On a possible cosmological evolution of galaxy cluster $Y_{\rm X}-Y_{\rm SZE}$ scaling relation

TL;DR

This study investigates whether the galaxy cluster $Y_{\rm X}-Y_{\rm SZE}$ scaling relation evolves with redshift, using observational data and the cosmic distance duality relation, finding compatibility with no evolution but allowing for other models.

Contribution

It explores the potential redshift evolution of the $Y_{\rm X}-Y_{\rm SZE}$ relation without assuming a specific cosmological model, highlighting its use in cosmological parameter estimation.

Findings

Data compatible with no redshift evolution within 2σ confidence level.

Bayesian analysis cannot discard alternative $C(z)$ functions.

Universal $C(z)$ could make the ratio a useful cosmological tool.

Abstract

An important result from self-similar models that describe the process of galaxy cluster formation is the simple scaling relation $Y_{\rm SZE}D_{\rm A}^{2}/C_{\rm XSZE}Y_{\rm X}= C$. In this ratio, $Y_{\rm SZE}$ is the integrated Sunyaev-Zel'dovich effect flux of a cluster, its x-ray counterpart is $Y_{\rm X}$, $C_{\rm XSZE}$ and $C$ are constants and $D_{\rm A}$ is the angular diameter distance to the cluster. In this paper, we consider the cosmic distance duality relation validity jointly with type Ia supernovae observations plus $61$ $Y_{\rm SZE}D_{\rm A}^{2}/C_{\rm XSZE}Y_{\rm X}$ measurements as reported by the Planck Collaboration to explore if this relation is constant in the redshift range considered ($z<0.5$). No one specific cosmological model is used. As basic result, although the data sets are compatible with no redshift evolution within 2$\sigma$ c.l., a Bayesian analysis indicates that other $C(z)$ functions analyzed in this work cannot be discarded. It is worth to stress that the observational determination of an universal $C(z)$ function turns the $Y_{\rm SZE}D_{\rm A}^{2}/C_{\rm XSZE}Y_{\rm X}$ ratio in an useful cosmological tool to determine cosmological parameters.