Gravitational redshifting of galaxies in the SPIDERS cluster catalogue
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 $\sim\!2500$ 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 $\hat{\Delta}=-13.5\pm4.7$ km s$^{-1}$, $\hat{\Delta}=-12.5\pm5.1$ km s$^{-1}$, and $\hat{\Delta}=-18.6\pm4.8$ 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 ($>2.5\sigma$) 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.
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