Galaxy Cluster Mass Estimation through the Splashback Radius

Abstract We present an analysis of the splashback radius ( R sp ) and the associated splashback mass ( M sp ) for a sample of galaxy clusters using Sloan Digital Sky Survey spectroscopic data and mock simulations. R sp marks a physical boundary between the virialized core and the outer infall regions of clusters, providing a robust measure of cluster mass accretion history without being affected by pseudo-evolution. We model the cumulative galaxy number profile of clusters, testing different halo density models and considering the impact of cluster properties, such as center definitions, magnitude limits, galaxy colors, and field contamination, on the estimation of splashback features. Our results show that observed splashback radii, measured in projection (2D), are consistently smaller than predicted by dark matter simulations, with R sp / R 200m ≈ 1, supporting previous discrepancies in the literature. We also explore the relationship between M sp and R sp , proposing a new scaling relation for future cosmological studies, as R sp is easily observable. Our findings indicate that splashback masses strongly correlate with radii, with a dispersion of ≈0.15 dex, competitive with other mass-observable relations. However, the fitted relation diverges from the constant density expectations of galaxy clusters around R sp . Additionally, the M sp – R sp relation shows significant redshift evolution, though the predominantly low-redshift range of our sample limits our ability to confirm this trend conclusively. The approach developed here may play a key role in cluster characterization and cosmology in the era of large galaxy surveys.