  It was recently suggested that, compared to its stellar mass (M*), the
central stellar velocity dispersion (sigma*) of a galaxy might be a better
indicator for its host dark matter halo mass. Here we test this hypothesis by
estimating the dark matter halo mass for central alaxies in groups as function
of M* and sigma*. For this we have estimated the redshift-space
cross-correlation function (CCF) between the central galaxies at given M* and
sigma* and a reference galaxy sample, from which we determine both the
projected CCF, w_p(r_p), and the velocity dispersion profile (VDP) of
satellites around the centrals. A halo mass is then obtained from the average
velocity dispersion within the virial radius. At fixed M*, we find very weak or
no correlation between halo mass and sigma*. In contrast, strong mass
dependence is clearly seen even when sigma* is limited to a narrow range. Our
results thus firmly demonstrate that the stellar mass of central galaxies is
still a good (if not the best) indicator for dark matter halo mass, better than
the stellar velocity dispersion. The dependence of galaxy clustering on sigma*
fixed M*, as recently discovered by Wake et al. (2012), may be attributed to
satellite galaxies, for which the tidal stripping occurring within halos has
stronger effect on stellar mass than on central stellar velocity dispersion.
