Tracing Dark Matter Halos with Satellite Kinematics and the Central Stellar Velocity Dispersion of Galaxies

Abstract

It has been suggested that the central stellar velocity dispersion of galaxies can trace dark matter halo mass directly. We test this hypothesis using a complete spectroscopic sample of isolated galaxies surrounded by faint satellite galaxies from the Sloan Digital Sky Survey Data Release 12. We apply a friends-of-friends algorithm with projected linking length Delta D < 100 kpc and radial velocity linking length Delta V < 1000 km s(-1) to construct our sample. Our sample includes 2807 isolated galaxies with 3417 satellite galaxies at 0.01 < z < 0.14. We divide the sample into two groups based on the primary galaxy color: red and blue primary galaxies separated at (g - r)(0) = 0.85. The central stellar velocity dispersions of the primary galaxies are proportional to the luminosities and stellar masses of the same galaxies. Stacking the sample based on the central velocity dispersion of the primary galaxies, we derive the velocity dispersions of their satellite galaxies, which trace the dark matter halo mass of the primary galaxies. The system velocity dispersion of the satellite galaxies shows a remarkably tight correlation with the central velocity dispersion of the primary galaxies for both red and blue samples. In particular, the slope of the relation is identical to 1 for red primary systems. This tight relation suggests that the central stellar velocity dispersion of galaxies is indeed an efficient and robust tracer for dark matter halo mass. We provide empirical relations between the central stellar velocity dispersion and the dark matter halo mass.