The effect of massive neutrinos on the Sunyaev-Zeldovich and X-ray observables of galaxy clusters

Massive neutrinos are expected to influence the formation of the large-scale structure of the Universe, depending on the value of their total mass, $\Sigma m_\nu$. In particular Planck data indicate that a non-zero $\Sigma m_\nu$ may help to reconcile CMB data with Sunyaev-Zel'dovich (SZ) cluster surveys. In order to study the impact of neutrinos on the SZ and X-ray cluster properties we run a set of six very large cosmological simulations (8$h^{-3}$ Gpc$^3$ comoving volume) that include a massive neutrino particle component: we consider the values of $\Sigma m_\nu$ = (0, 0.17, 0.34) eV in two cosmological scenarios to test possible degeneracies. Using the halo catalogues extracted from their outputs we produce 50 mock light-cones and, assuming suitable scaling relations, we determine how massive neutrinos affect SZ and X-ray cluster counts, the $y$-parameter and its power spectrum. We provide forecasts for the South Pole Telescope (SPT) and eROSITA cluster surveys, showing that the number of expected detections is reduced by 40 per cent when assuming $\Sigma m_\nu$ =0.34 eV with respect to a model with massless neutrinos. However the degeneracy with $\sigma_8$ and $\Omega_m$ is strong, in particular for X-ray data, requiring the use of additional probes to break it. The $y$-parameter properties are also highly influenced by the neutrino mass fraction, $f_\nu$, with $<\,y\,>\propto(1-f_\nu)^{20}$, considering the cluster component only, and the normalization of the SZ power spectrum is proportional to $(1-f_\nu)^{25-30}$. Comparing our findings with SPT and Atacama Cosmology Telescope measurements at $\ell$ = 3000 indicates that, when Planck cosmological parameters are assumed, a value of $\Sigma m_\nu\simeq0.34$ eV is required to fit with the data.