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 _ { 500 c } ^ { Planck } = M _ { 500 c } ^ { 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 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 .