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 Wide Field Infrared Survey Explorer (WISE) all-sky survey. We detect the statistical correlation between WISE and Planck data (gy) with a significance of 21.8σ. We also measure the autocorrelation spectrum for the thermal Sunyaev–Zel’dovich (tSZ) (yy) and the galaxy density field maps (gg) with a significance of 150σ and 88σ, respectively. We then construct a halo model and use the measured correlations , , and to constrain the tSZ mass bias . We also fit for the galaxy bias, which is included with explicit redshift and multipole dependencies as , with ℓ 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 , with 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.