Astrophysics: experimental astronomy + theoretical understanding of universe – cosmology. Solar system is a collection of planets, moons, asteroids, comets, and other rocky objects travelling in elliptical orbits around the Sun under the influence of gravitational force. Sun: star formed from a giant cloud of molecular hydrogen gas that gravitated together, forming clumps of matter that collapsed and heated up. A gas disc around the young, spinning Sun evolved into the planets about 4.6 × 109 years ago. The planets move in elliptical orbits with only Mercury occupying a plane significantly different to that ~ 4.5 billion years ago, the Earth’s moon is of the other planets. believed to have been formed from Asteroid belt situated between material ejected when a collision occurred Mars and Jupiter, between a Mars-size object and the Earth. contains millions of asteroids. Jupiter is the biggest planet in terms of Kuiper belt, similar to asteroid mass and volume. Mercury is the smallest. belt but much larger; beyond Neptune. Asteroids and comets are both celestial In addition to asteroids it is the bodies orbiting our Sun, and they both can source of short-period comets have unusual orbits, sometimes straying and contains dwarf planets close to Earth or the other planets. They are both “leftovers” — made from Comets are irregular objects a few kilometres across comprising frozen gases (ice), materials from the formation of our Solar rocky materials, and dust. Observable comets travel around the Sun in sharply elliptical AsteroidsSystem consist4.5 billion of metals years ago and rocky material. Those of orbits with periods ranging from a few years to thousands of years. As they draw near size less than 300 km have irregular shape because their to the Sun the gases in the comet are vaporized, forming the distinctive comet tail that gravity is too weak to compress them into spheres. can be millions of kilometres long and always points away from the Sun.

Star is a massive body of gas held together by gravity, with fusion going on at its center, giving off electromagnetic radiation. There is an (hydrostatic) equilibrium between radiation and gravitational pressure. This equilibrium is gained through nuclear fusion which provides the energy the star needs to keep it hot so that the star's radiation pressure is high enough to oppose gravitational contraction. This applies to all layers of a star. The fusing of hydrogen into helium takes up the majority of a star’s lifetime and is the reason Gravity pulls outer layers in, gas and why there are far more main sequence stars than those in other phases of their life-cycle. radiation pressure pushes them out. Stars initially form when gravity causes the gas in a nebula to condense. As the atoms move towards one another, they lose gravitational potential energy that is converted into kinetic energy. This raises the temperature of the atoms which then form a protostar. When the mass of the protostar is large enough, the temperature and pressure at the centre will be sufficient for hydrogen to fuse into helium, with the release of very large amounts of energy – the star has “ignited”. Ignition produces emission of radiation from the core, producing a radiation pressure that opposes the inward gravitational forces. Star will remain stable in hydrostatic equilibrium for up to billions of years. It is on the main sequence. As the hydrogen is used up the star will eventually undergo changes that will move it from the main sequence. During these changes the colour of the star alters as its surface temperature rises or falls and it will change size accordingly. The original mass of material in the star determines how the star will change during its lifetime. Groups of stars: believed ~ 50% of the stars are part of a star system comprising two or more stars. (Total estimates are higher, with NASA's reporting that up to 80% of all stars are in multiple star relationships. That is true for very massive stars). Binary stars consist of two stars that rotate about a common centre of mass. The ONLY way to find mass of the stars is when they are the part of binary stars. Knowing the period of the binary and the separation of the stars the total mass of the binary system can be calculated. Stellar cluster is a group of stars held together by gravitation in same region of space, formed roughly at the same time from the same nebula. Some clusters contain only a few dozen stars while others may contain millions. Open clusters consist of up to several hundred younger stars; contain some gas and dust; within our , and so lie within a single plane. Globular clusters contain many more older stars; contain very little gas and dust; spherically shaped just outside the in its galactic halo is a (nearly) spherical region surrounding the galaxy (like the diffuse light around the heads of saints, made up mostly of dark matter/ does not emit EM radiation - studied only through its gravitational interactions, in particular, with light passing by, an effect known as "gravitational lensing" the galactic spheroid (stars) the galactic corona (hot gas, i.e. a plasma) the . Constellation is a group of stars that form a pattern in the same general direction as seen from the Earth, but not bound by gravitation. Galaxy is a huge group of stars, dust, and gas held together by gravity, often containing billions of stars, measuring many light years across. Some in isolation, majority come in clusters which could have anything from a few dozen to a few thousand . Milky Way is part of a cluster of about 30 galaxies called the “Local Group” which includes Andromeda and Triangulum. Regular clusters consist of a concentrated core and are spherical in shape. Irregular clusters have no apparent shape and a lower concentration of galaxies within them. Hubble Space Telescope: In between the clusters there are voids that are apparently empty of galaxies. Superclusters – even larger structures observed since the launch of the Hubble Space Telescope Spiral galaxies the most common class of galaxies (both The Milky Way and Andromeda). a flat rotating disc-shape with spiral arms spreading out from a central that contains the greatest density of stars. Belief: at the centre of the galactic bulge, there is a black hole. The spiral arms contain many young blue stars and a great deal of dust and gas. Other galaxies are elliptical in shape, being ovoid or spherical – these contain much less gas and dust than spiral galaxies; they are thought to have been formed from collisions between spiral galaxies. Irregular galaxies are shapeless and may have been stretched by the presence of other massive galaxies – the Milky Way appears to be having this effect on some nearby dwarf galaxies.

Nebulae (stellar nurseries ) are regions of intergalactic cloud of dust and gas. As all stars are “born” out of nebulae. two different origins of nebulae: ▪ nebulae formed in the “matter era” around 380 000 years after the Big Bang. At about this time, neutral atoms are formed as electrons link up with hydrogen and helium nuclei. Dust and gas clouds were formed when these atoms gravitated together. ▪ nebulae formed from the matter which has been ejected from a explosion. nebulae can form in the final, red giant, stage of a low mass star such as the Sun.

Astronomical distances Resulting from the huge distances involved in astronomical measurements, some unique, non-SI units have been developed. This avoids using large powers of ten and allows astrophysicists to gain a feel for relative sizes and distances. The astronomical unit (AU): the average distance between the Sun and the Earth. It is really only useful when dealing with the distances of planets from the Sun. 1 AU= 1.50 × 10 11 m ≈ 8 light minutes 1 parsec (pc): This is the most commonly used unit of distance in astrophysics. 1 pc= 3.26 ly = 3.09 × 10 16 m Distances between nearby stars are measured in pc, while distances between distant stars within a galaxy will be in kiloparsecs (kpc), and those between galaxies in megaparsecs (Mpc) or gigaparsecs (Gpc).

Stars’ and planets’ radiation spectrum is approximately the same as

black-body radiation/ Plank’s law.

Intensity as a function of wavelength depends upon its temperature

Wien’s law: Wavelength at which the intensity -3 of the radiation is a maximum λmax, is: 2.9×10 max(m) T(K)

Luminosity (of a star) is the total power (total energy per second) radiated by an object (star). If we regard stars as black body, then luminosity is: L = A σT4 = 4πR2σT4 (Watts) Stefan-Boltzmann’s law A is surface area of the star, R is the radius of the star, T surface temperature (K), σ is Stefan-Boltzmann constant. (Apparent) brightness (b) is the power from the star received per square meter of the Earth’s surface L b = (W/m2) L is luminosity of the star; d its distance from the Earth 4π푑2 Can be measured, for example, by using a telescope and a charge-coupled device ? IB Internet says by Photometer!!! Explain how atomic spectra may be used to deduce chemical and physical data for stars. 2.9×10−3 •surface temperature of a star is determined by measuring the wavelength at which most of the radiation is emitted: 휆 (푚) = 푚푎푥 푇(퐾) •Most stars essentially have the same chemical composition, yet show different absorption spectra as they have different temperatures. • Absorption spectra gives information about the temperature of the star and its chemical composition. • Doppler shift information of speed relative to earth (red shift → longer wavelength, blue shift → shorter wavelength)

Techniques for determining stellar distances: stellar parallax, spectroscopic parallax and Cepheid variables.

1. Stellar parallax • two apparent positions of a close star with respect to position of distant stars as seen by an observer from two widely separated points are compared and recorded; • the maximum angular variation from the mean, p, is recorded; • the distance (in parsecs) can be calculated using geometry astronomical unit Sun-earth distance 1 AU 1 AU = 1.5 x 1011 m tan p = = for small angles: tan θ ≈ sin θ ≈ θ (in radians) Sun-star distance d 1 AU 1 d = if p = 1 sec of arc, d = 3.08x1016 m defined as 1 pc d (parsecs) = p p(arcseconds)

There is a limit to the distance that can be measured using stellar parallax – parallax angles of less than 0.01 arcsecond are difficult to measure from the surface of the Earth because of the absorption and scattering of light by the atmosphere. Turbulence in the atmosphere also limits the resolution because it causes stars to “twinkle”. 1 Using the parallax equation, gives a maximum range of 푑 = = 100 pc 0.01 In 1989, the satellite Hipparcos (an acronym for High Precision Parallax Collecting Satellite) was launched by the European Space Agency (ESA). Being outside the atmosphere, Hipparcos was able to measure the parallaxes of 118 000 stars with an accuracy of 0.001 arcsecsond (to distances 1000 pc); its mission was completed in 1993. Gaia, Hipparcos’s successor, was launched in 2013 and is charged with the task of producing an accurate three-dimensional map showing the positions of about a billion stars in the Milky Way. This is about one per cent of the total number of stars in the galaxy! Gaia is able to resolve a parallax angle of 10 microarcsecond measuring stars at a distance of 100 000 pc. limits because of small parallaxes: d ≤ 100 pc from Earth d ≤ 1000 pc from Hipparcos d ≤ 100 000 pc from Gaia

2. Spectroscopic parallax: no parallax at all!!!! (a lot of uncertainty in calculations) • light from star analyzed (relative amplitudes of the absorption spectrum lines) to give indication of stellar class/temperature • HR diagram used to estimate the luminosity • distance away calculated from apparent brightness: b = L/4πd2 limit: d ≤ 10 Mpc

Spectroscopic parallax is only accurate enough to measure stellar distances of up to about 10 Mpc. This is because a star has to be sufficiently bright to be able to measure the spectrum, which can be obscured by matter between the star and the observer. Even once the spectrum is measured and the star is classified according to its spectral type there can still be uncertainty in determining its luminosity, and this uncertainty increases as the stellar distance increases. This is because one spectral type can correspond to different types of stars and these will have different luminosities.

3. Cepheid variables are stars with regular variation in luminosity (rapid brightening, gradual dimming) which is caused by periodic expansion and contraction of outer surface (brighter as it expands). This is to do with the balance between the nuclear and gravitational forces within the star. In most stars these forces are balanced over long periods but in Cepheid variables they seem to take turns, a bit like a mass bouncing up and down on a spring. The period of these stars varies between twelve hours and a hundred days. Because they are so luminous it means that very distant Cepheids can be observed from the Earth.

period-luminosity relationship: Cepheids with longer periods are . intrinsically more luminous than those with shorter periods. Cepheids typically vary in brightness over a period of about 7 days.

Cepheid variable stars are known as “standard candles” because they allow us to measure the distances to the galaxies containing Cepheid variable stars. So, to find out how far away Cepheid is: • The apparent brightness is measured using a telescope and CCD to get period • Use graph period-luminosity relationship to find luminosity L • Calculate d from b = L/4πd2 • Distances to galaxies are then known if the Cepheid can be ascertained to be within a specific galaxy.

Cepheid stars are stars that have completed the hydrogen burning phase and moved off the main sequence (see later for an explanation of this). The variation in luminosity occurs because the outer layers within the star expand and contract periodically. This is shown diagrammatically as: (1) a layer loses hydrostatic equilibrium and is pulled inwards by gravity (2) the layer becomes compressed and less transparent to radiation (3) temperature inside the layer increases, building up the internal pressure (4) causing the layer to be pushed outwards (5) During expansion the layer cools, becoming less dense (6) and more transparent, allowing radiation to escape and letting the pressure inside fall (1) subsequently the layer falls inwards under gravity and the cycle repeats causing the pulsation of the radiation emitted by the star.

Class Temperature Colour Stellar Spectra classification system O 30 000 - 60 000 Blue B 10 000 - 30 000 Blue-white A 7 500 - 10 000 White F 6000 - 7500 Yellow-white G 5000 - 6000 Yellow K 3500 - 5000 Orange M 2000 - 3500 Red

The Hertzsprung–Russell (H – R) diagram is a scatte rgraph of stars showing the relationship between the stars' luminosities versus their surface temperature. It shows stars of different ages and in different stages, all at the same time. Vertical axis: luminosity/ luminosity of the Sun (L⊙= 3.839 × 1026 W). Axis is logarithmic and has no unit. The temperature axis is also logarithmic and doubles with every division from right (low) to left (high).

main sequence stars: nearly 90% of all stars

▪ fusing hydrogen into helium, the difference between

them is in mass

▪ during the lifetime of a star its position will move on the

diagram as its temperature and luminosity changes

▪ left upper corner more massive than right lower corner

▪ cooler red stars relatively low luminosity;

▪ hotter blue stars: high luminosity.

Red giants are cooler than the Sun

• emit less energy/m2 of surface.

• higher luminosity means they have a much greater surface

area.

• a much larger diameter than the Sun – “giant” stars.

White dwarfs Supergiant stars are gigantic and very bright.

• remnants of old stars • A supergiant has 100 000 times the power and

• constitute about 9%of all stars at the same temperature of the Sun must have

• energy not produced by nuclear fusion a surface area 100 000 times larger: a diameter that

• very hot when they stopped producing energy, is over 300 times the diameter of the Sun.

• they have a relatively low luminosity • Only about 1%of stars are giants and supergiants.

• a small surface area. • very small, hot, very dense stars • take billions of years to cool down.

• Relationship between the luminosity and the mass: L ∝ M3.5 (Observations of thousands of main sequence stars) L is the luminosity in W (or multiples of the Sun’s luminosity, L⊙ ) M is the mass in kg (or multiples of the Sun’s mass, M ⊙ ). • Even a slight difference in the masses of stars results in a large difference in their luminosities. • For a star to be stable it needs to be in hydrostatic equilibrium: the pressure due to the gravitational attraction of inner shells = the thermal and radiation pressure acting outwards. For a stable star of higher mass there will be greater gravitational compression and so the core temperature will be higher. Higher temperatures make the fusion between nuclei in the core more probable giving a greater rate of nuclear reaction and emission of more energy; thus increasing the luminosity. • The mass of a star is fundamental to the star’s lifetime – High mass stars have shorter lifetimes.

Stellar evolution

Formation of a star ▪ Gravitational attraction of hydrogen nuclei. ▪ Loss of PE leads to gain in KE and an increase in the gas temperature. ▪ The gas becomes denser and, when the protostar has sufficient mass, the temperature becomes high enough for nuclear fusion to commence. ▪ The star moves onto the main sequence where it remains for as long as its hydrogen is being fused into helium – this time occupies most of a star’s life. ▪ Eventually when most the hydrogen in the core has fused into helium the star moves off the main sequence. The fate of stars ▪ Star collapses when most of the hydrogen nuclei have fused into helium. ▪ Gravity now outweighs the radiation pressure and the star shrinks in size and heats up. ▪ The hydrogen in the layer surrounding the shrunken core is now able to fuse, raising the temperature of the outer layers which makes them expand, forming a giant star. ▪ Fusion of the hydrogen adds more helium to the core which continues to shrink and heat up, forming heavier elements including carbon and oxygen. ▪ The very massive stars will continue to undergo fusion until iron and nickel (the most stable elements) are formed. ▪ What happens at this stage depends on the mass of the star. A. Sun-like stars ▪ For stars up to about 4 solar masses the core temperature will not be high enough to allow the fusion of carbon. This means that, when the helium is used up, the core will continue to shrink while still emitting radiation. ▪ This “blows away” outer layers forming a planetary nebula around the star. When the remnant of the core has shrunk to about the size of the Earth it consists of carbon and oxygen ions surrounded by free electrons. ▪ It is prevented from further shrinking by an electron degeneracy pressure. Pauli’s exclusion principle prevents two electrons from being in the same quantum state and this means that the electrons provide a repulsive force that prevents gravity from further collapsing the star. The star is left to cool over billions of years as a white dwarf. Such stars are of very high density of about 109 kg m–3 .

The probable future for the Sun is shown as the purple line on the HR diagram.

B. Larger stars ▪ For the star much bigger than the Sun when in the red giant phase, the core is so large that the resulting high temperature causes the fusion of nuclei to create elements heavier than carbon. ▪ The giant phase ends with the star having layers of elements with proton numbers that decrease from the core to the outside (much like layers in an onion). ▪ The dense core causes gravitational contraction which, as for lighter stars, is opposed by electron degeneracy pressure. Even with this pressure, massive stars cannot stabilize. ▪ The Chandrasekhar limit is the maximum mass of a stable white dwarf: 1.4 times the mass of the Sun. ▪ When the mass of the core reaches this value the electrons combine with protons to form neutrons, emitting neutrinos in the process. The star collapses with neutrons coming as close to each other as in a nucleus. ▪ The outer layers of the star rush in towards the core but bounce off it in a huge explosion – a supernova. ▪ Although this process lasts just a few hours it results in the heavy elements being formed. ▪ This blows off the outer layers and leaves the remnant core as a neutron star. ▪ Now neutrons provide a neutron degeneracy pressure that resists further gravitational collapse. ▪ The Oppenheimer–Volkoff limit places an upper value on a neutron star for which neutron degeneracy is able to resist further collapse into a black hole. This value is currently estimated at between 1.5 and 3 solar masses.

Black holes It is not possible to form a neutron star having a mass greater than the Oppenheimer–Volkoff limit instead the remnant of a supernova forms a black hole. Nothing can escape from a black hole – including the fastest known particles, photons. For this reason it is impossible to see a black hole directly but their existence can be strongly inferred by the following. ● The X-rays emitted by matter spiralling towards the edge of a black hole and heating up. X-ray space telescopes, such as NASA’s Chandra, have observed such characteristic radiation. ● Giant jets of matter have been observed to be emitted by the cores of some galaxies. It is suggested that only spinning black holes are sufficiently powerful to produce such jets. ● The unimaginably strong gravitational fields have been seen to influence stars in the vicinity, causing them to effectively spiral. A black hole has been detected in the centre of the Milky Way and it has been suggested that there is a black hole at the centre of every galaxy.

COSMOLOGY: what is its age and origin of THE Universe

Newton’s model of the universe assumed that the universe was: ▪ infinite (in space and time) ▪ uniform (contains an infinite number of stars uniformly distributed) ▪ static Olber’s paradox: Why in the world is the sky dark??? According to these assumptions the sky should not be dark When we look up into the night sky we see darkness but, in an infinite universe, we should be able to see a star in every direction and, therefore, the night sky should be uniformly bright on a cloudless night. SHOULD BE. But it is not.

Olber's Paradox can be reconciled through 1. expansion of the Universe and 2. the finite age - and both of which are consequences of the Big Bang. 1. Universe is expanding 1a. Doppler’s redshift Hubble: that stars further away from us have a higher recession velocity. Consequently, these stars are more red shifted than those closer to us, so we could perhaps not even see the electromagnetic waves the most distant stars emit, since they don’t appear in the visible spectrum (dark regions of the night sky).

1b. Cosmological redshift Which is not a Doppler effect. Space itself is being stretched by expansion, so electromagnetic waves are also stretched and therefore redshifted. .

Expansion of space can cause the energy of emitted

light from the Big Bang to be reduced via redshift to

microwave wavelengths (1100 times longer than its

original wavelength), and thus form the cosmic

microwave background radiation

2. Universe has a finite age If the universe is approximately 14 billion years old, we can see light that is less than 14 billion ly away. And, so… if we receive light from a finite # of stars, the night sky would be dark

Doppler effect and z-parameter In the 1920's, Edwin Hubble realized that almost all galaxies have a positive redshift. λ of EM waves coming from stars are greater than those obtained in the laboratory emitted from same elements (He, H). The shift in a spectral line from a galaxy emission spectrum is given by: ∆λ = λ– λ0 λ0 is the wavelength emitted by the source λ is the wavelength measured on Earth The measured red shifts are usually stated in terms of a z parameter. v is recession speed of the source ∆흀 풗 풛 = ≈ 풗 ≪ 풄 c is the speed of light in vacuum 흀 풄 ퟎ Goal: the speed of the galaxy

Hubble’s Law He also noticed the farther the galaxy is, the greater the redshift, therefore the greater the recessional velocity. Recessional speed of the distant galaxies is proportional to their distance form Earth.

푣 = 퐻0푑 H0 is the Hubble constant. (Doppler-shift-measured velocity) v is usually being measured in km s−1 and d in Mpc, −1 −1 H0 is usually measured in km s Mpc .

How the Hubble constant may be determined • Measuring the distance to distant galaxies • Measuring their recessional speed using Doppler effect • Plotting a graph of v against distance. • Hubble’s constant is equal to the gradient of the graph • Average value of Hubble’s constant is • 72 km s-1 Mpc-1

• This means that for every megaparsec to a galaxy, the galaxy's speed away from us will increase by 72 kilometers/second.

• There are uncertainties in the distances measured precisely because it is quite difficult to measure distances to remote galaxies accurately.

EX: This question is about the Hubble constant. –1 –1 –1 –1 (a) The value of the Hubble constant H0 is accepted by some astronomers to be in the range 60 km s Mpc to 90 km s Mpc .

(i) State and explain why it is difficult to determine a precise value of H0 (2) ANS: The Hubble constant is the constant of proportionality between the recessional velocity of galaxies and their distance from Earth. The further galaxies are away (from Earth) the more difficult it is to accurately determine how far away they are. This is because of the difficulty of both locating a standard candle, such as finding a Cepheid variable within the galaxy, and the difficulties of accurately measuring its luminosity.

(ii) State one reason why it would be desirable to have a precise value of H0. (1)

ANS: Having a precise value of H0 would allow us to gain an accurate value of the rate of expansion of the universe and to determine an accurate value to distant galaxies. It would also allow us to determine a more reliable value for the age of the universe.

b) The line spectrum of the light from the 3C 273 contains a spectral line of wavelength 750 nm. The wavelength of the same line, measured in the laboratory, is 660 nm. –1 –1 Using a value of H0 equal to 70 km s Mpc , estimate the distance of the quasar from Earth. ∆휆 = 90 × 10−9푚 ∆휆 푣 푧 = ≈ → 푣 = 4.1 × 107푚푠−1 휆0 푐

푣 = 퐻0푑 4.1 × 104푚푠−1 푑 = = 590 푀푝푐 70

Why is Doppler effect so important? 1. red-shift of light from galaxies indicates that the universe is expanding. The universe is moving apart and expanding in all directions. The farther away they are, the faster they move. This is Hubble's Law. 2. So, if galaxies are moving away from each other then it they may have been much closer in the past.

Matter was concentrated in one point and some “explosion” may have thrown the matter apart.

When did Big Bang happen? d d t = = v H0d 1 This is called the Hubble time. Gives how long it took The time since the Big Bang is T = H0 for the galaxies to reach their current separation. It is the same for all of the galaxies!!

• This is only an upper band as the Universe expanded faster at the beginning (this would imply a younger Universe). The Universe cannot be older than this.

-1 -1 • H0 = 70 km s Mpc 1 푇 = = 4.29 × 1017푠 = 13.6 × 109푦푟 72 × 103 푚푠−1(푀푝푐)−1

Big Band – the theory that won Until the 1960s there were two competing theories of the origin of the universe. Steady State Theory (Hermann Bondi, Thomas Gold, and Fred Hoyle 1948) The density of matter in the expanding universe remains unchanged due to a continuous creation of matter, thus adhering to the perfect cosmological principle, a principle that asserts that observable universe is basically the same at any time as well as at any place.

Big Bang theory: One aspect of the Big Bang theory is that it suggested a very high temperature early universe that cooled as the universe expanded. In 1948, Gamow, Alpher, and Herman predicted that the universe should show the spectrum of a black-body emitter at a temperature of about 3 K. In the Big Bang model, at approximately 4 × 105 years after the formation of the universe, the temperature had cooled to about 3000 K and the charged ion matter was able to attract electrons to form neutral atoms. This meant that space had become transparent to electromagnetic radiation, allowing radiation to escape in all directions (previously, when matter Density of galaxies falls as universe expands was ionic, it had been opaque to radiation).

Background radiation In 1960 two physicists, Dicke and Peebles, realising that there was more He than it could be produced by stars, proposed that in the beginning of the Universe it was at a sufficiently high temperature to produce He by fusion. In this process a great amount of highly energetic radiation was produced. However, as the Universe expanded and cooled, the energy of that radiation decreased as wavelength increased. They predicted that the actual photons would have an maximum λ (around 7 cm) corresponding to a black body spectrum of 3K. So, they started to look for microwave radiation. Shortly after this prediction, Penzias and Wilson were working with a microwave aerial and found that no matter in what direction they pointed the aerial it picked up a steady, continuous annoying background radiation. Smoking gun for Big Bang theory was found. In every direction, there is a very low energy and very uniform radiation that we see filling the Universe. This is called the 3 Degree Kelvin Background Radiation, or the Cosmic Background Radiation, or the Microwave Background. These names come about because this radiation is essentially a black body with temperature slightly less than 3 degrees Kelvin (about 2.76 K), which peaks in the microwave portion of the spectrum.

Why is the background radiation an evidence for the Big Bang? The CMB in the sky looks essentially the same in all directions (it is “isotropic”) and does not vary with the time of day; this provides compelling support for the Big Bang model. With the discovery of CMB, the advocates of the steady state theory were forced to concede to the strength of evidence.

Big Bang It postulates that 12 to 14 billion years ago, the singular point at which space, time, matter and energy were created. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit. We can see remnants of this hot dense matter as the now very cold cosmic microwave background radiation which still pervades the universe and is visible to microwave detectors as a uniform glow across the entire sky. Main evidence:  Expansion of the Universe – the Universe is expanding (redshift)  it was once smaller  it must have started expanding sometime  “explosion”  Background radiation  evidence of an hot Universe that cooled as it expanded  He abundance  He produced by stars is little  there is no other explanation for the abundance of He in the Universe than the Big Bang model.

Fate of the Universe should depend on the mass (or not?) So, how do we measure the density of the Universe? If we take into account all the mass (stars) that we can see then the total mass would not be enough to keep the galaxies orbiting about a cluster centre So, there must be some matter that can not be seen – dark matter. Dark Matter is matter that emits minimal or no light, BUT does have gravitational influence. Evidence for dark matter appears to be present in  the motion of stars in galaxies.  the orbits of galaxies in galaxy clusters  the temperature of intracluster in galaxy clusters  the gravitational lensing of distant galaxies Some possible types of dark matter include:  MACHOS (Massive compact halo objects) – brown and black dwarfs and Jupiter-sized planets that exist in halos of galaxies. Or similar cold objects and even black holes.  WIMPS (Weakly interacting massive particles) – These are subatomic particles that have extremely small masses, but exist in great quantities. Neutrinos are an example of a such particle.

The redshift equation and the cosmic scale factor Although the cause of the redshift is the stretching of space rather than a constantly moving source, the electromagnetic Doppler equation holds ∆휆 true and can be used in astrophysics where the redshift ratio is denoted by the symbol z, giving 휆0 ∆휆 푣 푧 = ≈ 휆0 푐 Because CMB suggests that the universe is essentially isotropic and homogeneous at any point in space at a chosen (proper) time after the Big Bang, it is essentially true that the destiny of matter should be the same throughout the universe. Soon after the Big Bang the density would have been greater and at later smaller. The expansion of the universe can be considered to be a rescaling of it. As the universe expands, all distances are streched with the cosmic scale factor R. In other words, if the radiation had wavelength λ0 when it was emitted but λ when it was detected, the cosmic scale factor would have changed from R0 to R. This means that space has stretched by an amount ∆R in the time that the wavelength has stretched by the amount ∆λ. Hubble’s law holds because, rather than galaxies receding from one another, space is expanding; this results in the redshift being a Hubble redshift as opposed to a Doppler redshift. ∆휆 푣 ≈ 휆0 푐 and ∆휆 ∆푅 푅 − 푅0 푅 푧 = = = = − 1 휆0 푅0 푅0 푅0

Type Ia supernovae and the accelerating universe In the late 1990s, Type Ia supernovae were found to offer key evidence regarding the expansion of the universe. By using Type Ia supernovae as standard candles to estimate galactic distances up to around 1000 Mpc and measuring their redshifts, strong evidence was obtained suggesting the universe might currently be undergoing an accelerated expansion. The universe is known to contain a significant amount of ordinary matter that has a tendency to slow down its expansion. Acceleration, therefore, would require some sort of invisible energy source and, although none has been directly observed, it has been named “dark energy”.

What is DARK ENERGY? • It is the term used for a possible unseen influence that may be causing the universal expansion to accelerate. As same as dark matter, dark energy has been one of the most mysterious issues it exists in science. • Dark energy is hypotetical form of energy that permeates all of space and produces a negative pressure, resulting in repulsive gravitational force. Dark energy may account for accelerating expansion of the universe, as will as most of its mass. Recent obseravtions of supernovae have produced a value for an acceleration that implies a universe that is about 70% dark energy.

Or

It might be that once again we are wrong about gravitation, so

● there was Newton ● then there was Einstein ● And there might be ???????

Precision Cosmology “…as we know, there are known knowns; there are things we know we know.

We also know there are known unknowns; that is to say we know there are some things we do not know.

But there are also unknown unknowns -- the ones we don't know we don't know.”

EXTRA: Olber’s paradox density of stars n = N/V = number of stars per unit volume • divide the whole universe into concentric shells around Earth of constant thickness t • look at one shell of thickness t at distance d from the Earth • since stars are uniformly distributed the number of stars seen from Earth increases as d2: number of stars in shell = density x volume = n 4πd2 t • brightness of one star decreases as 1/d2 ; b = L/4 πd2 • brightness of shell is constant; assuming that luminosity L is the same for all stars, the received energy per sec per unit area (brightness) from all stars in the thin shell is: L × 4π d2nt = Lnt = const. 4π d2 • amount of light we receive from shell does not depend upon how far away the shell is • adding all shells to infinity; each contributing a constant amount of energy • the total energy is infinite • sky would be uniformly bright • but it’s dark in night

Solutions to Olber’s paradox • Perhaps the Universe is not infinite. But current model of the Universe is that it is infinite. • Perhaps the light is absorbed before it gets to us. But then Universe would warm up and eventually reradiate energy. Real help: the Big Bang model leads to the idea that the observable universe is not infinite and to the idea of the expansion of the universe; • Universe is not static, it is expanding, hence the most distant stars/ galaxies are strongly red - shifted, out of the visible part of the spectrum. • There is a finite time since the Big Bang. Some 12 to 15 billion years. That means we can only see the part of it that lies within 12 to 15 billion light-years from us. And the observable part of the universe contains too few stars to fill up the sky with light. Calculation shows that the helium produced by nuclear fusion within stars cannot account for the real amount of helium in Universe (24%). In 1960 it was proposed that sometime during the early history of the Universe, long before any star, Universe was at a sufficiently high temperature to produce helium by fusion. In this process many high energy photons would be produced. The CMB (Cosmic Microwave Background Radiation) radiation was emitted only a few hundred thousand years after the Big Bang, long before stars or galaxies ever existed. The photons would have a black body spectrum corresponding to the then temperature of the Universe. As the Universe expanded and cooled the photon spectrum would also change with their maximum wavelength shifting in accordance with Wien’s law. It is estimated that at the present time the photons should have a maximum wavelength corresponding to a black body spectrum of an extremely cold object of temperature of 2.7 K. Cosmological background radiation / Cosmic microwave background radiation (CMB) is microwave radiation - left over from the Big Bang that fills the universe roughly uniformly in all directions. The Big Bang predicts an expanding universe that had a very high temperature at the beginning; during the expansion the universe is cooling down and the temperature of the radiation should fall to its present low value of about 2.7 K. That radiation corresponds to a black body spectrum of about 2.7 K. The other way of explaining CMB is: Big Bang producing initially produced very short wavelength photons /EM radiation. As the universe expands, the wavelengths become red shifted to reach current value.

█ Explain how knowledge of the spectrum of a black body and the existence of cosmological background radiation is consistent with the “Big Bang” model of the universe. ► Big Bang predicts a low temperature radiation at 2.7 K (i.e. CMB radiation). The Big Bang theory also predicts an expanded universe which we observe through red- shifting of the galaxies and the lowering of CMB radiation temperature. This expanding universe is the result of the initial energy released in the Big Bang

█ State one piece of evidence that indicates that the Universe is expanding. ► light from distant galaxies/stars is red-shifted (which means they move away from us – as the red-shifting occurs in all direction, the universe must be expanding) ► existence of CMB ► the helium abundance in the universe which is about 25 % and is consistent with a hot beginning of the universe;

The eventual fate of the Universe is determined by the amount of mass in the Universe. Critical density is the density of the Universe which produces a flat universe, i.e. it would take an infinite amount of time to stop expansion of it. Critical density is the density of the Universe that would be necessary to stop the expansion after an infinite amount of time. • Closed Universe A model of the universe in which density of the Universe is such that gravity will stop the universe expanding and then cause it to contract. Eventually the contraction will result in a ‘Big Crunch’ after which the whole creation process could start again. • Open Universe A model of the universe in which density is such that gravity is too weak to stop the Universe expanding forever. • Flat Universe means that the density is at a critical value whereby the Universe will only start to contract after an infinite amount of time.

non-coincident starts (not at beginning);

correct shapes and correctly labelled;

coincident at appropriate place;

Dark matter is the matter that makes up for most of the mass in the universe, but cannot easily be detected because it does not emit radiation . Examples of dark matter. ► two of Neutrinos / WIMPS / MACHOS / black holes / exotic super symmetric particles / grand unified predicted particles / magnetic monopoles etc.; or maybe our current theory of gravity is again not correct

Magnitude Scale • Magnitudes are a way of assigning a number to a star so we know how bright it is Apparent magnitude (m) of a celestial body is a measure of its brightness as seen from Earth. The brighter the object appears the lower its apparent magnitude. Greeks ordered the stars in the sky from brightest to faintest… Later, astronomers accepted and quantified this system. 3 • Every one step in magnitude corresponds to a factor of 2.51 change in brightness. Ex: m1 = 6 and m2 = 9, then b1 = (2.51) b2 Absolute magnitude (M) of a star is the apparent magnitude that a star would have if it were at distance of 10 pc from Earth. It is the true measurement of a star’s brightness seen from a set distance. d m – apparent magnitude M – absolute magnitude of the star m – M = 5 log ( ) 10 d – its distance from the Earth measured in parsecs. • If two stars have the same absolute magnitude but different apparent magnitude they would have the same brightness if they were both at distance of 10 pc from Earth, so we conclude they have the same luminosity, but are at different distances from Earth !!!!!!!!!!!!!! 7 • Every one step in absolute magnitude corresponds to a factor of 2.51 change in luminosity. Ex: M1 = – 2 and M2 = 5, then L1 / L2 = (2.51) Binary star is a stellar system consisting of two stars orbiting around their common center of mass. The ONLY way to find mass of the stars is when they are the part of binary stars. Knowing the period of the binary and the separation of the stars the total mass of the binary system can be calculated (not here). Most of our knowledge of stellar masses comes from binary systems. Careful measurement of the motion of the stars in a binary system allows their masses to be estimated.

Visual binary: a system of stars that can be Spectroscopic binary: A binary-star system Eclipsing binary: (Rare) binary-star system seen as two separate stars with a telescope which from Earth appears as a single star, in which the two stars are too close to be and sometimes with the unaided eye. but whose light spectrum (spectral lines) seen separately but is aligned in such a shows periodic splitting and shifting of way that from Earth we periodically spectral lines due to Doppler effect as two observe changes in brightness as each star stars orbit one another. successively passes in front of the other, that is, eclipses the other.

They are sufficiently close to Earth and the stars are well enough separated. Sirius A, brightest star in the night sky and its companion first white dwarf star to be discovered Sirius B.