of data, and one surprise after another, new methods coming in, new results.

[BRIAN] And it's really far from over, because every week goes by with a new discovery, and one thing is clear is that planets are everywhere in the universe.

[PAUL] and that our own Solar System is far from being typical.

[BRIAN] That's right, so, I think it's good to stay tuned and keep watching what goes on, and you can continue to learn in this field well beyond this course.

[PAUL] Hopefully this course has given you the basis to be able to actually understand what's being going on in the media at a deeper level.

Now if you enjoyed this course, this is only one of the four courses that together make up the ANU, Australian National University's first year astrophysics unit.

You can now go on and do any of the other three; there's an introductory course on greatest unsolved mysteries of the universe and that doesn't overlap with this course very much, so you can certainly go back and do that, There are also two more specialised courses, the next course to run will be on the violent universe, the things that go bang in the night.

And then there will be a course on cosmology.

[BRIAN] So we hope you've enjoyed learning about the cutting edge of exoplanets and that you've enjoyed learning with us about this exciting area of astrophysics.

[PAUL] It's been a great pleasure to teach you, and we hope to see you again in some of the other parts of this course.