What is the Cosmic Microwave Background? II: Recombination

So, I mentioned in the previous post that the CMB was "decoupled" from matter at z~1100 and that this era is also referred to as "recombination". I'll explain why that is in this post.

First, what does "recombination" mean? In general, it's a term used to describe a process in which a free electron "recombines" with an ion to form either an atom or another ion of different charge. In a hot gas in local thermodynamic equilibrium, there will be a balance between a process that removes electrons from their host atoms or ions (ionization) and the process that puts them back (recombination). If the gas is really hot, then most of the electrons will be free. Why? It's mainly because a faster-moving electron is less likely to be captured by an ion and recombine.

We said before that the universe was getting colder with time, so if we assume that the universe was once really hot, then there must have been a time in which nearly all of the electrons were free. This was basically the case prior to z~1100. As the universe expanded and cooled, however, it eventually reached a point at which a given ion would recombine with an electron much more quickly than it would be ionized. It is at this time that "recombination" occurred and the universe switched from a plasma with mainly free electrons and protons to a gas composed mainly of neutral atoms.

Let's get to the main issue at hand; that is, why recombination implies a decoupling of photons from the gas. The answer to this question can be understood classically by looking at the natural frequency of an atom. Since the universe is 90% hydrogen, we can get a rough idea of what's going on just by looking at this simple atom. We know that it has many resonant frequencies, ranging from the UV (the Lyman series) to the optical (the Balmer series) and even on into the infrared (the Paschen series). Thus, one might expect that any frequency of radiation has a decent chance of being absorbed by neutral hydrogen. However, a given atom will only absorb in a specific series and the series in which it absorbs will depend on its energy state. It turns out that most hydrogen atoms in space are in their ground state (n=1), meaning that it will have resonant frequencies in the UV (Lyman series). This will apply to the newly-recombined atoms at z~1100 as well.

Now, let's look at the frequency of the CMB light and determine whether or not we expect it to be absorbed. If we plug z=1100 into the temperature equation I gave in my previous post, we find that the CMB was at ~3000 K at decoupling. From the Wein displacement law that followed, we can determine the peak frequency at this temperature and we find that it lies in the infrared range. There we have it! Since hydrogen in its ground state absorbs mainly in the UV, we won't expect the CMB photons to interact with it very much. Prior to recombination, the electrons were free and could resonate at any frequency they desired, so light was much more readily absorbed. Afterwards, resonances were restricted mainly to the UV and CMB light could readily pass through the see of neutral atoms.

Thus, the light we see in the CMBR today is a very sensitive probe of the distribution of matter at the time of decoupling. This, it turns out, is why the CMB is such a good cosmological probe.