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 ∼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 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 Δ with radial distance is predicted for SPIDERS galaxies in General Relativity (GR), and f(R) gravity, and compared to the observations. The values of Δ =-13.5\pm 4.7 km s-1, Δ=-12.5pm 5.1 km s-1, and Δ =-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 Δ. 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, ∼500,000, will be required-a possible feat with the forthcoming Vera C. Rubin Observatory, Euclid and eROSITA.