Testing the gas mass density profile of galaxy clusters with distance duality relation

TL;DR

This study tests galaxy cluster gas mass density profiles using the distance duality relation, finding the non-isothermal double-beta model aligns better with theoretical expectations than the isothermal beta model, though data precision limits definitive conclusions.

Contribution

It compares two gas density models of galaxy clusters under the distance duality assumption, highlighting the better fit of the non-isothermal double-beta model with current data.

Findings

Non-isothermal double-beta model agrees better with the distance duality relation.

Isothermal beta model is marginally incompatible with Etherington theorem at 68.3% CL.

Current data accuracy is insufficient to distinguish models definitively.

Abstract

In this paper, assuming the validity of distance duality relation, $\eta=D_L(z)(1+z)^{-2}/D_A(z)=1$, where $D_A(z)$ and $D_L(z)$ are the angular and the luminosity distance respectively, we explore two kinds of gas mass density profiles of clusters: the isothermal $\beta$ model and the non-isothermal double-$\beta$ model. In our analysis, performed on 38 massive galaxy clusters observed by \textit{Chandra} (within the redshift range of $0.14<z<0.89$), we use two types of cluster gas mass fraction data corresponding to different mass density profiles fitted to the X-ray data. Using two general parameterizations of $\eta(z)$ (phenomenologically allowing for distance duality violation), we find that the non-isothermal double-$\beta$ model agrees better with the distance duality relation, while the isothermal $\beta$ model tends to be marginally incompatible with the Etherington theorem at 68.3% CL. However, current accuracy of the data does not allow to distinguish between the two models for the gas-density distribution at a significant level.