Including massive neutrinos in thermal Sunyaev Zeldovich power spectrum and cluster counts analyses

We consistently include the effect of massive neutrinos in the thermal Sunyaev Zeldovich (SZ) power spectrum and cluster counts analyses, highlighting subtle dependencies on the total neutrino mass and data combination. In particular, we find that using the transfer functions for Cold Dark Matter (CDM) + baryons in the computation of the halo mass function, instead of the transfer functions including neutrino perturbations, as prescribed in recent work, yields a $\approx$ 0.25\% downward shift of the $\sigma_8$ constraint from tSZ power spectrum data, with a fiducial neutrino mass $\Sigma m_\nu=0.06$ eV. In $\Lambda$CDM, with an X-ray mass bias corresponding to the expected hydrostatic mass bias, i.e., $(1-b)\simeq0.8$, our constraints from Planck SZ data are consistent with the latest results from SPT, DES-Y1 and KiDS+VIKING-450. In $\nu\Lambda$CDM, our joint analyses of Planck SZ with Planck 2015 primary CMB yield a small improvement on the total neutrino mass bound compared to the Planck 2015 primary CMB constraint, as well as $(1-b)=0.64\pm0.04$~(68\%~CL). For forecasts, we find that competitive neutrino mass measurements using cosmic variance limited SZ power spectrum require masking the heaviest clusters and probing the small-scale SZ power spectrum up to $\ell_\mathrm{max}\approx10^4$. Although this is challenging, we find that SZ power spectrum can realistically be used to tightly constrain intra-cluster medium properties: we forecast a 2\% determination of the X-ray mass bias by combining CMB-S4 and our mock SZ power spectrum with $\ell_\mathrm{max}=10^3$.