Cross Correlation between the Thermal Sunyaev-Zel'dovich Effect and Projected Galaxy Density Field

TL;DR

This paper analyzes the correlation between the thermal Sunyaev-Zel'dovich effect and galaxy density using Planck and WISE data, constraining galaxy bias and mass bias with high significance.

Contribution

It presents the first joint analysis of tSZ and galaxy density power spectra, constraining key cosmological parameters with high statistical significance.

Findings

Detected the cross-correlation with 21.8σ significance.

Measured auto-correlation spectra for tSZ and galaxy maps with over 88σ significance.

Constrained the hydrostatic mass bias and galaxy bias parameters with detailed uncertainties.

Abstract

We present a joint analysis of the power spectra of the Planck Compton $y$-parameter map and the projected galaxy density field using the Wide Field Infrared Survey Explorer (WISE) all-sky survey. We detect the statistical correlation between WISE and Planck data (g$y$) with a significance of $21.8\,\sigma$. We also measure the auto-correlation spectrum for the tSZ ($yy$) and the galaxy density field maps (gg) with a significance of $150\,\sigma$ and $88\,\sigma$, respectively. We then construct a halo model and use the measured correlations $C^{\rm gg}_{\ell}$, $C^{yy}_{\ell}$ and $C^{{\rm g}y}_{\ell}$ to constrain the tSZ mass bias $B\equiv M_{500}/M^{\rm tSZ}_{500}$. We also fit for the galaxy bias, which is included with explicit redshift and multipole dependencies as $b_{\rm g}(z,\ell)=b_{\rm g}^0(1+z)^{\alpha}(\ell/\ell_0)^{\beta}$, with $\ell_0=117$. We obtain the constraints to be $B =1.50{\pm 0.07}\,(\textrm{stat}) \pm{0.34}\,(\textrm{sys})$, i.e. $1-b_{\rm H}=0.67\pm 0.03\,({\rm stat})\pm 0.16\,({\rm sys})$ (68\% confidence level) for the hydrostatic mass bias, and $b_{\rm g}^0=1.28^{+0.03}_{-0.04}\,(\textrm{stat}) \pm{0.11}\,(\textrm{sys})$, with $\alpha=0.20^{+0.11}_{-0.07}\,(\textrm{stat}) \pm{0.10}\,(\textrm{sys})$ and $\beta=0.45{\pm 0.01}\,(\textrm{stat}) \pm{0.02}\,(\textrm{sys})$ for the galaxy bias. Incoming data sets from future CMB and galaxy surveys (e.g. Rubin Observatory) will allow probing the large-scale gas distribution in more detail.