  We examine the relation between stellar mass and central stellar velocity
dispersion-the M-sigma relation-for massive quiescent galaxies at z<0.7. We
measure the local relation from the Sloan Digital Sky Survey and the
intermediate redshift relation from the Smithsonian Hectospec Lensing Survey.
Both samples are highly complete (>85%) and we consistently measure the stellar
mass and velocity dispersion for the two samples. The M-sigma relation and its
scatter are independent of redshift with sigma ~ M^0.3 for M>10^10.3 M_solar.
The measured slope of the M-sigma relation is the same as the scaling between
the total halo mass and the dark matter halo velocity dispersion obtained by
N-body simulations. This consistency suggests that massive quiescent galaxies
are virialized systems where the central dark matter concentration is either a
constant or negligible fraction of the stellar mass. The relation between the
total galaxy mass (stellar + dark matter) and the central stellar velocity
dispersion is consistent with the observed relation between the total mass of a
galaxy cluster and the velocity dispersion of the cluster members. This result
suggests that the central stellar velocity dispersion is directly proportional
to the velocity dispersion of the dark matter halo. Thus the central stellar
velocity dispersion is a fundamental, directly observable property of galaxies
that may robustly connect galaxies to dark matter halos in N-body simulations.
To interpret the results further in the context of Lambda-CDM, it would be
useful to analyze the relationship between the velocity dispersion of stellar
particles and the velocity dispersion characterizing their dark matter halos in
high-resolution cosmological hydrodynamic simulations.
