Empirical Test for Relativistic Kinetic Theories Based on the Sunyaev–Zel’dovich Effect

Abstract

Abstract We propose a new method to determine the electron velocity (EV) distribution function in the intracluster gas (ICG) in clusters of galaxies based on the frequency dependence of the Sunyaev–Zel’dovich (SZ) effect. It is generally accepted that the relativistic equilibrium EV distribution is the one suggested by Jüttner. However, there is an ongoing debate on the foundation of relativistic kinetic theory, and other distributions have also been proposed. The mildly relativistic ICG provides a unique laboratory to test relativistic kinetic theories. We carried out Monte Carlo simulations to generate SZ signal from a single-temperature gas assuming the Jüttner EV distribution assuming a few percent errors. We fitted SZ models based on nonrelativistic Maxwellian, and its two relativistic generalizations, the Jüttner and modified Jüttner distributions. We found that a 1% error in the SZ signal is sufficient to distinguish between these distributions with high significance based on their different best-fit temperatures. However, in any line of sight (LOS) in a cluster, the ICG contains a range of temperatures. Using our N-body/hydrodynamical simulation of a merging galaxy cluster and assuming a 1% error in the SZ measurements in an LOS through a bow shock, we find that it is possible to distinguish between Jüttner and modified Jüttner distributions with high significance. Our results suggest that deriving ICG temperatures from fitting to SZ data assuming different EV distribution functions and comparing them to the temperature in the same cluster obtained using other observations would enable us to distinguish between the different distributions.