Analytical model for non-thermal pressure in galaxy clusters - III.
  Removing the hydrostatic mass bias
  Non-thermal pressure in galaxy clusters leads to underestimation of the mass
of galaxy clusters based on hydrostatic equilibrium with thermal gas pressure.
This occurs even for dynamically relaxed clusters that are used for calibrating
the mass-observable scaling relations. We show that the analytical model for
non-thermal pressure developed in Shi & Komatsu 2014 can correct for this
so-called 'hydrostatic mass bias', if most of the non-thermal pressure comes
from bulk and turbulent motions of gas in the intracluster medium. Our
correction works for the sample average irrespective of the mass estimation
method, or the dynamical state of the clusters. This makes it possible to
correct for the bias in the hydrostatic mass estimates from X-ray surface
brightness and the Sunyaev-Zel'dovich observations that will be available for
clusters in a wide range of redshifts and dynamical states.
