Inferring Host Dark Matter Halo Masses of Individual Galaxies from Neighboring Galaxy Counts

Abstract

How well can we infer host dark matter halo masses of individual galaxies? Based on the halo occupation distribution (HOD) framework, we analytically compute the number of neighboring galaxies within a cylinder of some redshift interval and radius in transverse comoving distance. The result is used to derive the conditional probability distribution function (PDF) of the host halo mass of a galaxy, given the neighboring galaxy counts. We compare our analytic results with those obtained using a realistic mock galaxy catalog, finding reasonable agreements. We find the optimal cylinder radius to be $\sim 0.5-1h^{-1}{\rm Mpc}$ for the inference of halo masses. The PDF is generally broad, and sometimes has two peaks at low- and high-mass regimes, because of the effect of chance projection along the line-of-sight. Potential applications and extensions of the new theoretical framework developed herein are also discussed.