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