Measuring Cosmological Distances Using Cluster Edges as a Standard Ruler

The line-of-sight velocity dispersion profile of galaxy clusters exhibits a "kink" corresponding to the spatial extent of orbiting galaxies. Because the spatial extent of a cluster is correlated with the amplitude of the velocity dispersion profile, we can utilise this feature as a gravity-calibrated standard ruler. Specifically, the amplitude of the velocity dispersion data allows us to infer the physical cluster size. Consequently, observations of the angular scale of the "kink" in the profile can be translated into a distance measurement to the cluster. Assuming the relation between cluster radius and cluster velocity dispersion can be calibrated from simulations, we forecast that with existing data from the Sloan Digital Sky Survey (SDSS) we will be able to measure the Hubble constant with $3\%$ precision. Implementing our method with data from the Dark Energy Spectroscopic Instrument (DESI) will result in a $1.3\%$ measurement of the Hubble constant. Adding cosmological supernova data improves the uncertainty of the DESI measurement to $0.7\%$.