1. Relativistic Universe
Quasars and cosmology

2. The Discovery
In 1962, Cambridge University just completed a radio survey of the sky. Maarten Schmidt took their radio positions and looked for optical counterparts. He found a few peculiar “radio” stars.
3C 273 looked like an ordinary, fairly-bright star (with possibly a little fuzz). But ordinary stars do not emit much in the radio part of the spectrum.

3. The Spectrum The spectrum of the star was odd. It had
Emission lines instead of absorption lines
Broad (~10,000 km/s) emission lines, instead of narrow lines
Emission lines at “strange” wavelengths
The solution: the emission lines were those of hydrogen, but at enormous redshift. The object was moving away at 0.1 the speed of light!

4. Quasars Properties of quasi-stellar radio sources (quasars, or QSOs):
Star-like appearance (with possibly some “jets”)
Emission-line spectra with internal motions of ~10,000 km/s
Does not emit as a blackbody (at least, not at a single temperature). The objects emit light in x-rays, ultraviolet, optical, infrared, and sometimes microwave and radio
Irregularly variable on timescales of days/months
Enormous redshifts (up to 90% or more of the speed of light)
Stars in the Milky Way cannot move that fast. The only way to have such a redshift is through the Hubble Law. So, through v = H D, the objects must be incredibly far away. They are therefore incredibly bright – as bright as 1000 supernovae.

5. Size and Variability
Since many quasars vary in brightness we have a crude way to estimate their size.
Imagine that there is some mechanism near the center of the QSO that controls the object’s brightness. It says “get bright”.
That command goes forth no faster than the speed of light.
Within a few months, the object gets bright.
Since no signal can go faster than the speed of light, the object must be no bigger than a few light-months across!

6. The Energy Source
What can outshine ~1000 supernovae for millions of years, and be just slightly larger than our Solar System. Theoretically, not much – only a very, very big black hole.
Start with a 10,000,000,000 M black hole
Have a star come close enough to be tidally disrupted
Have the material form into an accretion disk. Energy is released via the friction in the disk. If you accrete ~ 1 M per year, you get the luminosity of a quasar.

7. Feeding the Monster
If a star comes too close, the enormous gravity of the black hole will cause tides on the star and rip it apart. Some of that material will be trapped in orbit about the hole.

8. Feeding the Monster
If a star comes too close, the enormous gravity of the black hole will cause tides on the star and rip it apart. Some of that material will be trapped in orbit about the hole.

9. Explaining a Quasar’s Properties
Near the event horizon, the gas is moving close to the speed of light. Any emission lines which are produced will be broad.
Because of the high speed of the gas, there is a lot of friction in the disk. A lot of light is produced.
The temperature of disk depends on the speed of the gas. Near the event horizon, the friction produces x-rays. At larger radii, where the gas revolves more slowly, optical and infrared light is made.

10. Black Holes and Jets
As matter accretes onto the black hole, particles can get ejected out the poles of the system at % of the speed of light. How this occurs is almost a complete mystery. But it’s often observed.

11. Where are the Quasars Today?
The nearest quasar is 25% of the way across the universe; most belong to an era when the universe was only 15% of its present age. If supermassive black holes existed then, where they now?
In the centers of galaxies!

12. The Quasar-Galaxy Connection
When a supermassive black hole is accreting, it can be thousands of times brighter than its surrounding galaxy. On the other hand, if the black hole is not accreting, it will be invisible.

13. Active Galactic Nuclei
Many nearby galaxies have some activity in their nucleus: they may have an extremely bright nucleus, or show a jet of emission, or have broad emission lines, or emit at radio wavelengths. These objects (which are probably just accreting a little mass) are said to have an Active Galactic Nucleus.
The energy produced by an AGN is still often many times that of the stars.

14. Galaxies with Active Galactic Nuclei

15. Sleeping Monsters
When a black hole is not accreting matter, then it’s invisible. But it’s gravitational influence on its surroundings can still be detected – the stars surrounding the hole must move fast (due to Kepler’s and Newton’s laws).

16. Sleeping Monsters
There’s even a 2,000,000 M black hole at the center of the Milky Way. We can measure its mass by the motions of stars which pass close to it.

17. AGN and Starbursts
In the present day universe, AGN are rare. However, they are more common in interacting galaxies. This suggests that the orbits of some stars have been perturbed enough to pass close to the black hole. It also suggests that all galaxies possess supermassive black holes.

18. AGN and the Universe
Since quasars can be seen 90% of the way across the universe, they allow us to detect gas throughout the universe. We can therefore examine galaxies (and proto-galaxies) that we can’t even see!
Any time the light from a quasar goes through a galaxy that has hydrogen gas, there will be absorption at the wavelength appropriate to hydrogen. But remember – this hydrogen is moving, due to the Hubble Law. So …

19. AGN and the Universe
Each absorption is due to hydrogen gas at a different redshift (i.e., distance). Quasars allow us to probe structure throughout the universe!

20. Principles of cosmology
The Cosmological Principle is the assertion that, on sufficiently large scales the Universe is both homogeneous and isotropic.
Homogeneity is the property of being identical everywhere in space;
Isotropy is the property of looking the same in every direction.

21. Can construct models of the Universe in which the Cosmological Principle principle holds?
Since general relativity is a geometrical theory, we must begin by investigating the geometrical properties of homogeneous and isotropic spaces.

22. Let us suppose we can regard the Universe as a continuous fluid and assign to each fluid element the three spatial coordinates xa (a = 1, 2, 3). Thus, any point in space–time can be labeled by the coordinates xa, corresponding to the fluid element which is passing through the point, and a time parameter which we take to be the proper time t measured by a clock moving with the fluid element. The coordinates xa are called comoving coordinates.

23. Robertson-Walker-Friedman metric
r , q and f are the comoving coordinates (r is by convention dimensionless);
t is the proper time;
a(t) is a function to be determined which has the dimensions of a length and is called the cosmic scale factor or the expansion parameter;
the curvature parameter K is a constant which can be scaled in such a way that it takes only the values 1, 0 or −1.