The Euclid photometric survey of galaxy clusters stands as a powerful
cosmological tool, with the capacity to significantly propel our understanding
of the Universe. Despite being sub-dominant to dark matter and dark energy, the
baryonic component in our Universe holds substantial influence over the
structure and mass of galaxy clusters. This paper presents a novel model to
precisely quantify the impact of baryons on galaxy cluster virial halo masses,
using the baryon fraction within a cluster as proxy for their effect.
Constructed on the premise of quasi-adiabaticity, the model includes two
parameters calibrated using non-radiative cosmological hydrodynamical
simulations and a single large-scale simulation from the Magneticum set, which
includes the physical processes driving galaxy formation. As a main result of
our analysis, we demonstrate that this model delivers a remarkable one percent
relative accuracy in determining the virial dark matter-only equivalent mass of
galaxy clusters, starting from the corresponding total cluster mass and baryon
fraction measured in hydrodynamical simulations. Furthermore, we demonstrate
that this result is robust against changes in cosmological parameters and
against varying the numerical implementation of the sub-resolution physical
processes included in the simulations. Our work substantiates previous claims
about the impact of baryons on cluster cosmology studies. In particular, we
show how neglecting these effects would lead to biased cosmological constraints
for a Euclid-like cluster abundance analysis. Importantly, we demonstrate that
uncertainties associated with our model, arising from baryonic corrections to
cluster masses, are sub-dominant when compared to the precision with which
mass-observable relations will be calibrated using Euclid, as well as our
current understanding of the baryon fraction within galaxy clusters.Comment: 18 pages, 10 figures, 4 tables, 1 appendix, abstract abridged for
arXiv submissio