Constraining the mass and redshift evolution of the hydrostatic mass
  bias using the gas mass fraction in galaxy clusters
  The gas mass fraction in galaxy clusters is a convenient probe to use in
cosmological studies, as it can help derive constraints on a collection of
cosmological parameters. It is however subject to various effects from the
baryonic physics inside galaxy clusters, which may bias the obtained
cosmological constraints. Among different aspects of the baryonic physics, in
this paper we focus on the impact of the hydrostatic equilibrium assumption. We
analyse the hydrostatic mass bias $B$, constraining a possible mass and
redshift evolution of this quantity and its impact on the cosmological
constraints. To that end we consider cluster observations of the {\it
Planck}-ESZ sample and evaluate the gas mass fraction using X-ray counterpart
observations. We show a degeneracy between the redshift dependence of the bias
and cosmological parameters. In particular we find a $3.8 \sigma$ evidence for
a redshift dependence of the bias when assuming a {\it Planck} prior on
$\Omega_m$. On the other hand, assuming a constant mass bias would lead to the
extreme large value of $\Omega_m > 0.849$. We however show that our results are
entirely dependent on the cluster sample we consider. In particular, the mass
and redshift trends that we find for the lowest mass-redshift and highest
mass-redshift clusters of our sample are not compatible. Nevertheless, in all
the analyses we find a value for the amplitude of the bias that is consistent
with $B \sim 0.8$, as expected from hydrodynamical simulations and local
measurements, but still in tension with the low value of $B \sim 0.6$ derived
from the combination of cosmic microwave background primary anisotropies with
cluster number counts.
