Understanding Photon Thermalization and Its Impact on CMB Anisotropies

[guest1234]

Quick question: what is meant by thermalization of photons? And how could this effect distort CMB spectrum (anisotropies)?

Any references are also welcome.

 

[bapowell]

Thermalization of photons means that photons are coming into thermal equilibrium with other particles through interactions.

Regarding CMB distortions, fluctuations in the baryon-photon plasma below the Jeans scale oscillate as acoustic waves during radiation domination. The energy of these fluctuations is dissipated via diffusion damping, resulting in a redistribution of this energy from the fluctuations into the baryon-photon plasma. At early times (redshifts z > 10^6 or so), frequent and efficient interactions quickly thermalize the baryon-photon plasma, preserving its black body spectrum. As the universe cools interactions become insufficient to maintain a black body: a frequency-dependent chemical potential develops and the spectrum shifts to that of a Bose-Einstein distribution. So, while small-scale perturbations are erased before recombination, they leave behind a record of their existence: the energy lost by the perturbations is injected into the CMB distorting the spectrum away from a black body by an amount that depends on the shape and amplitude of the power spectrum on the relevant scales.

 

[Mordred]

your probably, though just a guess with the info you provided referring to thermalization of photons by a colder plasma. This is a possible effect that occurred during the early universe. This is a process that photons transfer energy to a cooler electron plasma. This results in a lower frequency of photons.

this article covers this process in better detail than my poor attempts

"Does Bose-Einstein condensation of CMB
photons cancel μ distortions created by dissipation of sound waves in the early Universe?"

http://arxiv.org/pdf/1110.0475v3.pdf

 

[Mordred]

Just saw Bapowell's post which is a far better answer, the article still helps as it expands a bit on his reply

 

[guest1234]

Thanks, your answers cleared up some of the things.

One thing bugs me though, FTA:

The cooling of electrons and the corresponding spectral distortions are easy to calculate and only depend on the standard cosmological parameters, such as baryon to photon number density $\frac{n_B}{n_\gamma}$ [...]

How is this accomplished? I know that CMB anisotropies are quantitatively obtained by perturbing the metric, but afaik no abundances nor densities don't kick in the derivation.
In particular, how does baryon (or, as I am already at it, any species of particles) number density affect CMB energy spectrum?

Disclaimer: I have only read first 100 p of Dodelson and only glimpsed at later chapters. If there is no short answer, then don't bother answering to these questions.

 

[bapowell]

Are you clear on the fact that CMB temperature anisotropies and spectral distortions are two different effects?

 

[Mordred]

Thanks, your answers cleared up some of the things.

One thing bugs me though, FTA:


How is this accomplished? I know that CMB anisotropies are quantitatively obtained by perturbing the metric, but afaik no abundances nor densities don't kick in the derivation.
In particular, how does baryon (or, as I am already at it, any species of particles) number density affect CMB energy spectrum?

Disclaimer: I have only read first 100 p of Dodelson and only glimpsed at later chapters. If there is no short answer, then don't bother answering to these questions.

If your referring to Scott Dodelsons "Modern Cosmology 2nd edition" I have a copy. Good book however I found I needed additional resources to help fill in a few blanks lol. The chapters 3, 4 and 8 are related to your question. However as I stated a few aspects he expects you to already understand. One of the aspects is the ideal gas laws treatments. The Boltzmann-Einstein equations involve those ideal gas laws. Each species of particles adds complexities and degrees of freedom due to spin, anti-particles, chemical reactions, relativistic vs non relativistic etc. Photons being its own anti-particle with spin 1, has an entropy value of S=2 (including its anti-particle). In thermal equilibrium this is described as a Bose-Einstein condensate with a fermi-Dirac distribution. When you add Baryons the distributions gets far more complex. Baryons have spin 1/2 or 3/2 not including its anti-particle, however if the reaction rate is higher than the expansion rate, these two can be described in thermal equilibrium. However this isn't always the case. Eventually the amount of volume can no longer allow particles to remain in thermal equilibrum. When this occurs different species of particles will have differing distribution patterns. Google Maxwell-Boltzmann distributions, or Boltzmann-Einstein distributions for some examples. When this non-equilibrium occurs, anistrophies due to the different particle species properties occur.

"Particle Physics of the early Universe" by Uwe-Jens Wiese has an excellent coverage of the thermodynamic treatments, I found this article of particular use to fill in some of the gaps in Dodelsons Modern Cosmology.

http://www.wiese.itp.unibe.ch/lectures/universe.pdf


Hope this helps and didn't add additional confusion.

 

[bapowell]

In thermal equilibrium this is described as a Bose-Einstein condensate with a fermi-Dirac distribution.

Don't you mean Bose-Einstein distribution?

 

[Mordred]

Yeah thanks