Galaxy cluster hydrostatic masses using Tolman-Oppenheimer-Volkoff equation

TL;DR

This study assesses relativistic effects on galaxy cluster mass estimates by comparing TOV equation-based masses with Newtonian estimates, finding negligible differences for relaxed clusters.

Contribution

It introduces a method to calculate cluster masses using the TOV equation and demonstrates that relativistic corrections are minimal in relaxed galaxy clusters.

Findings

Relativistic corrections to hydrostatic masses are negligible (~10^{-5}).

TOV and Newtonian mass estimates agree closely for relaxed clusters.

Analytical profiles effectively used for mass calculations.

Abstract

Motivated by previous studies in literature about the potential importance of relativistic corrections to galaxy cluster hydrostatic masses, we calculate the masses of 12 relaxed clusters (with Chandra X-ray data) using the Tolman-Oppenheimer-Volkov (TOV) equation of hydrostatic equilibrium and the ideal gas equation of state. Analytical formulae for gas density and temperature profiles for these clusters, previously derived by Vikhlinin et al (astro-ph/0507092) were used to obtain these masses. We compare the TOV-based masses with those obtained using the corresponding Newtonian equation of hydrostatic equilibrium. We find that the fractional relative difference between the two masses are negligible, corresponding to $\sim \mathcal{O}(10^{-5})$.