Tracing the non-thermal pressure and hydrostatic bias in galaxy clusters
  We present a modelization of the non-thermal pressure, $P_{NT}$, and we apply
it to the X-ray (and Sunayev-Zel'dovich) derived radial profiles of the X-COP
galaxy clusters. We relate the amount of non-thermal pressure support to the
hydrostatic bias, $b$, and speculate on how we can interpret this $P_{NT}$ in
terms of the expected levels of turbulent velocity and magnetic fields. Current
upper limits on the turbulent velocity in the intracluster plasma are used to
build a distribution $\mathcal{N}(<b) - b$, from which we infer that 50 per
cent of local galaxy clusters should have $b < 0.2$ ($b<0.33$ in 80 per cent of
the population). The measured bias in the X-COP sample that includes relaxed
massive nearby systems is 0.03 in 50% of the objects and 0.17 in 80% of them.
All these values are below the amount of bias required to reconcile the
observed cluster number count in the cosmological framework set from Planck.
