  Galaxy cluster mass determinations achieved using X-ray and
Sunyaev-Zel'dovich data combined with the assumption of hydrostatic equilibrium
are generally biased. The bias exists for two main reasons: non-thermal
pressure forces are expected to contribute to the overall pressure balance and
deviations from spherical symmetry and hydrostatic equilibrium can be present.
In this paper, we use a sample of zoom-in hydrodynamical simulations of galaxy
clusters to measure the magnitude of hydrostatic bias and the non-thermal
contribution to the total pressure. We propose a new empirical model for
non-thermal pressure based on our simulations that can be applied to
observations. We show that our model can be successfully applied to remove most
of the bias related to neglection of non-thermal pressure, which is usually not
included in hydrostatic cluster mass profile reconstructions. The use of this
model may significantly improve the calibration of cluster scaling relations
that are a key tool for cluster cosmology.
