Predicting the non-thermal pressure in galaxy clusters

Abstract

Abstract We investigate the relationship between a galaxy cluster’s hydrostatic equilibrium state, the entropy profile, K, of the intracluster gas, and the system’s non-thermal pressure (NTP), within an analytic model of cluster structures. When NTP is neglected from the cluster’s hydrostatic state, we find that the gas’ logarithmic entropy slope, $k\equiv \mathrm{d}\ln K/\mathrm{d}\ln r$ , converges at large halocentric radius, r, to a value that is systematically higher than the value $k\simeq1.1$ that is found in observations and simulations. By applying a constraint on these ‘pristine equilibrium’ slopes, $k_\mathrm{eq}$ , we are able to predict the required NTP that must be introduced into the hydrostatic state of the cluster. We solve for the fraction, $\mathcal{F}\equiv p_\mathrm{nt}/p$ , of NTP, $p_\mathrm{nt}$ , to total pressure, p, of the cluster, and we find $\mathcal{F}(r)$ to be an increasing function of halocentric radius, r, that can be parameterised by its value in the cluster’s core, $\mathcal{F}_0$ , with this prediction able to be fit to the functional form proposed in numerical simulations. The minimum NTP fraction, as the solution with zero NTP in the core, $\mathcal{F}_0=0$ , we find to be in excellent agreement with the mean NTP predicted in non-radiative simulations, beyond halocentric radii of $r\gtrsim0.7r_{500}$ , and in tension with observational constraints derived at similar radii. For this minimum NTP profile, we predict $\mathcal{F}\simeq0.20$ at $r_{500}$ , and $\mathcal{F}\simeq0.34$ at $2r_{500}$ ; this amount of NTP leads to a hydrostatic bias of $b\simeq0.12$ in the cluster mass $M_{500}$ when measured within $r_{500}$ . Our results suggest that the NTP of galaxy clusters contributes a significant amount to their hydrostatic state near the virial radius and must be accounted for when estimating the cluster’s halo mass using hydrostatic equilibrium approaches.