Is the universe macroscopically transparent to CMB? Is the fraction intercepted by stars and dust so tiny that it doesn't have a correction factor?

Question

Background

The question Why do some electromagnetic waves continue travelling while others disappear? is interesting, and in addition to the answer there I started to write:

This is a supplementary answer to @ConnorGarcia's answer using the example in the question. It's not very accurate but it does address part of the question:

Cosmic background radiation emitted when the Universe was very young still exists. But my wifi signal seems to disappear a short distance from my apartment. Why?

Imagine walking around in the middle of a city with a receiver that can pull in 900 MHz to 5 GHz. It will tell you that you are in a "soup" of radio photons; no matter where you go inside the city you'll...

and then realized I didn't know what I was talking about.

Question

So instead I'd like to ask about the following:

I think that CMB photons are believed to be "pristine photons" from soon after the big bang rather than absorbed and re-emitted and thermalized, and I seem to remember recently reading an answer here or in Physics SE saying that a measured CMB spectra (in any given direction) is fit with a Planck distribution with unity emissivity; there was no "fudge" or scaling factor in front for the absolute spectral radiance measured.

But now I can't find that answer anywhere!

Together those suggest to me that macroscopically the universe is essentially transparent to CMB, and the fraction intercepted by stars and dust between us and it is so tiny that it doesn't require a correction factor.

Question: Have I got this right?

Answer 1

For the most part, the CMB photons travel directly to our telescopes from the surface of last scattering. Some corrections need to be made to determine the blackbody nature of the spectrum, but they are not corrections for absorption of the photons.

The two main corrections are shown clearly by this COBE image sequence:

(from here).

First, the motion of us as observers, relative to the rest frame of the CMB, distorts its single-temperature blackbody shape, making it appear hotter in one direction and cooler in the opposite direction.

Once this is removed (by a sky-position-dependent frequency shift), the foreground emission of the Milky Way becomes apparent (middle panel), and that must be modeled and subtracted. The dust in our Galaxy is on average hotter than the CMB, so its contribution can be measured well by observing over a range of wavelengths, and of course it is most heavily concentrated toward the Galactic plane.

After that is subtracted, the remaining emission (bottom panel) is that of a blackbody to very high precision, with of course the remaining structure that gives us so much interesting information about the early universe.

Here is part of the key concluding paragraph from the Mather et al. 1992 paper on measuring the spectrum:

The FIRAS spectrum of the cosmic microwave background radiation agrees with a blackbody spectrum to high accuracy. The CMBR spectrum is the result of fitting a model including a dipole and a dust map derived from 240 micron data, excluding a region around the Galactic center. The final temperature is 2.726 +/- 0.010 K (95% CL systematic), where the error is dominated by our estimate of the thermometry errors.

So they are shifting the emission and subtracting the foreground emission, but not applying any overall correction for absorption of the emission.

Answer 2

Let me add a minor addendum to Eric's excellent answer.

The primary way in which CMB photons interact with matter is via scattering off of electrons in plasmas. After recombination (redshift $\sim 1100$, about 370,000 years after the Big Bang), the baryonic matter of the universe was overwhelmingly not ionized, so there weren't any free electrons to scatter CMB photons. But starting around a redshift or 10 or so (a few hundred million years later), something began "reionizing" the H and He atoms, to the point that most of the universe was ionized again by a redshift of around 6 (about a billion years after the Big Bang). (This "something" is generally understood to be UV radiation from the first generations of stars, aided by UV radiation from active galactic nuclei.)

CMB photons traveling through the reionized universe can interact with the electrons in the reionized plasma -- mostly earlier on, since the expanding universe dilutes the plasma and makes it harder for photons to encounter an electron. For electrons in plasmas with temperatures of $\sim 100,000$ K or less (which is most of the universe!), this takes the form of Thomson scattering, which has the net effect of altering the paths of the photons and increasing their polarization; the former effect does introduce a slight blurring effect. It does not, however, change the overall distribution of photon energies, and so the CMB blackbody spectrum is unaffected. As the Physics stackexchange answer by pela notes, this effect is computed as part of analyzing the CMB, and the current estimates are a total optical depth $\tau$ (from recombination to us) of $\sim 0.06$, which means that only $\sim 6$% of the CMB photons end up scattered this way.

In massive galaxy clusters, however, the intergalactic plasma is denser and hotter, with temperatures reaching $\sim 10$ million K or higher. Electrons with temperatures like this are moving at significant fractions of the speed of light, and scatter photons in a process called inverse Compton scattering. This includes the deflection and polarization seen in Thomson scattering; but it also, on average, boosts the photon energies. This has the effect of shifting the observed CMB temperature to slightly higher values. This "Sunyaev-Zeldovich (SZ) effect" has actually been measured, and is used for some cosmological calculations. However, since only a very small fraction of the universe's volume is in the form of galaxy clusters, this has a very small overall effect; the SZ optical depth through a massive cluster is only $\sim 0.01$, so even there only about 1% of the photons are affected.