# The polytropic state of the intracluster medium in the X-COP cluster sample

## TL;DR

This study analyzes the thermodynamic properties of the intracluster medium in galaxy clusters, revealing a transition in behavior at a specific radius and proposing a new method to estimate cluster mass profiles from gas density measurements.

## Contribution

It introduces a detailed analysis of the ICM thermodynamics, identifies a transition radius, and proposes a novel, cost-effective method for reconstructing hydrostatic mass profiles using gas density.

## Key findings

- Pressure correlates strongly with density with minimal scatter.
- Temperature correlates with density with similar low scatter.
- A transition radius at approximately 0.19 R500 marks a change in thermodynamic behavior.

## Abstract

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.