Galaxy cluster hydrostatic masses using Tolman–Oppenheimer–Volkoff equation

Abstract

Motivated by previous studies 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 [1] 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 ∼ O(10 −5 ).

Compact stars with non-uniform relativistic polytrope

“…The observed mass and radius values ( M = 1.49 M ʘ , R = 9.51 km) fit approximately model_Cen4 with a total mass M = 1.48 M ʘ and radius R = 10.28 km. Comparison of the interface range of density and pressure of our models ( = 0.7707–0.8162 g cm −3 , P i = 0.6787–0.9414 dyne cm −2 ) for the star Cen X-3 and that from 28 ( g cm −3 and dyne cm −2 ) gives smaller values of the interface density and pressure but a larger radius for the four models, that is simply because the core in our models represents about 60% of the total radius of the star while in 28 the core occupied about 33% only.…”

“…The Tolman–Oppenheimer–Volkoff (TOV) equation constrains the structure of spherically symmetric objects of isotropic material in static gravitational equilibrium, as modeled by general relativity. Besides applying the TOV equation to compact stars, there are many applications in astrophysics; for example, Gupta et al 28 determined the hydrostatic masses of the Galaxy cluster observed using Chandra X-ray data. Inspired by the new findings of star motions under the influence of dark matter, Bors and Stańczy 29 explore the model representing the interaction of relativistic gravitationally attractive diffusive fermionic particles evaporating at high energy clusters of stellar systems 30 .…”

A test of Radial Acceleration Relation for the {\it Giles et al Chandra} cluster sample

“…This is a variant of the double-β profile used by Vikhlinin et al [40], which was also used in our previous works [4,31,41,42] The second term in the double-β profile was dropped so as to fit both the low and high quality data in the sample.…”

Galaxy cluster hydrostatic bias in Kottler spacetime

“…In this work, we carry out a pilot study to study how the X-ray masses for galaxy clusters and galaxy groups change under the aegis of Kottler metric, and whether it alleviates the galaxy cluster mass bias problem. Previously, relativistic corrections to Newtonian hydrostatic masses have been computed for galaxy clusters using Tolman-Oppenheimer-Volkoff equation and shown to be negligible [26].…”