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.
