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

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 21.8 sigma. 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 150 sigma and 88 sigma, respectively. We then construct a halo model and use the measured correlations C-l(gg), C-l(yy), and C-l(gy) to constrain the tSZ mass bias B M-500/M-500(tSZ). We also fit for the galaxy bias, which is included with explicit redshift and multipole dependencies as b(g)(z, l) = b(g)(0) (1 + z)(alpha)(l/l(0))(beta), 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 b(g)(0) = 1.28(-0.04)(+0.03)(stat) +/- 0.11(sys), with alpha = 0.20(-0.07)(+0.11)(stat) +/- 0.10(sys) and beta = 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.