4 december 2001astronomy 102, fall 20011 image: bob wilson (left) and arno penzias with the horn...

4 December 2001 Astronomy 102, Fall 2001 1

Image: Bob Wilson (left) and Arno Penzias with the horn antenna they used to discover the cosmic microwave background.

Today in Astronomy 102: the Big Bang

General relativistic Universes: dynamic and static.

The Universe expands: no use for static models.

Cosmological models: Big Bang and steady state.

Observational tests of the models, and the direct observation of the Big Bang.


“Mid”-lecture break will be at the end of class.

That’s so we can issue the Student Course Opinion Questionnaires. Stick around. Note, also, that Homework

#7 is available now on WeBWorK, and due on 14 December.

This is Edwin Hubble, pretending he’s observing at the Newtonian focus of the Mt. Wilson 100-inch Telescope. It would be dark if he were really observing, of course. (Caltech Archives)


Back to general relativity and the structure of the Universe …

Einstein and de Sitter (late 1910s and 1920s, Germany), Friedmann (1922, USSR), Lemaître (1927, Belgium), and Robertson and Walker (1935, US/UK) produced the first solutions of the field equations for an isotropic and homogeneous Universe.The types of solutions they found: Collapse, ending in a singularity. Expansion from a singularity, gradually slowing

and reversing under the influence of gravity, ending in a collapse to a singularity.This, and the previous outcome, are for universes with total kinetic energy (energy stored in the motions of galaxies) less than the gravitational binding energy. They are called closed universes.


General relativity and the structure of the Universe (continued)

Expansion from a singularity, that gradually slows, then stops. (Total kinetic energy = gravitational binding energy.)This is generally called a marginal, or critical, Universe.

Expansion from a singularity, that continues forever (total kinetic energy greater than gravitational binding energy). This is called an open universe.

Model 1 is of course a lot like what we now call black hole formation, since it ends in a singularity. Note that models 2-4 all involve expansion from a singularity, so the creation and development of the Universe must be rather like black hole formation running in reverse.


Einstein doesn’t like it.

All the solutions have these features in common: singularities, and dynamic behavior: the structure given by the solutions

is different at different times between singularities (at which time doesn’t exist, of course).

Einstein thought that singularities such as these indicated that there were important physical effects not accounted for in the field equation. He also thought that the right answer would involve static behavior: large-scale structure should not change with time. He also saw how he could “fix” the field equation to eliminate singular and dynamic solutions: introduce an additional constant term, which became known as the cosmological constant, to represent the missing, unknown, physical effects.


The field equation and the cosmological constant: hieroglyphics (i.e. not on the

exam or homework)The field equation under a particularly simple set of assumptions and conditions for a homogeneous and isotropic Universe:

The same equation modified by Einstein (1917):

22

21 8

3dR G k

cR dt R

Typical distance between galaxies

Mass per unit volume

Spacetimecurvature

2 22

21 8

3 3dR G c k

cR dt R

Cosmological constantA certain positive value of leadsa static solution.


Edwin Hubble strikes again: the Universe expands.

Then, in 1929, Hubble made his third great contribution to cosmology; he observed that: distant galaxies are always seen to have redshifted

spectra. Thus they all recede from us. the magnitude of this Doppler shift for any given

distant galaxy is in direct proportion to the distance to this galaxy: with V = velocity and D = distance to galaxy,

where H0 = 20 km/sec/Mly according to the most recent measurements by the Hubble Space Telescope.

This means that the Universe is expanding.

(Hubble’s Law)


Relation between galaxy redshift and distance

Visible-light spectra (left) of several different galaxies (right). The extent of the redshift, denoted by the horizontal yellow arrows, and the distance to each galaxy (in the center) increase from top to bottom. 1 parsec = 3.26 ly. (Figure: Chaisson and McMillan, Astronomy Today.)


Einstein gives up.

The Universe is observed to be expanding; it is not static. Thus the real Universe may be described by one of

the dynamic solutions to the original Einstein field equation. Of the four types we discussed above, the last three spend at least part of their time, if not all, expanding.

Thus there appeared to be no point in Einstein’s cosmological constant, so he let it drop, calling it “my greatest blunder.”

Thereafter he began trying to show that the singularities in the dynamic solutions simply wouldn’t be realized. His effort resulted in the steady-state model of the Universe, which we’ll describe later.

This isn’t the last we’ll see of the cosmological constant, though.


Possibilities for the structure of the expanding Universe

All three expanding solutions predict that the matter in the universe was concentrated at earlier times, and that the expan-sion started as an explosion of this concentration: the Big Bang.

Typical distance between galaxies Time

Unbound (open)

Bound (closed)

Marginal (total kinetic energy = binding energy)

Big Bang Big Squeez

e


Possibilities for the structure of the expanding Universe (continued)

Typical distance between galaxies Time

Unbound (open)

Marginal (total kinetic energy = binding energy)

To tell which solution describes the real Universe, we need to measure the acceleration of the galaxies as well as their velocities. Astronomers have been working on this for decades.

Bound (closed)


Summary of Hubble’s findings

The Universe is isotropic: on large scales it looks the same in all directions, from our viewpoint.

The Universe is homogeneous: it is uniform on large scales. In other words, the Universe looks the same from any viewpoint.

The Universe is expanding: • The galaxies recede from us, faster the further

away they are.• And since the Universe is homogeneous, we

would see the same recession no matter where we stood. That is, there is no unique center in space, of the expansion, as in an ordinary explosion and blast wave.


Why galaxies recede from an observer in the expanding Universe, no matter

where she stands.

Universal expansion

A

B

A’

B’

All intergalaxy distances increase: A’ > A, B’ > B.(The galaxies themselves donot expand, though.)


Why galaxies recede from an observer in the expanding Universe, no matter

where she stands.A

B

A’

B’

Galaxies recede from one another, and recede faster the further apart they are: B’-B > A’-A. Because the galaxies recede, the Doppler shifts are all redshifts.

Universal expansion


Results by Hubble and Humason, 1929

Graph from Ned Wright’s Cosmology Tutorial.

1 Mly = 106 ly

V H D

H

0

0 142

,

km/ sec/ Mly


An up-to-date Hubble-constant determination (Riess, Press and

Kirschner 1996)

0 19.6 0.9 km/ sec/ MlyH

In AST 102 we’ll take the Hubble constant to be H0 = 20 km/sec/Mly.

Graph from Ned Wright’s Cosmology Tutorial.


Example. The redshift of 3C 273 corresponds to a speed of 48,000 km/sec. How far away is 3C 273?

Example. The center of the nearest cluster of galaxies, the Virgo Cluster, is 70 Mly away. What is the recession speed we expect for galaxies near the center of this cluster?

Simple use of Hubble’s Law

3

0

km48000

sec 2.4 10 Mlykm

20 sec Mly

VD

H

0km km

20 70 Mly=1400 sec Mly sec

V H D


Cosmological models

Once Hubble’s observations made it clear that the Universe is not static, two types of model remained for the structure of the Universe:The Big Bang model: based upon non-static universes with constant total mass and energy, presently in a state of expansion, but originating in a singularity. Major proponents: Friedmann, Lemaitre, Robertson, Gamow, Pope Pius XII, Sandage.The Steady-State model: in which the singularities are not realized, because steady creation of new matter leads to a constant density on the average, expansion, and no “beginning” or “end”. Major proponents: Einstein, Bondi, Gold, Hoyle, Chairman Mao, Arp.


Observational tests of cosmological models

Big Bang Universe proponents made these specific predictions on the basis of their models: On very large scales - a substantial fraction of the total

size of the Universe - galaxies would be closer together on average than they are now, owing to the expansion and early curvature of the Universe. (Recall: far away = far back in time; spacetime is warped close to singularities.)

Evolution: very distant (young) galaxies should be qualitatively different on average from nearby galaxies.

We should be able to see the blast of the Big Bang itself, by looking far enough away. It would look like a hot, opaque body, but with its light Doppler-shifted to extremely long wavelengths because it is so far away. (V = H0D and = 0(1 + V/c): much larger than 0.)


Observational tests of cosmological models (continued)

And for their part, those studying the steady-state model predicted: that galaxies would appear to be distributed

uniformly, and spacetime would appear to be flat, no matter how far away we look.

no evolution: the internal properties of galaxies – what kinds of stars they have in them, what concentrations of heavy elements they possess, etc. – would be the same, on the average, everywhere in the Universe. That is, there should be no tendency for distant galaxies to look young.

A few steady-state proponents even predicted that galaxy redshifts would turn out not to be of cosmological origin, but instead would represent material ejected at high speeds by galaxies with small Doppler shifts.


Observational tests I: radio galaxies at large redshifts

Soon after radio galaxies were identified in the 1950s it was realized that most of the faint radio sources in the sky must be radio galaxies, mostly at distances much greater than those determined for visible galaxies. Counting the numbers of these faint sources as a

function of their brightness basically provides a repeat of Hubble’s demonstration that galaxies are distributed homogeneously on large scales.

However, the faint radio sources should be much farther away than the faint galaxies observed by Hubble: far enough away to expect these galaxies to be closer together on average than present-day galaxies in a Big Bang model.


Observational tests I: radio

galaxies at large redshifts

(continued)Results by Pooley and Ryle (1968) (points) and a big-bang model (curve) in black, compared to a steady-state Universe, in red.

Nu

mb

er

or

rad

io g

ala

xie

sp

er

squ

are

deg

ree o

f sk

y

Brightness (power per cm2 of telescope area)

Data

Steady-stateUniverse


Observational tests I: radio galaxies at large redshifts (continued)

Implications of radio-source counts like those by Pooley and Ryle: As one looks back through time, the number of

radio galaxies per unit volume increases (or typical separation decreases) up to very great distances.

At the largest distances, the number of radio galaxies per unit volume decreases again.

Thus either the Universe is not homogeneous, or is not flat, or contains galaxy populations that evolve (with radio-galaxy appearance as one phase of development), or all three.

In any case, this is inconsistent with the predictions of the Steady State model, but explicable in Big Bang models.


Observational tests II: direct observation of the Big Bang

In the 1940s, George Gamow’s students, Ralph Alpher and Bob Herman, predicted that the blast from the Big Bang should be detectable someday. Specifically: light would be seen that arose at the

time when the Universe had cooled to the point that atoms could form.

The light started off visible, but owing to the great distance of its source it would be redshifted into the microwave band (wavelengths of a millimeter to a few centimeters), and look like a black body with a temperature a few degrees Kelvin (above absolute zero).

Since it was close to a singularity when emitted, the light should appear isotropic: spread uniformly across the sky. (We’ll explain why it should look like this, in a bit.)


Observational tests II: direct observation of the Big Bang (continued)

In 1965, Bob Wilson and Arno Penzias (AT&T Bell Telephone Laboratories) were working on a very sensitive microwave receiver and antenna they built for satellite communication. They were trying to tune it up to reach ideal performance, but persistently found extra noise power for which they couldn’t account. They knew nothing of Gamow’s prediction. The extra power was like that of a black body with

temperature 2.7 K (2.7 degrees above absolute zero). It was the same no matter which direction they

pointed their antenna. ( If it comes from the sky, it’s isotropic.)

They were grasping at straws for an explanation, when they were paid a visit by radio astronomer Bernie Burke, a professor at MIT.


Observational tests II: direct observation of the Big Bang (continued)

Burke knew of efforts at Princeton U. by Dicke and Peebles to build a sensitive microwave receiver and antenna to look for the Big Bang radiation predicted by Gamow, but were having technical troubles. He introduced the Bell Labs group to the Princeton group. It was quickly noticed that Penzias and Wilson had

indeed detected that relict radiation (now called the Cosmic Microwave Background).

Thus the blast from the Big Bang is seen directly. This is the sturdiest nail in the coffin of the Steady-State Universe.

For this epochal discovery, Penzias and Wilson shared the 1978 Nobel Prize in Physics.

4 december 2001astronomy 102, fall 20011 image: bob wilson (left) and arno penzias with the horn...

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