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

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 WISE all-sky survey. We detect the statistical correlation between WISE and Planck data (gy) with a significance of 21.8 σ. We also measure the auto-correlation spectrum for the tSZ (yy) and the galaxy density field maps (gg) with a significance of 150 σ and 88 σ, respectively. We then construct a halo model and use the measured correlations C gg , C yy and C gy to constrain the tSZ mass bias B ≡ M 500 /M tSZ 500 . We also fit for the galaxy bias, which is included with explicit redshift and multipole dependencies as b g (z, ) = b 0 g (1 + z) α ( / 0 ) β , with 0 = 117. We obtain the constraints to be B = 1.50±0.07 (stat) ± 0.34 (sys), i.e. 1 − b H = 0.67 ± 0.03 (stat) ± 0.16 (sys) (68% confidence level) for the hydrostatic mass bias, and b 0 g = 1.28 +0.03 −0.04 (stat) ± 0.11 (sys), with α = 0.20 +0.11 −0.07 (stat) ± 0.10 (sys) and β = 0.45±0.01 (stat) ± 0.02 (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.