Data from the SPectroscopic IDentification of ERosita Sources (SPIDERS) are searched for a detection of the gravitational redshifting of light from ${\sim}20\, 000$ galaxies in ∼2500 galaxy clusters using three definitions of the cluster centre: its Brightest Cluster Galaxy (BCG), the redMaPPer identified Central Galaxy (CG), or the peak of X-ray emission. Distributions of velocity offsets between galaxies and their host cluster’s centre, found using observed redshifts, are created. The quantity $\hat{\Delta }$, the average of the radial velocity difference between the cluster members and the cluster systemic velocity, reveals information on the size of a combination of effects on the observed redshift, dominated by gravitational redshifting. The change of $\hat{\Delta }$ with radial distance is predicted for SPIDERS galaxies in General Relativity (GR), and f(R) gravity, and compared to the observations. The values of $\hat{\Delta }=-13.5\pm 4.7$ km s−1, $\hat{\Delta }=-12.5\pm 5.1$ km s−1, and $\hat{\Delta }=-18.6\pm 4.8$ km s−1 for the BCG, X-ray, and CG cases, respectively, broadly agree with the literature. There is no significant preference of one gravity theory over another, but all cases give a clear detection (>2.5σ) of $\hat{\Delta }$. The BCG centroid is deemed to be the most robust method in this analysis, due to no well-defined central redshift when using an X-ray centroid, and CGs identified by redMaPPer with no associated spectroscopic redshift. For future gravitational redshift studies, an order-of-magnitude more galaxies, ${\sim}500\, 000$, will be required – a possible feat with the forthcoming Vera C. Rubin Observatory, Euclid and eROSITA.

中文翻译：

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SPIDERS 星团目录中星系的引力红移

使用星团中心的三个定义，搜索来自 ERosita 源的光谱识别 (SPIDERS) 的数据，以检测来自 ${\sim}20\, 000$ 星系的光的引力红移：其最亮星团银河系 (BCG)，redMaPPer 确定了中央银河系 (CG)，或 X 射线发射的峰值。创建了使用观测到的红移发现的星系与其宿主星团中心之间的速度偏移分布。$\hat{\Delta }$ 是星团成员之间径向速度差的平均值和星团系统速度的平均值，它揭示了观测到的红移效应组合的大小信息，主要是引力红移。预测了广义相对论 (GR) 和 f(R) 引力中 SPIDERS 星系的 $\hat{\Delta }$ 随径向距离的变化，并与观测结果进行了比较。$\hat{\Delta }=-13.5\pm 4.7$ km s−1, $\hat{\Delta }=-12.5\pm 5.1$ km s−1, $\hat{\Delta }= BCG、X 射线和 CG 病例分别为 -18.6\pm 4.8$ km s-1，与文献大体一致。一种引力理论相对于另一种没有明显的偏好，但所有情况都给出了 $\hat{\Delta }$ 的明确检测（>2.5σ）。BCG 质心被认为是该分析中最稳健的方法，因为使用 X 射线质心时没有明确定义的中心红移，并且由 redMaPPer 识别的 CG 没有相关的光谱红移。对于未来的引力红移研究，一个数量级的星系，${\sim}500\, 000$,