Galaxy cluster hydrostatic bias in Kottler spacetime

TL;DR

This study investigates whether relativistic corrections in Kottler spacetime can resolve the hydrostatic mass bias in galaxy clusters, finding that these corrections are negligible and do not significantly affect mass estimates.

Contribution

The paper introduces the application of Kottler spacetime to assess relativistic corrections to hydrostatic X-ray masses, showing these effects are minimal.

Findings

Relativistic corrections do not significantly alter hydrostatic mass estimates.

The ratio of X-ray to lensing mass remains close to unity in Kottler spacetime.

Relativistic effects are negligible for galaxy cluster mass calculations.

Abstract

We calculate the relativistic corrections to hydrostatic X-ray masses for galaxy clusters in Kottler spacetime, which is the spherically symmetric solution to Einstein's equations in General relativity endowed with a cosmological constant. The hydrostatic masses for clusters (calculated assuming Newtonian gravity) have been found to be underestimated compared to lensing masses, and this discrepancy is known as hydrostatic mass bias. Since the relativistic hydrostatic X-ray masses are automatically lower than lensing masses, under the edifice of Kottler metric, we check if the hydrostatic mass bias problem gets alleviated using this {\it ansatz}. We consider a sample of 18 galaxy clusters for this pilot test. We find that the ratio of X-ray to lensing mass is close to unity even in Kottler spacetime. Therefore, the effect of relativistic corrections to hydrostatic X-ray masses for galaxy clusters is negligible.