The polytropic state of the intracluster medium in the X-COP cluster
  sample
  In this work, we investigate the relation between the radially-resolved
thermodynamic quantities of the intracluster medium in the X-COP cluster
sample, aiming to assess the stratification properties of the ICM. We model the
relations between radius, gas temperature, density and pressure using a
combination of power-laws, also evaluating the intrinsic scatter in these
relations. We show that the gas pressure is remarkably well correlated to the
density, with very small scatter. Also, the temperature correlates with gas
density with similar scatter. The slopes of these relations have values that
show a clear transition from the inner cluster regions to the outskirts. This
transition occurs at the radius $r_t = 0.19(\pm0.04)R_{500}$ and electron
density $n_t = (1.91\pm0.21)\cdot10^{-3} cm^{-3} E^2 (z)$. We find that above
0.2 $R_{500}$ the radial thermodynamic profiles are accurately reproduced by a
well defined and physically motivated framework, where the dark matter follows
the NFW potential and the gas is represented by a polytropic equation of state.
By modeling the gas temperature dependence upon both the gas density and
radius, we propose a new method to reconstruct the hydrostatic mass profile
based only on the quite inexpensive measurement of the gas density profile.
