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

Abstract

An important result from self-similar models that describe the process of galaxy cluster formation is the simple scaling relation $Y_{\mathrm{SZE}}{D}_{\mathrm{A}}^2/C_{\mathrm{XSZE}}{Y}_{\mathrm{X}}=C$. In this ratio, $Y_{\mathrm{SZE}}$ is the integrated Sunyaev-Zel'dovich effect flux of a cluster, its x-ray counterpart is $Y_{\mathrm{X}}$, $C_{\mathrm{XSZE}}$ and $C$ are constants and $D_{\mathrm{A}}$ 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 $61$ $Y_{\mathrm{SZE}}{D}_{\mathrm{A}}^2/C_{\mathrm{XSZE}}{Y}_{\mathrm{X}}$ 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 $Y_{\mathrm{SZE}}{D}_{\mathrm{A}}^2/C_{\mathrm{XSZE}}{Y}_{\mathrm{X}}$ ratio in an useful cosmological tool to determine cosmological parameters.

6 pages, 1 figure, 2 tables, accepted by JCAP

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