New constraints on the mass bias of galaxy clusters from the power spectra of the thermal Sunyaev–Zeldovich effect and cosmic shear

Abstract

Abstract The thermal Sunyaev–Zeldovich (tSZ) power spectrum is a powerful probe of the present-day amplitude of matter density fluctuations, and has been measured up to $\ell \approx 10^3$ from the Planck data. The largest systematic uncertainty in the interpretation of this data is the so-called “mass bias” parameter B, which relates the true halo mass to the mass proxy used by the Planck team as $M\,_{\rm 500c}^{\rm Planck}=M\,_{\rm 500c}^{\rm true}/B$. Since the power spectrum of the cosmic weak lensing shear is also sensitive to the amplitude of matter density fluctuations via $S_8\equiv \sigma _8 \Omega _{\rm m}^{\alpha }$ with $\alpha \sim 0.5$, we can break the degeneracy between the mass bias and the cosmological parameters by combining the tSZ and cosmic shear power spectra. In this paper, we perform a joint likelihood analysis of the tSZ power spectrum from Planck and the cosmic shear power spectrum from Subaru Hyper Suprime-Cam. Our analysis does not use the primordial cosmic microwave background (CMB) information. We obtain a new constraint on the mass bias as $B = 1.37 ^{+0.15}_{-0.23}$ or $(1-b) = B^{-1}=0.73^{+0.08}_{-0.13}$ ($68\%$ confidence limit), for $\sigma _8 < 0.9$. This value of B is lower than that needed to reconcile the tSZ data with the primordial CMB and CMB lensing data, i.e., $B = 1.64 \pm 0.19$, but is consistent with the mass bias expected from hydrodynamical simulations, $B = 1.28 \pm 0.20$. Thus our results indicate that the mass bias is consistent with the non-thermal pressure support from mass accretion of galaxy clusters via the cosmic structure formation, and that the cosmologies inferred from the tSZ and the cosmic shear are consistent with each other.