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Thermal Sunyaev-Zeldovich (tSZ) power spectrum is a powerful probe of thepresent-day amplitude of matter density fluctuations, and has been measured upto $\ell\approx 10^3$ from the {\it Planck} data. The largest systematicuncertainty 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{\it Planck} team as $M_{\rm 500c}^{Planck}=M_{\rm 500c}^{\rm true}/B$. Sincethe power spectrum of the cosmic weak lensing shear is also sensitive to theamplitude of matter density fluctuations via $S_8\equiv \sigma_8\Omega_m^{\alpha}$ with $\alpha\sim 0.5$, we can break the degeneracy betweenthe mass bias and the cosmological parameters by combining the tSZ and cosmicshear power spectra. In this paper, we perform a joint likelihood analysis ofthe tSZ power spectrum from {\it Planck} and the cosmic shear power spectrumfrom Subaru Hyper Suprime-Cam. Our analysis does not use the primordial cosmicmicrowave background (CMB) information. We obtain a new constraint on the massbias as $B = 1.37 ^{+0.15}_{-0.23}$ or $(1-b) = B^{-1}=0.73^{+0.08}_{-0.13}$(68\%~C.L.), for $\sigma_8 < 0.9$. This value of $B$ is lower than that neededto 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 fromhydrodynamical simulations, $B = 1.28 \pm 0.20$. Our results thus indicate thatthe mass bias is consistent with the non-thermal pressure support from massaccretion of galaxy clusters via the cosmic structure formation, and that thecosmologies inferred from the tSZ and the cosmic shear are consistent with eachother.

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