An important result from self-similar models that describe the process of galaxy cluster formation is the simple scaling relation $Y_{SZE}D_{A}^{2}/C_{XSZE}Y_X= C$. In this ratio, $Y_{SZE}$ is the integrated Sunyaev-Zel'dovich effect flux of a cluster, its X-ray counterpart is $Y_X$, $C_{XSZE}$ and $C$ are constants and $D_A$ 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 $61$ $Y_{SZE}D_{A}^{2}/C_{XSZE}Y_X$ 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 $Y_{SZE}D_{A}^{2}/C_{XSZE}Y_X$ ratio in an useful cosmological tool to determine cosmological parameters. Moreover, the approach proposed here can also be used as a cross-check for those scaling relation calibration methods that use weak-lensing analyses.

中文翻译：

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星系团YX-YSZE标度关系可能的宇宙演化

描述星系团形成过程的自相似模型的一个重要结果是简单的标度关系 $Y_{SZE}D_{A}^{2}/C_{XSZE}Y_X= C$。在这个比率中，$Y_{SZE}$ 是一个星团的综合 Sunyaev-Zel'dovich 效应通量，它的 X 射线对应物是 $Y_X$，$C_{XSZE}$ 和 $C$ 是常数，$D_A$是到簇的角直径距离。在本文中，我们将宇宙距离对偶关系的有效性与 Ia 型超新星观测值以及普朗克合作报告的 $61$ $Y_{SZE}D_{A}^{2}/C_{XSZE}Y_X$ 测量值相结合来探讨如果此关系在所考虑的红移范围内保持不变 ($z<0.5$)。没有使用一种特定的宇宙学模型。作为基本结果，虽然数据集兼容 2$\sigma$cl 内没有红移演化，贝叶斯分析表明，在这项工作中分析的其他 $C(z)$ 函数不能被丢弃。值得强调的是，通用 $C(z)$ 函数的观测确定将 $Y_{SZE}D_{A}^{2}/C_{XSZE}Y_X$ 比率转变为有用的宇宙学工具来确定宇宙学参数。此外，这里提出的方法也可以用作对那些使用弱透镜分析的比例关系校准方法的交叉检查。