FRS 113, Writeup 1: The Big Bang Model

The Expanding Universe

The universe is expanding. How do we know this? We measure the spectra of galaxies. Galaxies are made of stars, and thus the spectra of galaxies look very much like those of stars. In particular, the spectra of stars show strong absorption lines, at wavelengths corresponding to transitions of elements in their atmospheres. One sees the same pattern of absorption lines in galaxy spectra, but they are not at the same wavelengths: they are shifted systematically to the red.

The interpretation: the galaxy is moving away from us. The wavelength tex2html_wrap_inline43 of light waves from an object moving away from us at speed v is shifted by an amount:
where c is the speed of light, tex2html_wrap_inline51 centimeters per second. This is the Doppler Effect, which also occurs for sound waves (as written, it is strictly correct only for speeds much less than the speed of light). Thus the observation that galaxies are redshifted, implies that they are moving away from us.

Edwin Hubble also measured the distances to galaxies. He used the Inverse Square Law, which states that the more distant an object of a given luminosity, the fainter it appears:
Make sure you understand the distinction between luminosity (the total amount of energy per second an object is giving off; units of ergs/second) and brightness (the amount of that energy per second that we perceive through our eyeballs or telescope; units of ergs/second/square centimeter).

Thus if we measure the brightness of a star whose luminosity we know (therein lies a lengthy tale), we can infer its distance. Hubble measured the brightness of stars called Cepheid variables in galaxies to infer their distances.

He then compared the galaxy distances he measured to their redshifts. He found that the larger the distance r, the larger the redshift z (or equivalently, the recession speed v that one infers from the Doppler formula above):
where tex2html_wrap_inline63, the Hubble Constant, is approximately:
(A Megaparsec, or tex2html_wrap_inline67 parsecs, is a measure of distance. The nearest big galaxies to our own are a bit less than one Megaparsec away. One parsec is 3.26 light years, so one Megaparsec is about tex2html_wrap_inline69 centimeters).

Thus, the galaxies are all moving away from us; the further they are from us, the faster they are moving. This is what one expects if all the galaxies were very close together at one point in time, and went flying apart in what we now call The Big Bang.

Consider two galaxies separated by a distance r; the Hubble Law says that they are moving apart at a speed tex2html_wrap_inline73. So how long ago were the two galaxies together? Just the time it takes to travel a distance r at that speed:

What was the Early Universe like?

One of the properties of an expanding gas is that it cools. The universe is expanding, therefore it was much hotter in the past. Indeed, the early universe was extremely hot and extremely dense (but not extremely small; that's another story). Indeed it was so hot and dense early on that galaxies couldn't exist, nor could stars or planets... If you turn the clock back far enough, neither could molecules or neutral atoms. About one minute after the Big Bang, the temperature was about tex2html_wrap_inline79 degrees; the constituents of the universe consisted of electrons, protons, neutrons, photons (particles of light), neutrinos, and whatever it is that makes up the dark matter. And that's it. As the universe cooled and expanded, the neutrons and protons came together to make several atomic nuclei in a process called primordial nucleosynthesis, in particular:

And that's it. (Neutrons decay with a half-life of about 10 minutes if they are not incorporated into a nucleus, so there will be none that survive to the present.)

Astronomers have done detailed calculations of the amounts of these various elements that should have been produced in the first minutes after the Big Bang. They conclude that:

These numbers are in excellent accord with what is observed in the universe. Thus the Big Bang model gives us a quantitative explanation of the atomic constituents of the universe. (Later in the course, we'll talk about where all the rest of the atoms, in particular the Carbon, Oxygen, Nitrogen, Iron, Nickel, Silicon, etc., so important for planets and life, come from).

The Cosmic Microwave Background

An ordinary atom consists of an atomic nucleus, with electrons in orbitals around it. It was much too hot for the nuclei to hold onto their electrons in the early universe, so the atoms were all ionized. Indeed, the universe had to cool down to a temperature of 3000 K before electrons and nuclei could stick together, and neutral atoms could form. This happened roughly 400,000 years after the Big Bang.

The ionized gas, or plasma of the early universe acted as a sort of fog; photons could not travel very far before being deflected. But when neutral atoms formed when the electrons and nuclei came together, the photons were free to travel straight. Thus the Big Bang model predicts that there should be photons arriving at the Earth right now that were ``set free'' 400,000 years after the Big Bang. The detection of these photons in 1965 (the Cosmic Microwave Background) was the defining moment at which the astronomical community became convinced that the Big Bang model was correct. The detailed properties of these photons: their spectrum, their uniformity across the sky, and so on, are in excellent accord with the Big Bang model. (The details of that statement are worth an entire course in itself!).

The Age of the Universe

Our interpretation of the expansion of the universe implies an age of 14 billion years. It turns out that we can also infer the ages of clusters of stars. As stars age, stars of ever lower mass burn out, so in a cluster of stars of a certain age, all the stars more massive than a certain mass will have died out. The oldest clusters are thereby inferred to have an age of about 13 billion years, in excellent agreement with (and reassuringly slightly smaller than) the age inferred from the expansion rate of the universe.

The Universe Evolves

Light travels at tex2html_wrap_inline51 centimeters per second: fast, but not infinitely so. When we see a galaxy at a distance of a few million light years, those photons left the galaxy a few million years ago. Thus in astronomy, looking at great distances is looking back in time. Therefore, we are seeing the most distant galaxies in our telescopes at a time when they were appreciably younger than the galaxies we see nearby. Astronomers are currently testing the Big Bang model further by checking these ideas: do distant galaxies really look younger than those today? The way galaxies evolve with time is poorly understood, so it is not completely obvious what we would look for as signs of youth, but the basic answer to this question is yes.

Michael Strauss
Sun Sep 12 13:28:55 EDT 2004