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It has been suggested that the central stellar velocity dispersion ofgalaxies can trace dark matter halo mass directly. We test this hypothesisusing a complete spectroscopic sample of isolated galaxies surrounded by faintsatellite galaxies from the Sloan Digital Sky Survey Data Release 12. We applya friends-of-friends algorithm with projected linking length $\Delta D < 100$kpc and radial velocity linking length $\Delta V < 1000$ km s$^{-1}$ toconstruct our sample. Our sample includes 2807 isolated galaxies with 3417satellite galaxies at $0.01 < z < 0.14$. We divide the sample into two groupsbased on the primary galaxy color: red and blue primary galaxies separated at$(g-r)_{0} = 0.85$. The central stellar velocity dispersions of the primarygalaxies are proportional to the luminosities and stellar masses of the samegalaxies. Stacking the sample based on the central velocity dispersion of theprimary galaxies, we derive the velocity dispersions of their satellitegalaxies, which trace the dark matter halo mass of the primary galaxies. Thesystem velocity dispersion of the satellite galaxies shows a remarkably tightcorrelation with the central velocity dispersion of the primary galaxies forboth red and blue samples. In particular, the slope of the relation isidentical to 1 for red primary systems. This tight relation suggests that thecentral stellar velocity dispersion of galaxies is indeed an efficient androbust tracer for dark matter halo mass. We provide empirical relations betweenthe central stellar velocity dispersion and the dark matter halo mass.

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