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Astronomy Div C 2015 Help Session V1

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Astronomy Div C 2015 Help Session V1 1 2015 Div. C (High School) Astronomy Help Session Sunday, Feb 22, 2015 Stellar Evolution and star and planet formation Scott Jackson Mt. Cuba Astronomical Observatory • SO competition on March 7 th . • Resources – two laptop computers or two 3 ring binder or one laptop plus one 3 ring binder – Programmable calculator – Connection to the internet is not allowed! – Help session 2 weeks (Sunday, Feb 22) before competition – at Mt. Cuba Observatory 2 3 Study aid -1 • Google each object, – Know what they look like in different parts of the spectrum. For example, the IR, optical, UV and Xray – Understand what each part of the spectrum means – Have a good qualitative feel for what the object is doing or has done within the astrophysical concepts that the student is being asked to know. 4 Study aid - 2 • Know the algebra behind the physics – Just because you think you have the right “equation” to use does not mean you know how to use it!!! – Hint for math problems: Solve equations symbolically BEFORE you put in numbers. Things tend to cancel out including parameters you do not need to have values for. – Know how to use scientific notation. 5 The test – 2 parts • Part 1 – multiple choice and a couple fill in the blanks • Part 2 – word problems for astrophysics there will be some algebra Solve the equations symbolically first then put in numbers!!!! Hint: most problems will not need a calculator if done this way Exo Planets • ~25 years ago, planets and solar systems thought to be unique – Now, stars not having planets may be unique • What have we so far discovered? • Solar systems (stars with more than one planet) • Hints of atmospheres • How they are “discovered” • How astronomers estimate – masses – distance from the stars they are orbiting – densities • How and why they are formed. • Solves a basic “problem” in astronomy – conservation of angular momentum and a stars rotation rate How to define “planet”? Mass, and the way in which it formed 1. Star: massive enough for nuclear fusion H He; M > 0.1 Msun. Light comes from heating by nuclear fusion. Formed by cloud collaspe 2. Brown dwarf: mass too small for nuclear fusion. M < 0.1 Msun (~ 80 Mjup) Light from from slow contraction, release of gravitational energy. Probably formed in a similar manner as stars. 3. Planet: Upper limit usually taken as ~ 10 - 20 MJup. Lower mass limit not too relavent. Mars counts as a planet (0.1 Mearth), Pluto doesn’t. Most of their light is reflected light from their parent star, plus a smaller amount coming from their own thermal infrared radiation. Formed from protostellar disk or disks surrounding young stars. Exoplanets classified by what they resemble most in our own solar system. Jupiters (or “gas giants”); Neptunes (~ 20 Mearth); and Super-Earths (~ 5-10 Mearth). When we refer to (yet to be discovered) extrasolar planets whose masses are similar to Earth, they are called “terrestrial-like” or “Earth-like” or “rocky” planets Current Planet Counts •Total Exoplanet Discoveries 4826 •Confirmed Exoplanets 1523 •Exoplanet Candidates (Keplar) 3303 * Exoplanet candidates are discoveries that have yet to be confirmed as actual exoplanet discoveries. These candidates are 80-90% likely to be actual exoplanet discoveries. http://exoplanets.org/ http://exep.jpl.nasa.gov/presentations/blackwoodJHU/JHU_Astrobiology_Blackwood.pdf http://exep.jpl.nasa.gov/presentations/blackwoodJHU/JHU_Astrobiology_Blackwood.pd f ~1500 confirmed discovered (and growing) Lots of hot Jupiter's-- Large planet traveling close to their star. First one discovered ~15 years ago. ~1/3 of sun like stars have earth like planets(!) http://exoplanets.org/table Solar Systems? – yes! • About 17% of stars with planets contain more than one planet (artist diagram of 55 Cancri next to our solar system is below) http://en.wikipedia.org/wiki/Image:Extrasolar_planet_NASA2.jpg Atmospheres? – Yes! Detection • Astronomers can not easily “see” an exoplanet directly • Does not shine • Glare of the star hides stars • Must use “indirect” methods** • **Gliese 229b is one exception Detection Direct imaging • “Observe” the planet from reflected light from the star • Star is generally too close and too bright • Need to block out glare from star to image planet Using Hubble space telescope http://planetquest.jpl.nasa.gov/page/methods Detection • Astrometry: • Stars move in straight line • Wobble or drift from straight line is from the pull of a planet • Astrometry precisely measures the star's position in the sky and sees the wobble • Simulation at right is if the star did not move straight through sky • Ability to detect depends on 1. Distance to star (closer the better) 2. Lots of time to observe (years) 3. NOT edge on 4. Massive planets away from small star http://en.wikipedia.org/wiki/Extrasolar_planet#Detection_methods • Microlensing • The star (with the planet) goes Detection directly in front of a very distant object. • The space is curved around the star, the light from the distant object is magnified or “Microlensed” • Creates a very symmetrical brightening of the distant object • If the star has a planet, there will be strange looking spikes in the light curve • Can only be observed once (No repeats!) http://planetquest.jpl.nasa.gov/documents/RdMp272.pdf Detection • Doppler method: • As the star is pulled by the planet, its speed varies (even though we do not see the wobble by astrometry) • The change in speed is detected as a change in color – the Doppler shift • The spectrum of a star has well defined lines in it that move like the simulation. • Remember the train whistle • Ability to detect depends on: 1. No need to have the star close to us 2. Best if edge on (inclination ~0) 3. Heavy planet close to star (hot Jupiters) 4. Small star http://exoplanets.org/doppframe.html Transit method: • If the plane of a planet’s orbit is along our line of sight, the planet Detection will go in front of the star • Its like an eclipse – can measure diameter of the planet • The observed brightness of the star drops by a small amount. • The amount by which the star dims depends on its size and on the size of the planet. • ***Combined with other techniques, astronomers can determine the mass and density of the planet – Gas giant? – Terrestrial planet? • Best if: 1. Star is big 2. Planet is big (Hot Jupiters) 3. Planet is close to star 4. View orbit nearly edge on http://www.iac.es/project/tep/tephome.html Limit of techniques • Plot has – Size of orbit or orbital period on horizontal axis – Mass of planet on vertical axis. • Snow line is where planets will condense out water or ammonia as a solid (cold!) http://www.mpia.de/homes/ppvi/chapter/fischer.pdf http://exep.jpl.nasa.gov/presentations/blackwoodJHU/JHU_Astrobiology_Blackwood.pdf Measuring mass (and density) of exoplanets Need to use Doppler method and the Transit method • Measure distance to star (later) and using apparent magnitude get luminosity (assumes the star is a normal star) • Use luminosity to determine stars mass (m1, suns) (mass needs to be consistent with star’s spectral type) • Doppler or Transit method gives you periodicity of the orbit (P, measured in years) • Use Kepler’s law (next slide) to determine the distance between the planet and star (next slide) “a” in AU [assume mass of planet is much less than the mass of the star, i.e., m2 << m1] This is a plot of the log (base 10) • Use the Doppler method to measure velocity of of a stars luminosity (L) relative to the luminosity of our sun on star (v1) as it orbits around the center of mass. the y axis as a function of the Use star’s velocity (v1) to determine the mass of mass of the star on the x axis the planet (m2 or mplanet ) using (relative to our suns mass). So m1 * v1 = m2 * v2 where v2= 2*pi * a /P a star that is 100x of our sun will have a mass that is ~3.7 times that of our sun 22 Kepler’s laws 1. Orbits are ellipses with sun at one focus 2. Equal areas swept out in equal time 3. Harmonic law: Square of the period (P) is proportional to the cube of the semimajor axis (a). -- Gold standard for determining masses in the universe – exoplanets and binary stars. Kepler’s law 2 3 P = a / (m1 + m2) P = orbital period (years) a = Distance between the two bodies (expressed in astronmical units [AU] – distance from earth to sun) 1 AU = 107.5 sun diameters or 215 sun’s radius m , m = mass of the two bodies orbiting each other (solar masses) 1 2 23 Density of hot Jupiters ~ 1 gr/cc Density of terrestrial planets (like earth) ~ 5 gr/cc 24 • “Habitable zones” is the distance from a star that is the right temperature to support life as we know it • Depends on the size of star and stage of life. • Temperature allows for liquid water (Earth’s T average = about 15C) • How do we estimate a planet’s temperature Life?? Energy balance to estimate a planets temperature Stefan-Boltzmann Law (black body radiation) for the star: σσσ 4 – Energy/time/area = T star σσσ = a constant (Stefan Boltzmann constant) Tstar = absolute surface temperature of star (Kelvin) πππ 2 • The total surface area of a spherical star is = 4 R star • The total energy output by a star, Stellar Luminosity (energy emitted per second) is: πππ 2 σσσ 4 – L = 4 R star T star (this is the same L as you saw before) • BUT the energy that is intercepted by the planet with a cross sectional area πππ 2 of R planet is reduced at the planet distance to the sun (“a”) since the total energy output is “spread out” on a sphere that is 4πππa2 in area πππ 2 πππ 2 • So energy area intercepted by the planet is L/(4 a ) * R planet • But some of this energy is reflected by the planet’s albedo, x (reflectivity) and so the intercepted energy is reduced by a factor of (1-x) πππ 2 σσσ 4 • The planet re-emits this energy as a black body as 4 R planet T planet πππ 2 σσσ 4 πππ 2 πππ 2 • SO… 4 R planet T planet =(1-x)* L/(4 a )* R planet 26 Solve for the temperature of the planet….
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