CosmologyStructure of the universe(a) describe the principal contents of the universe, including stars, galaxies and radiation;(b) describe the solar system in terms of the Sun, planets, planetary satellites and comets;(c) describe the formation of a star, such as our Sun, from interstellar dust and gas;(d) describe the Sun’s probable evolution into a red giant and white dwarf;(e) describe how a star much more massive than our Sun will evolve into a super red giant and then either a neutron star or black hole;(f) define distances measured in astronomical units (AU), parsecs (pc) and light-years (ly);(g) state the approximate magnitudes in metres, of the parsec and light-year;(h) state Olbers’ paradox;(i) interpret Olbers’ paradox to explain why it suggests that the model of an infinite, static universe is incorrect (j) select and use the equation (k) describe and interpret Hubble’s redshift observations;(l) state and interpret Hubble’s law (m) convert the Hubble constant H0 from its conventional units (km s-1 Mpc-1 ) to SI (s-1); (n) state the cosmological principle;(o) describe and explain the significance of the 3K microwave background radiation

The evolution of the universe (a) explain that the standard (hot big bang) model of the universe implies a finite age for the universe (b) select and use the expression age of universe 1/H0;(c) describe qualitatively the evolution of universe 10-43 s after the big bang to thepresent;(d) explain that the universe may be ‘open’, ‘flat’ or ‘closed’, depending on its density (e) explain that the ultimate fate of the universe depends on its density;(f) define the term critical density;(g) select and use the expression for critical density of the universe(h) explain that it is currently believed that the density of the universe is close to, and possibly exactly equal to, the critical density needed for a ‘flat’ cosmology

Formation of a Star 1. Stars form from clouds of interstellar dust and

gas, which consist mainly of the elements hydrogen and helium.

2. Where it is denser, its own gravity causes the material to pull together and contract to form a denser mass. This has a stronger pull, so more matter is pulled in. This is gravitational collapse.

3. As the interstellar dust collapses, it heats up. This is because it is losing gravitational potential energy and gaining kinetic energy. Mean kinetic energy is directly proportional to thermodynamic temperature, so the temperature of the dust increases.

4. At the centre of the collapsing dust and gas cloud, the material becomes very hot and dense. At 3000K, plasma forms – electrons leave atoms, leaving nuclei.

5. When temperatures reach 107 K, fusion reactions begin and hydrogen nuclei fuse to become helium. This is hydrogen burning.

A protostar is a concentration of dust and gas with a mass great enough to form a star.

Main Sequence Stars Two forms of equilibria exist when a star is in its main sequence phase: A star reaches a steady temperature when the power released by fusion reactions is equal to the power radiated away from the star.

A star is a stable size when attractive gravitational forces and outward forces due to radiation pressure (from photons released in star fusion reactions) are equal.

As stars age… Hydrogen begins to run out Loss of radiation pressure because

nuclear fusion isn’t occurring The core of the star begins to collapse

under gravitational attraction Thin shell of helium nuclei surrounding the

core of the star start to fuse to produce beryllium, carbon and oxygen nuclei.

Thin layer of hydrogen surrounding the helium rich core becomes sufficiently hot to fuse hydrogen again.

This increased power production from the helium shell causes the outer shell of the star to expand due to radiation pressure.

The size of the star increases and its surface temperature drops.

The star

is a red giant.

As stars age… The core continues to collapse. Its

density and temperature increase.

The helium nuclei in the outer shell reach a temperature of about 108 kelvin and start to fuse together at a phenomenal rate.

A helium flash occurs: the material surrounding the core is ejected away as a planetary nebula.

A bright central core is left behind – this is known as a white dwarf. The white dwarf eventually cools and dims over a period of millions of years.

A white dwarf is very dense. No fusion occurs in a white dwarf – it glows because photons produced by fusion reaction in the past are still leaking away from it. As the material of the white dwarf star becomes more compressed, electrons are no longer attached to individual atoms but move freely throughout the star in a plasma state.

A white dwarf is prevented from further gravitational collapse by electron degeneracy pressure (also known as Fermi pressure). This comes from Pauli’s exclusion principle, which states that no two electrons can exist in the same quantum state. As gravity tries to cause the star to collapse further, a limit is reached when further collapse would require two or more electrons to exist in the same quantum state.

The maximum mass of a white dwarf star is about 1.4 solar masses. This upper limit is known as the Chandrasekhar limit.

As stars age… More massive stars (with a mass above 3 solar

masses) swell to become super red giants. When they collapse to form a white dwarf, provided

that their mass is still more than 1.4 solar masses, its gravity is strong enough to cause it to collapse even further.

The gravitational pressures are enormous and overcome to Fermi electron degeneracy pressure.

Electrons combine with protons to produce neutrons and neutrinos. The neutrinos escape and the central core of the star is now made entirely of closely packed neutrons.

The outer shells surrounding the neutron core collapse and rebound against the solid neutron core.

This generates a shockwave which explodes the surface layers of the star as a supernova. The supernova blasts off heavier elements such as carbon, oxygen and iron into the galaxy, which can then be incorporated into future stellar systems.

After a supernova: For lighter stars the core is entirely made up of neutrons. The

result is a neutron star. Neutrons stars have densities of 1018 kgm-3.

For even heavier stars, the supernova leads to a neutron star that is so massive that it continues to collapse inwards under its own gravity to form a black hole. A black hole forms when matter collapses almost to a point – a singularity. The gravitational field is so strong that not even light can escape from it.

Stellar death…

Olbers’ Paradox

For an infinite, static and uniform

universe, the night sky should

be bright because of light received in all directions

from stars.

Newton suggested that the universe was infinitely large and roughly uniform in its composition. He said that an infinite universe had no centre, and each star is pulled equally in all directions. If the universe was finite, it would collapse under the pull of its own gravity.

So why was Newton wrong? Introducing Heinrich Olbers… Olbers pictured a universe that was

infinite, uniform and static. He said that if we lived in such a universe, the sky would always be brightly lit, even at night. He argues that in no matter what direction you looked, your line of sight would eventually reach a star – so every point in the sky would be lit by a star. In an infinite universe, the number of stars

increases with the square of the distance from Earth. The intensity of the light from these stars decreases according to the inverse square law with distance. These two effects cancel each other out, so …

The night sky should be bright!

Conclusions from Olbers’ Paradox: The sky is not bright at night The universe is therefore not infinite

because there is not a star at every point in the sky.

The universe is not an infinite age because light would have already reached us from infinitely many other stars. The universe is not infinite!

The universe therefore cannot be static because otherwise it would collapse in on itself as Newton suggested. The universe must therefore be expanding!

The universe is not static!

The Cosmological Principle The universe has the same large

scale structure when observed from any point within it.

The universe is homogeneous – on a large scale the universe is the same in all places – its density is

the same everywhere. The universe is isotropic – it is the

same in all directions

The Expanding Universe

𝜟𝝀𝝀 =

𝒗𝒄

When we look at galaxies far away from Earth, the line spectra are slightly out of place – the lines are shifted towards the red end of the spectrum. Their wavelengths have increased.

The longer wavelength indicated that the galaxies

were moving

away from us! This is the Doppler

Equation: it can be used to calculate the speed of recession of a galaxy from the change in wavelength.

Hubble’s Law The speed of recession of a galaxy is directly proportional to the distance of the galaxy away from Earth.

V = H0x

The gradient of a recessional velocity vs distance graph gives the value of the Hubble constant, H0. Galaxies that are further away from us are moving at a greater velocity; the implication is therefore that the universe is expanding! If we work backwards, Hubble’s graph provides evidence that the universe was at one stage all in one place – it then exploded in a big bang and all of space and time evolved.

The age of the

universe

The history of the universe…0s

• The universe was infinitely small and infinitely dense – a point. All four fundamental forces were unified

10-6 s

• Universe consisted of a soup of quarks and leptons.• The particles were travelling too fast to combine

10-3 s• Quarks slowed down enough to start combining to form hadrons.

1s

• Most of the mass of the universe created in the first second of its existence through pair production. Pairs of high energy photons interact and produce particle-antiparticle pairs

• Pair production stopped at 1s when temperatures had dropped to 6 x109 K• Particles and antiparticles annihilated forming photons: more matter than antimatter.

100s• Protons and neutrons fused together to form helium nuclei. As

temperature dropped below 107 K, fusion stopped.

300000 years

• Atoms started to form as hydrogen nuclei and helium nuclei grabbed electrons. The universe consisted mainly of hydrogen and helium atoms with photons of electromagnetic radiation moving in between.

• Gravity became the dominant force – stars and galaxies formed

• Continued expansion lead to cooling. The present temperature of the universe is 2.7 K.

Decreasing Tem

perature and Expansion

Evidence for the Standard Hot Big Bang Model1. Redshift

The light from distant galaxies is shifted towards the red end of the spectrum - it has a longer wavelength. This suggests that the galaxies are moving away from us and so at some point, all of the galaxies were at one point – a singularity – from which the big bang exploded and galaxies began moving away from each other.

2. Chemical composition of the universe : The existence of ‘primordial helium’ produced in the early stages of the universe.

3. Cosmic microwave background radiation When microwave detectors are sent into space,

they can detect electromagnetic radiation. The radiation detected is in the microwave region of the EM spectrum and it is almost perfectly uniform. This confirms the isotropic nature of the universe and backs up the cosmological principle. The universe expanded and the

temperature of the photons has dropped close to absolute zero – so the CMB represents to cooled remnants of radiation that first started to travel through the universe 13 billion years ago. But why does the universe expanding result in cooler photons?

Think of the photons as waves. The universe has expanded because space itself is expanding. This has the effect of stretching the waves as they move through space. They have longer wavelengths and so now, at a temperature of 2.7K, we detect them in the microwave region of the spectrum.

The future of the universeOpen Universe: The universe may continue to expand forever. The rate of expansion decreases with time but is still finite after infinite time. This will happen if there is insufficient matter in the universe: gravitational force cannot provide the necessary deceleration to slow down the expansion of the universe.

Closed Universe: If there is enough matter in the universe so that gravity is strong enough, expansion of the universe may come to a halt and go into reverse, resulting in a big crunch.

Flat universe: The universe expands forever but the rate of expansion tends to zero after infinite time.

The critical density is the density of the universe that

will give rise to a flat universe, given by the

equation ρ0

The fate of the universe depends on its density. Density of universe > critical density:

gravitational forces halt expansion of matter and reverse the process towards a big crunch: the universe in closed.

Density of the universe < critical density: gravitational forces cannot halt the expansion of matter. The universe expands forever: the universe is open.

Density of the universe = critical density : the universe will expand forever but the rate of expansion tends to zero after infinite time: universe is flat.

The future of the universeThe fate of the universe depends on its density.

In a low density universe, gravitational force is too weak to stop it expanding , s o it will expand forever. In a high density universe, gravitational force will be strong enough to halt and then reverse its expansion. There must therefore be a critical density above which the universe will return back to a big crunch. Below the critical density, the universe will expand forever.

Measuring the Universe The astronomical unit (AU) is the average distance of the Earth from the Sun. 1AU = 1.496x1011m 1.5x1011mThe light year is the distance travelled by light through a vacuum in one year1ly = 9.46x1015m 9.5x1015m

1 AU

1 pc

1 arc second

Parallax is the apparent change in position of an object. In the case of stars, this is the change in position of a nearby star against the background of more distant stars, which changes when observed at different times of the year as a consequence of the Earth’s orbit around the sun.

1 second of arc = degrees

The parsec is defined as the distance that gives a parallax angle of 1 arc second. The parsec 3.09x1016m

Stars with smaller angles of parallax are further away, so the distance of a

star =