# Correlation between large-scale galaxy structure and CMB fluctuations?

During a relatively non-technical astronomy seminar the other day, the speaker displayed the famous WMAP full-sky image as an aid to describing what the CMB is, the scale of its fluctuations, etc. This speaker mentioned that there are correlations between the higher-temperature regions on the map and regions of large-scale galaxy structure seen in deep-sky surveys.

I was surprised to hear this. My understanding is that CMB is an image of events currently about 14 billion light years away, while the observed large-scale filaments of galaxies are at approximately half that distance. I wouldn't have expected any density fluctuation 14 billion light years away to share any correlation with a density fluctuation 7 billion light years away.

When I asked, the speaker admitted to being "mostly a star guy" and continued with his excellent talk.

Is there actually a correlation between the warmer, denser regions of the CMB and the distribution of dense galaxy clusters? Is there a causal reason for these distant objects to be correlated with each other? Is there a lensing effect on the CMB temperature? Or is this "correlation" just an enticing-sounding mistake, slowly working its way into common knowledge?

## 1 Answer

Yes, indeed there is a correlation between warm regions of the CMB and galaxy clusters.

The CMB fluctuations depends on what scale of perturbation that you look at. For large scale perturbations, the opposite to what we expect is true. On the large scales, an overdense region at the time of recombination results in a cold spot in the CMB map. This is because an overdense region will have a higher gravitational potential. While indeed temperature is warmer in such areas, the photons escaping from this potential-well loose more energy. Hence we get a cold spot on the CMB map.

As regards the Large Scale Structures, like galaxy clusters, the reason they are correlated with warm spots is due to what's know as the Sunyaev-Zel-Dovich Effect.

What happens here, is that, as you correctly say, the CMB photons are comming from about 380,000 years after the Big Bang. On their journey towards us, to measure them, they may pass through some galaxy clusters. Since the electrons in the galaxy cluster are hot in the plasma core, Compton scattering occurs between the CMB photons and the hot electrons, resulting in the hot electrons imparting energy to the CMB photons. Thus the CMB photons have more energy when they emerge on our side of the galaxy cluster. That is, they appear as warmer regions on the CMB map in the direction of galaxy clusters.

It's actually very cool, since as you say, it's a suprising result! And is certainly not a mistake "working its way into common knowledge".

According to wikipedia the core of a galaxy cluster can be as much as $10\times10^6$ and $100\times10^6$K. Funnily enough, I know nothing about stars, except for maybe some very basic fresher undergrad courses!

• The SZ effect is not the only correlation between the CMB anisotropies and structure. Some anisotropies correspond to the initial background perturbations that evolved after horizon crossing to become the large-scale structure we see today. In a sense, the temperature fluctuations in the CMB helped to define the positioning and magnitude of the structure that exists today – Jim Apr 17 '14 at 22:32
• @Jim Are you very sure about that? That is what I was addressing in the second paragraph above. In our lectures we were tought that large scale perturbations an overdense region at recombination correspond to cold sopts on the CMB map. This is the opposite to what you would expect, because these regions do indeed become LLS. The question was specifically about the reason that there are warm spots on the CMB map in the direction of LLS... – Flint72 Apr 18 '14 at 15:51
• @Jim ...In fact, re-reading your comment, I agree with all three sentences you say. However "some anisotropies" could be either warm or cold spots, while we are here interested only in the warm spots. – Flint72 Apr 18 '14 at 15:51
• @rob Well, not the exact same perturbations, of course, as they happen at different points in space, but same kind of perturbations. This is because these perturbations are basically density fluctuations in Dark Matter, which dominates the matter distribution in the Universe. Dark Matter doesn't collide and therefore there is no pressure causing acoustic oscillations like ther would for gas. Once DM stars collapsing gravtiationally, this effect continues; from small-amplitude perturbations at CMB to galaxies and clusters and supercluster structure. – Thriveth May 5 '14 at 10:53
• @rob Think of it like this: After horizon decoupling, dark matter starts to form structure, while baryons still collide which means they cannot. Once they recombine to form atoms, they fall into already existing gravity wells (of very small depth), which causes the intrinsic temperature fluctuations of the CMB. These gravity wells since grow larger as more Dark (and baryonic) Matter fall into them, eventually becoming the structure of the Universe as we observe it at later times. The S-Z effect comes on top of these other effects, somewhat confusing the image. – Thriveth May 5 '14 at 10:56