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My understanding of the CMB radiation is that it comes from everywhere, and goes in every direction.

But how can this be the case, when there is a lot of matter in space which could absorb, or for that matter, reflect, scatter, or refract it?

We see a non-uniform density of CMB, how do we know that was from the initial conditions 378k years after the big bang, and not due (at least in part) to some of the initial CMB being absorbed by or otherwise interacting with other matter between then and now?

Is there simply not enough matter to "soak up" that much CMBR before it reaches Earth? Or are photons of that wavelength simply hard to absorb, maybe passing through common types of matter like gas and dust as easily as infrared? Or have these interactions already been considered and factored out of the picture?

Could taking a CMBR picture of the sky every so often (as the Earth moves around the sun and the sun moves around the solar system) discount this? Or might our perspective relative to early absorbers not be enough to make the readings change noticably?

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This is a good question, scattering of CMB photons is a real effect, but it is not so big that we can not use the CMB radiation to do cosmology. However I don't think actual absorbtion is a large effect, because the photons have so low energy.

The CMB photons mostly scatter elastically off free electrons in the intergalactic medium, in a process called Thomson scattering. This happens only after the universe gets reionized at a redshift $z>6$, since only then do we get a significant number of free electrons for the photons to scatter off. The physical quantity we use to describe such scattering is the optical depth, $\tau$, it basically measures how transparent a substance is at a certain frequency. It gives us the change in intensity $$I_{after} = e^{-\tau}I_{before}.$$ For the CMB photons we would get something like this $$ \tau = \int_0^{z_{ion}} \frac{c\sigma_Tn_e(z)}{H(z)[1+z]}dz,$$ where $$ \sigma_T = \frac{8\pi}{3}\left(\frac{\alpha \hbar}{m_ec}\right)^2$$ is the Tomson scattering cross-section and $n_e,\ H(z)$ and $z_{ion}$ are the number density of free electrons, the Hubble constant and reionization redshift respectively.

The value of $\tau$ is about 0.09, which means that the intensity of the light is reduced by about 9%, or that 91% of the original CMB photons reach us.

Note that the scattering is not dependent on the frequency of the photons, and as long as their energy is alot lower than the hydrogen lines (which is definitely the case for the CMB), they do not interact with the neutral hydrogen in the IGM.

You ask if this scattering could explain the non-uniform intensity of the CMB, but the scattering would have the effect of washing out these non-uniformities (not the other way around).

Groups like the Planck team surely take all these things into account, although I don't know the details of how that is done.

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