New constraints on the mass bias of galaxy clusters from the power
  spectra of the thermal Sunyaev-Zeldovich effect and cosmic shear
  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 {\it 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
{\it Planck} team as $M_{\rm 500c}^{Planck}=M_{\rm 500c}^{\rm true}/B$. Since
the power spectrum of the cosmic weak lensing shear is also sensitive to the
amplitude of matter density fluctuations via $S_8\equiv \sigma_8
\Omega_m^{\alpha}$ 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 {\it 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\%~C.L.), 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, $B = 1.28 \pm 0.20$. Our results thus 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.
