Correlating galaxies with the temperature of Cosmic Microwave Background photons to probe cosmology

Title: The Atacama Cosmology Telescope: Large-scale velocity reconstruction with the kinematic Sunyaev–Zel’dovich effect and DESI LRGs

Authors: Fiona McCarthy, Nicholas Battaglia, Rachel Bean, J. Richard Bond et al 

First author institution: DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, UK
Status: Available on ArXiv

A prediction of a universe that started with a Big Bang is that, today, we should see a background of photons (radiation) coming from all directions in space. This background was discovered in 1965 and is today accepted as an extremely important piece of evidence for the Big Bang Theory. These photons are referred to as the Cosmic Microwave Background (CMB). They are largely all the same temperature everywhere you look – the CMB is quite isotropic. However, it does have some anisotropies – see this image here. Some of these are due to the physical conditions of the Universe at the moment the CMB radiation started moving freely through space around ~380,000 years after the Big Bang. These are called primary anisotropies. However, some of these are a consequence of physics that occurred later – called secondary anisotropies. We can measure these anisotropies in the detectors that collect the photons across different angles in the sky.

As photons move through space and make their way to our telescopes, they can gain energy or lose energy in different processes – these create secondary anisotropies in the CMB. One way in which this energy change occurs is when they move through changing gravitational potentials in an accelerating universe; this also alters their wavelength (and is called the Integrated Sachs-Wolfe Effect). Another way their energy can change is via an effect called the Sunyaev-Zel’dovich (SZ) Effect. In the thermal SZ effect, photons get a doppler shift (a shift in their wavelength) by interacting with hot electrons along their path. These electrons transfer thermal energy to the photons via a process called inverse-Compton scattering. In the kinematic SZ Effect (kSZ), they transfer energy purely via their own motion relative to the photon. This occurs due to the bulk motions of galaxies sourced by their gravitational interactions with other galaxies. The impact of any of these effects can be seen in a map of the CMB and thus can tell us something about the amount of electrons in the Universe and how fast they are moving.

In the paper for today’s bite, the authors look at correlating the motions of galaxies (and their content which includes matter like electrons) in space with the anisotropies one can see in the CMB due to the kinematic SZ (kSZ) Effect. In fact, they find the first statistically significant kSZ signal by cross-correlating measured galaxy velocities with measurements of the secondary anisotropies in the CMB. While this has been attempted previously, the data available which was used was not of high enough resolution. With the CMB data from the Atacama Cosmology Telescope (ACT) and Planck 2018, in addition to measurements of the distribution of galaxies from the Dark Energy Spectroscopic Instrument (DESI) Legacy Survey and the Baryon Oscillation Spectroscopic Survey (BOSS) it has now been proved to be possible.

kSZ tomography and correlation with galaxy velocities

kSZ information from the CMB, when combined with an external measurement of the density or velocity field in the Universe, can allow us to compare observations to cosmological models. Combining this information is called ‘kSZ tomography’ or ‘kSZ velocity reconstruction’. It gives astrophysicists a new way to observe properties of the Universe and how structure is growing and moving due to gravity and the density of matter in the Universe.

The authors of today’s paper go a step further than just performing a kSZ velocity reconstruction. They construct a power spectrum of the cross-correlation between the kSZ velocity reconstruction, and a galaxy velocity signal. Essentially, this power spectrum is a correlation function projected onto a 2D sky, which has been decomposed with spherical harmonics. A spherical harmonic decomposition is similar to a Fourier decomposition but is useful for a 2D spherical map; it allows one to decompose a function defined on the surface  of a sphere into a sum of the spherical harmonic functions (this is actually a standard way of analysing the CMB alone – see Figure 2 in this bite). The resulting power spectrum is a plot of the coefficients from the decomposition as a function of – where is the inverse of the angular scale on the map (larger s meaning smaller angles and vice versa, and larger coefficients correspond to a larger correlations). 

To get this cross power spectrum, the authors require three datasets overall used in various steps to arise at this measurement:

• the CMB measurement which contains the kSZ signal, 
• measurements of the spatial distribution of Luminous Red Galaxies (LRGs) from the DESI Legacy Survey, 
• and measurements of the spatial distribution of galaxies measured by the BOSS survey. These datasets can be used to get information of velocities of galaxies. 

Firstly, the kSZ velocity reconstruction is shown in Figure 1. Essentially, the kSZ, which is a secondary anisotropy, has been separated from the primary anisotropies in the CMB by correlating the temperature fluctuations in the CMB with the density of DESI LRGs on a 2D map. The signal is constructed for 4 different redshift bins (you can think of this as different sky depths – galaxies with higher redshifts are further away).

Next, the authors construct a measurement of a velocity field of galaxies on a 2D map from BOSS data and DESI data. Then, BOSS data is used to construct a 3D velocity field of galaxies (this is estimated theoretically from their spatial distribution in the sky). Then, these velocities are projected onto a 2D map by averaging over them in a way where they are weighted by the relative number of DESI galaxies in the sky to BOSS galaxies. A 2D map is constructed for different depths (redshift bins). The velocity field on the sky is shown for the first redshift bin below (Figure 2) for the BOSS data.

Then, the next step is to cross-correlate each of these velocity signals. Figure 3 shows the resulting power spectrum that arises from a spherical harmonic decomposition of the cross-correlation of the velocity fields.

In reality this measurement is not so simple to do. One must account for the fact that the velocity field of the kSZ signal is mainly sensitive to the motions of electrons which Compton-scatter the photons, while the galaxy velocity field is sensitive to all matter in the Universe (normal matter like electrons and even dark matter). This can lead to a bias in the measurement that needs to be accounted for.

The authors show their signal (the cross power spectrum) is statistically significant in the plot below with a chi-squared analysis. A chi-squared can be used to determine the goodness-of-fit of a model to data, and here they show the goodness-of-fit relative to a model with no cross power spectrum signal. A larger delta-chi-squared shows a higher significance that the detected signal is not consistent with a zero-signal model. The authors find the probability of there being no signal in the data is very low (> 99.7% probability).

Summary

Overall, the authors have demonstrated, as a proof of principle, it is possible to measure a cross-correlation between a kSZ velocity reconstruction and the velocity field that can be inferred from the distribution of galaxies in space. This may help lead to exciting new measurements and tests of cosmological models with future data to help us constrain the properties of the Universe.

Edited by Maria Vincent

Featured image credit: This image is an edited version of two original images (CCA by 4.0), by the ESA and Planck collaboration and by CTIO/NOIRLab/NSF/AURA by Wikimedia Commons.