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 C ℓ gg , C ℓ yy , and C ℓ g y 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 ) α ( ℓ / ℓ 0 ) β , 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 ) ±