Chapter 22 Neutron stars, gamma ray bursters, black holes

Result of Supernova explosion of massive star (Type II) is a neutron star, if the remnant core is less than about 3 solar masses. Neutron star held up by degenerate neutron pressure; density ~ 1018 kg/m3

magnetic axis

rotation axis

Pulsars: synchrotron radiation by spiralling electrons around magnetic field lines make beacons. Pulse milliseconds to seconds

Gamma ray bursts of fraction of second duration. May be associated with rotating black hole whose magnetic field makes an electic generator.

Special relativity: laws of physics the same in all inertial frames; speed of light the same in all frames.

General relativity: mass and energy warp space and time. Objects move near large masses on curved geodesics.

In General relativity, can form black holes – objects so massive that nothing can escape, not even light. Radius within which nothing can escape is Schwarzchild radius – at the Event Horizon.

Supernova remnants with mass above about 3 solar masses will form black holes. See evidence for black holes that are part of binary systems. We see the visible star orbitting around a very massive invisible companion. See X ray emission when material from the companion streams into the black hole.

We believe a very massive black hole exists (3 million solar masses) at the center of our galaxy – see stars orbiting rapidly around a very massive core that is dark.

Chapter 23 : Milky Way

Our Milky Way galaxy is disk shaped with a central bulge, and a low density spherical halo. Disk and halo are about 30kpc across. The central bulge is a few kpc across. There are about 1011 (100 billion) solar masses in the galaxy, so about that many stars.

Measuring distances in the galaxy uses variable stars – RR lyra and Cepheid variables, whose atmospheres are unstable and oscillate up and down, producing temperature, hence luminosity, variations. The period of oscillation in luminosity is related observationally to the absolute peak luminosity, so they are ‘standard candles’.

The sun lies in one of the spiral arms, about 8kpc from the center (~2/3 of the way out).

The halo consists mainly of globular clusters which orbit in elongated ellipses around the center of the galaxy. A globular cluster has Population II stars, all formed at the same early time in the Milky Way’s history. Observations of Cepheids in globular clusters enabled the early size measurements of the galaxy. There is little gas in the halo.

The disks are rich in dust and gas and young (Population I) stars. See 21 cm radio emission characteristic of neutral hydrogen gas.

Formation of the Milky Way came through gravitational forces pulling gas into regions of slightly higher density, creating the seeds for stars. The disk was formed by the rotation of the initial cloud.

Spiral arms do not rotate like a rigid body. (Rigid body would have all parts of disk rotate in same time – same angular speed). The sun takes about 200 million years to make one circuit (much less than the life of the galaxy).

The differential rotation would tend to wind up the spiral. So the arms must be constantly forming and reforming. We believe that they are caused by spiral density waves that travel outward from the center. Where the density is higher, stars form rather quickly and give the light we see as the spiral arms.

Near the galaxy center there is a bright region that emits strongly also in radio and X-ray: ‘Sagitarius A’. We believe there is a massive black hole there with about 3 million solar masses.

Ch 24: Normal galaxies

Spirals, Elliptical and Irregular galaxies.

Spirals have many young stars and gas clouds. Spirals arms in the disk, a central core, spherical halo. Milky Way and Andromeda are typical spirals with ~ 1011 stars and 30 kpc across

Ellipticals have mainly older stars. Can be huge (1012 stars) or dwarf (107 stars) Size up to 1 Mpc

Get distances from Cepheid variables, Tully Fisher, Supernovae Type Ia. Standard candles and use Ltrue = 4d2 Iapp

Galaxies come in clusters: ours is Local Group of 45 galaxies; nearby Virgo cluster has 1000’s of galaxies. Cluster sizes are several Mpc

Superclusters of clusters ~ 50 Mpc across.

Superclusters form filaments, patches, voids

Galaxies collide rather frequently – can merge or pass through to change the shape and size of the galaxies.

Cosmological red shift (Doppler effect) See distant galaxies moving away from us, with speed proportional to distance.

Hubble Law: v = H0 d

Measure mass of galaxies by looking at rotational velocity of stars at some distance from center.

P2 = a3/(M + m) P2 a3/M

Find that there is mass well outside the visible galaxy – Dark Matter

Ch. 25 : Active galaxies and quasars

Seyfort galaxies and Radio Galaxies: 10 to 100 times radiation from normal galaxy. Non-thermal radiation (radio and infrared). Often have jets. Vary output over short times (days/months) so radiation region is small.

Quasars: huge red shifts (up to z = 6) and very energetic: 1000 to 100,000 times Milky Way luminosity; rapid time variations; much radio emission (non-thermal); seem to have existed between 2 and 3 billion years after Big Bang, then quit. Jets are common.

Energy believed to be generated by accretion of material (stars, clouds) on to supermassive black holes at the centers of young galaxies (BH of billions of solar masses). Infalling material is ionized (broken into pieces) with electrons being squirted out along the magnetic field lines and we see the synchrotron radiation in IR and radio.

When supermassive BH eats all the material in its vicinity, the period of intense radiation stops and quasar/active galaxy becomes a normal galaxy.

Light from distant quasars can be used to probe intermediate space – Lyman alpha absorption by intervening dust clouds maps the clouds. Gravitational lensing of qausar light maps dark matter.

Chapter 26: Cosmology and the expanding universe

Cosmological Principle assumes that on the largest scale, the universe is homogeneous and isotropic.

The cosmological red shift lets us map the distant universe: Doppler red shift tells us velocity of recession; Hubble Law then gives a distance; Converting the distance to a time using d=ct gives the time at which the light was emitted.

When we calculate when any distant galaxy was on top of us, all give a common answer around 13-14 billion years ago. The time when everything in the universe was at the same point is called the BIG BANG.

All galaxies see all others receding with the Hubble expansion. We attribute this to the expansion of the universe itself – the space coordinates are growing with time. The cosmological red shift is attributed to the universe expanding the wavelength of the light.

What will happen in future (or what happened in past) depends on the amount of matter and energy in the universe. If the matter has a density equal to the critical density 0 = 8x10-27 kg/m3 at present, then we would expect the universe to coast to zero expansion velocity in future. If less, universe expands forever; if more, universe recollapses to a big crunch.

Previous history of universe also depends on : less matter means it is slowing down less and is older (Big Bang earlier)

Actual age of universe is less in bound than unbound case

Counting up the visible matter (atoms) and dark matter gives about the critical density.

Good evidence for the big bang comes from the cosmic microwave background. This is photons emitted when radiation ‘decoupled’ from matter at the time neutral atoms formed. At that time, the temperature of the universe was about 3000K and the photons had a blackbody spectrum appropriate to that temperature. Since then the expansion has cooled the universe and stretched the original visible light to microwaves.

Observations show an excellent blackbody spectrum now with 2.73K. This is the earliest snapshot available of the universe – at 380,000 years after the big bang.

A new wrinkle. Looking at distant supernovae whose distance AND velocity are measured shows us that the universe is actually decelerating, not accelerating as it would if there were only matter.

velocity

dis

tance

The deceleration forces us to conclude there is a new ingredient in the universe that we call Dark Energy – something that tries to repel the galaxies, or expand the universe.

Velocity of expansion was smaller in the past – accelerating universe

Another measure of the density of matter and energy in the universe comes from measuring the curvature of space. Flat universe has critical density, =1 . Closed or positive curvature universe has higher than critical density and Open or negative curvature universe has lower than critical density.

The cosmic microwave background lets us measure the curvature. CMB has tiny fluctuations in temperature due to density fluctuations in early universe. The spacing of these tells us that space is flat – so the total amount of matter plus energy is the critical density.

The supernovae tell us about the difference of matter and dark energy (one tries to contract, the other tries to expand).

Two measurements together give 27% of critical density of matter and 73% of dark energy. The matter is about 4% atoms and 23% dark matter.

Chapter 27 : Evolution of the early universe

Two problems with the observations:

Why is the CMB have so nearly the same temperature everywhere? The different parts of the universe were not in contact when the radiation left the atoms. Horizon problem

Why is the density of matter and energy so nearly equal to one? This seems too much an accident. Flatness problem.

Both of these are solved by Inflation – postulate that the universe underwent a very rapid increase in size in its early moments due to ‘supercooling’ ( phase transition ). The blowing up makes the universe much flatter than it previously was. And before inflation, different places were in contact, so it is sensible that all points had the same temperature.

8 epochs of the history of the universe:

1) Planck epoch when all forces unified and all particles present

2) GUT epoch when gravity decoupled; inflation occurred when strong force decoupled (phase transition leading to large energy deposit)

3) Hadron epoch when ordinary particles in equilibrium with photon bath. At end of hadron epoch almost all protons disappear

4) Lepton epoch when only electrons in equilibrium with photon bath. At end of lepton epoch, most electrons disappear.

5) Nuclear epoch: cool enough that protons and neutrons fuse into deuterons and these rapidly form helium. Origin of deuterium and helium.

6) Atomic epoch: cool enough for electrons to be trapped on nuclei; cosmic microwave background is launched.

7) Galactic epoch: clumpings of matter develops enabling first stars and galaxies to form. Dark matter needed to make galaxies form so soon as 1 billion years.

8) Stellar epoch: star formation in existing galaxies – our present era.

Matter dominates in universe today (and since the atomic epoch); Gravity is the dominant force shaping the structure of the universe in this era.

Radiation dominates in the early universe (before a few 1000 years). Particles like electrons, protons, quarks are in equilibrium with the radiation and the fundamental particle forces are dominant in shaping the universe.

Fundamental forces:

1. Strong nuclear force (makes nuclear reactions go)]

2. Electromagnetic force (makes chemistry work: force between charges)

3. Weak nuclear force (radioactive decay, inportant in stellar burning)

4. Gravity (between all masses; very weak compared to the others)