# Lecture 19: Expansion of The Universe

Reading Assignment: Arny: Chapter 16 & 17, Cosmos: Chapter 10.

Around 1913, even before it was established that the "spiral nebulae" were outside our own Galaxy, Vesto Slipher found that the spectral lines for most galaxies were shifted to the red portion of the spectrum.

## The Hubble Law

In 1929, Edwin Hubble, using the period-luminosity law for the Cepheid variables (discovered by Harvard Astronomer Henrietta Leavitt), was able to make a plot of the velocity of a galaxy (determined by the doppler shift of its spectral lines) plotted against distance. This plot showed that the more distant a galaxy is, on average, the faster it moves away from the Milky Way.

Redshift is Proportional to Distance

Hubble's Law:

v = Hod

Where Ho (H-nought) is known as the Hubble constant (now; it changes with time) and the modern value is about 65 km/s per Mpc, or 65 km/s/Mpc +/- 15.

Redshift: z = /o = v/c

Example: How far away is a galaxy whose redshift is measured to be z = 0.003?

z = v/c --> v = cz = 3x105km/s * 0.003 = 900 km/s
d = (900 km/s)/(65 km/s/Mpc) = 13.9 Mpc.

All galaxies are moving away from us. The Universe is EXPANDING!!!
Do we smell bad or something? Are we at the center of the expansion? NO! There is no center!

Imagine an "infinite raisin cake" expanding uniformly. As the dough rises (expands) the raisins move away from each-other. The raisins farther away from you move a greater distance away than do the raisins near you in any given time period. Thus, they must be moving away from you faster than the ones nearby.

A 1-D example of this is a rubberband with knots in it.

A 2-D example is the surface of a spherical balloon, or a Hoberman Sphere.

Why do we think this is so? Occam's Razor. It's a simpler Universe than one designed such that everything races away from us. (there is also plenty of observational evidence to support it, but we'll talk about that next week.)

The Final step in the Copernican Revolution: we are not the center of the Universe, there is no center of the Universe.

Distance
Measuring distances accurately is very difficult. Measuring redshifts is actually pretty easy, however.

Obtain distances and redshifts of many galaxies, at different distances --> determine Ho. Then, use Ho to deduce distances of extremely distant galaxies and quasars.
Problem: must account for deviations from the "Hubble Flow" (uniform expansion) to determine Ho. (e.g. the Local Group is "falling into" the Virgo Cluster). Peculiar Velocity, vp = cz - Hod. At larger distances the Hubble Flow dominates the redshift.

NOTE: v = Hod does NOT imply that the speed of a galaxy increases with time. In simple models of the Universe H 1/t. So, the speed of a given galaxy decreases with time (or at best remains constant). Hubble's constant is a constant in space not in time.

ALSO: Space between clusters (or superclusters) expands. Clusters, galaxies, stars, planets, people, DO NOT. Gravity (or electromagnetic and/or nuclear forces) holds them together.
Thus, properly speaking, it is the scale of the Universe that is expanding.

## Active Galaxies

We use redshifts and Hubble's Law to get distances of galaxies. Combine with measured brightness and get luminosity: L = 4d2b.

Find that some galaxies have extremely luminous center (nucleus). "Active". Radio, X-rays, UV, Optical, ... Quasars are related.

"Radio Galaxies": Often 2 lobes of radio emission, far from nucleus. Jets of particles and radiation shot out of nucleus: over 1 Mpc in size!

Gas in active galactic nuclei (AGN) often has huge speed (> 104 km/s). Stars probably NOT responsible for activity.

Radio Astronomers had been trying to get better and better positions for radio sources, to try to find out what they were. Development of radio interferometry made it possible to get accurate positions.

In 1960, certain stars were found to be associated with two of these radio sources, but the stars have very strange spectra.

• Emission lines and no or few absorption lines.
• Lines corresponded to no known elements
These were called Quasi-stellar radio sources, or QSRs because they looked starlike, but didn't have stellar-like spectra. At that time, no stars were known to emit radio waves, and the radio emission from the Sun at the distances of other stars would have been too faint to detect.

Different quasars had different spectral lines in different places!

In 1963, Maarten Schmidt and Jesse Greenstein of Caltech realized that 3C 273 has basically the spectrum of hot (10,000 K) hydrogen, redshifted by 16%! (z = 0.16) That's a huge redshift! Other quasars had even higher z!

If the redshift was due to expansion of the Universe, the quasars must be very far away.

With a redshift of z = 0.16 = /o = v/c --> 48,000 km/s. So, by Hubble's Law: v = Hod, so if Ho = 65 km/s/Mpc, then d = v/H0 = 740 Mpc = 2.4 billion light-years !

Extremely distant, butmuch brighter (100 - 1000 times) than galaxies with the same redshift (i.e., distance).

NOTE: "Radio quiet" quasars were subsequently found. Sometimes called QSOs (quasi-stellar objects). Tend to use the terms interchangeably.

The next surprise: variability
Brightness of some quasars varies dramatically over months or years (some: weeks). Therefore, light-emitting region is not larger than a few light-months or light-years!

For an object that is about 1 light-year in diameter it would take at least 1 year for the brightness, as seen by a distant observer, to vary, even if the intrinsic variation occurs instantaneously throughout the object.

Thus, quasars are very small (relatively) yet release tremendous amounts of energy!

What produces so much energy in such a small volume? Nuclear Energy? - Nope. Regis Philbin? - Nope.

By process of elimination we come to one conclusion: HUGE BLACK HOLES (MBH = 107 - 109M) in the centers of galaxies, swallowing (accreting) 1-10M of gas per year.

Matter falls and gains speed. Viscous friction in the accrection process heats the gas. Energy is radiated away before the matter is swallowed. ~10% efficiency.

High speed, well focused jets of particles shoot out perpendicular to the accretion disk: due to magnetic field, etc. Radio Galaxies also do this.

Recently, high-quality CCD images (HST) and spectra (Keck) of relatively nearby QSOs (z = 0.2 - 0.3) show conclusively that they are at the centers of galaxies. Some are interacting or merging with other galaxies --> gas driven toward BH, and emits energy before being eaten.

Soon after the discovery of quasars, some were found with z > 1 (e.g., 2 - But this DOES NOT mean v = 2c, since v = cz works only for v/c < 0.2). Use relativistic Doppler shift:

z = [(1+v/c)/(1-v/c)]1/2 - 1
Even this isn't exactly correct, since redshift is due to the expansion of space not physical motion of galaxies.

Highest known: z = 5.8 (1000 Å at 6800 Å) --> v = 0.98c. We see the QSO when the Universe was ~10% of current age!

The most luminous QSOs are extremely distant: few nearby. Denizens of the young Universe. What happened to them?? They probably faded with time, as the central black holes gobbled up most of the surrounding gas and dust.

Some nearby active and normal galaxies may have been QSOs in the distant past. The Milky Way Galaxy has a somewhat active nucleus. MBH ~ 4x106M. Perhaps is was a QSO long ago...

How do we know there are black holes there with these huge masses?:
Speed of gas in QSOs and active galaxies (measured via the doppler broadening of the emission lines) suggests the presence of supermassive BHs. Recently, however, stars very close to the centers of several normal (or mildly active) galaxies (including the Milky Way) have been shown to be moving very rapidly, along with disks of rapidly rotating gas.

Kepler's 3rd Law: P2 = 42/G(M1 + M*) * r3. M* << M1 And just as in the case of the stars around the galaxy we find:

M1 = rv2/G
For r = 10pc, v = 600 km/s --> M1 = 8 x 108M. Has to be a Black Hole.

## Gravitational Lenses

In a few cases we see two QSOs close together in the sky (just a few arc seconds apart) with identical spectra (redshift and emission lines). We can understand this as a gravitational lensing event.

Light from the QSO is bent by gravity of galaxy or cluster (warped spacetime: it's following the shortest path through the space).

If had a sphere lensed by a perfectly aligned, point-like lens, would get an "Einstein Ring". This is occasionally seen; usually deviations from symmetry lead to discrete images.

When distant galaxies (instead of QSOs) are lensed, tend to get arcs. these are seen around many rich clusters of galaxies.

The clusters act as gravitational lenses. The number and distribution of arcs depends on the mass of the cluster. ---> measure total mass (luminous and dark). --> Conclude that clusters are dominated by dark matter (~90% of total mass). Yet, more evidence for dark matter.

Why is the sky dark at night?

Seems simple but is in fact quite profound.

If the Universe is infinite, every line of sight would intersect a star...so the sky should be bright! (Like looking through a forest).

Several Possible Solutions. Each with profound implications.

1. Universe is not infinite in size.
2. Universe has few stars far away
3. Universe has finite age.