Non-Equilibrium Electrons in the Outskirts of Galaxy Clusters

The analysis of X-ray and Sunyaev-Zel\'dovich measurements of the intracluster medium (ICM) assumes that electrons are in thermal equilibrium with ions in the plasma. However, electron-ion equilibration timescales can be comparable to the Hubble time in the low density galaxy cluster outskirts, leading to differences between the electron and ion temperatures. This temperature difference can lead to systematic biases in cluster mass estimates and mass-observable scaling relations. To quantify the impact of non-equilibrium electrons on the ICM profiles in cluster outskirts, we use a high resolution cosmological simulation with a two-temperature model assuming the Spitzer equilibration timescale for the electrons. First, we show how the radial profile of this temperature bias depends on both the mass and mass accretion rate of the cluster; the bias is most pronounced in the most massive and most rapidly accreting clusters. For the most extreme case in our sample, we find that the bias is of order 10% at half of the cluster virial radius and increases to 40% at the edge of the cluster. We also find that gas in filaments is less susceptible to the non-equilibrium effect, leading to azimuthal variations at large cluster-centric radii. By analyzing mock Chandra observations of simulated clusters, we show that such azimuthal variations can be probed with deep X-ray observations. Finally, the mass-dependent temperature bias introduces biases in hydrostatic mass and cluster temperature, which has implications for cluster-based cosmological inferences. We provide a mass-dependent model for the temperature bias profile which can be useful for modeling the effect of electron-ion equilibration in galaxy clusters.