Cross-correlating the Thermal Sunyaev-Zel'dovich Effect and the Distribution of Galaxy Clusters

TL;DR

This paper develops analytical formulas based on the halo model to analyze the cross-correlation between the thermal Sunyaev-Zel'dovich effect and galaxy cluster distributions, enabling detection of SZ signals below individual detection thresholds.

Contribution

It introduces a method to compute the stacked SZ signal and its covariance, forecasting its detectability with upcoming CMB and optical surveys, and explores gas physics at cluster outskirts.

Findings

Stacked SZ signals can be detected with S/N > 10 across various masses and redshifts.

The stacking method probes SZ profiles out to the virial radius.

Forecasts indicate significant detection prospects with future surveys.

Abstract

We present the analytical formulas, derived based on the halo model, to compute the cross-correlation between the thermal Sunyaev-Zel'dovich (SZ) effect and the distribution of galaxy clusters. By binning the clusters according to their redshifts and masses, this cross-correlation, the so-called stacked SZ signal, reveals the average SZ profile around the clusters. The stacked SZ signal is obtainable from a joint analysis of an arcminute-resolution cosmic microwave background (CMB) experiment and an overlapping optical survey, which allows for detection of the SZ signals for clusters whose masses are below the individual cluster detection threshold. We derive the error covariance matrix for measuring the stacked SZ signal, and then forecast for its detection from ongoing and forthcoming combined CMB-optical surveys. We find that, over a wide range of mass and redshift, the stacked SZ signal can be detected with a significant signal to noise ratio (total S/N \gsim 10), whose value peaks for the clusters with intermediate masses and redshifts. Our calculation also shows that the stacking method allows for probing the clusters' SZ profiles over a wide range of scales, even out to projected radii as large as the virial radius, thereby providing a promising way to study gas physics at the outskirts of galaxy clusters.