The polytropic approximation and X-ray scaling relations: constraints on gas and dark matter profiles for galaxy groups and clusters

TL;DR

This paper models gas and dark matter profiles in galaxy groups and clusters using X-ray scaling relations, constraining key parameters like the polytropic index and DM slope to match observations and simulations.

Contribution

It introduces a polytropic approximation framework to interpret X-ray scaling relations, constraining gas and dark matter parameters across different mass scales and redshifts.

Findings

Constraints on the polytropic index Gamma consistent with simulations.

Reproduction of the observed steepening of the M-T relation at low masses.

Discrimination between different mass-concentration relations based on luminosity-temperature data.

Abstract

We constrain gas and dark matter (DM) parameters of galaxy groups and clusters, by comparing X-ray scaling relations to theoretical expectations, obtained assuming that the gas is in hydrostatic equilibrium with the DM and follows a polytropic relation. We vary four parameters: the gas polytropic index Gamma, its temperature at large radii T_xi, the DM logarithmic slope at large radii zeta and its concentration c_vir. When comparing the model to the observed mass-temperature (M-T) relation of local clusters, our results are independent of both T_xi and c_vir. We thus obtain constraints on Gamma, by fixing the DM profile, and on zeta, by fixing the gas profile. For an NFW DM profile, we find that 6/5<Gamma<13/10, which is consistent with numerical simulations and observations of individual clusters. Taking 6/5<Gamma<13/10 allows the DM profile to be slightly steeper than the NFW profile at large radii. Upon including local groups, we constrain the mass-dependence of Gamma and the value of T_xi. Interestingly, with Gamma=6/5 and zeta=-3, we reproduce the observed steepening/breaking of the M-T relation at low M, if 10^6 K<T_xi<10^7 K, consistent with simulations and observations of the warm-hot intergalactic medium. When extrapolated to high redshift z, the model with a constant Gamma reproduces the expected self-similar behaviour. We also account for the observed, non-self-similar relations provided by some high-z clusters, as they provide constraints on the evolution of Gamma. Comparing our model to the observed luminosity-temperature relation, we discriminate between different M-c_vir relations: a weak dependence of c_vir on M is currently preferred by data. This simple theoretical model accounts for much of the complexity of recent, improved X-ray scaling relations, provided that we allow for a mild dependence of Gamma on M or for T_xi consistent with intercluster values. [abridged]