During the recombination era, two things happened:

  1. Electrons and protons bonded to form neutral hydrogen atoms.
  2. As a result of #1, Compton scattering is no longer efficient enough to keep photons and electrons in equilibrium. Thus photons decoupled from other particles and the CMB formed.

However, based on what I gather from this other post here, Compton scattering can still occur between photons and composite neutral particles. A photon can interact with the quarks of a neutron and it can interact with the charged parts of a neutral hydrogen atom.

Even for neutral fundamental particles, there can still be scattering cased by the coupling between the particle and the EM field due to the spin of the particle.

Given this, how can we say #2 above is true? How does the fact that charged particles are combining into neutral particles lead to photon decoupling if Compton scattering can still occur with the charged components of the new particles? And moreover, how can this happen if scattering can occur between neutral particles and photons?


1 Answer 1


As a general remark before getting into more detail, you should keep in mind that the fact that a process can occur, is not sufficient to argue that it is relevant for determining equilibrium. One must also consider the reaction rate for that process, compared to other rates in the problem.

CMB photons after recombination do not have nearly enough energy to interact with a nucleus at an appreciable rate. Just to give a rough order of magnitude, nuclear energy scales are of order of ${\rm MeV}$ (and to probe the quarks within a nucleon requires several of orders of magnitude more energy than that), and photons had energy less than $13.6\ {\rm eV}$ after recombination. Actually the average energy of a photon was much less than this; because of the huge value of the photon-to-baryon ratio $\eta\approx 10^{10}$, recombination occurred only when the temperature was small enough that of order or fewer than $1$ in $10^{10}$ photons had a high enough energy to ionize Hydrogen, at a temperature of around $0.3\ {\rm eV}$.

Photons can interact with bound electrons in Hydrogen, however one must keep in mind two things:

  • Photons will only strongly interact with Hydrogen at discrete energies, corresponding to transitions between states in Hydrogen, so the blackbody spectrum of the CMB formed after recombination will only be affected at discrete lines (or, a superposition of redshifted lines).
  • Generally, photons do not have enough energy to cause transitions between the ground state and first excited state of hydrogen ($3.4\ {\rm eV}$, which is a substantial fraction of the ionization energy), so interactions will only be possible for more subtle, lower energy transitions.

In fact, there is a source of background radiation that does occur after recombination due to the hyperfine structure transition in Hydrogen, leading to the 21-cm line (although this radiation has a different source and signature than CMB photons). The 21-cm emission is an important probe of structure formation that is a target of observatories like the Square Kilometer Array (SKA). Because photons will redshift between the time that they participate in the hyperfine transition and the time we observe them, we can use observations of the strength of the 21-cm signal at different frequencies to observe structure formation as a function of redshift, during the "dark ages" when there is no other source of light strong enough to observe.


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