The Scaling of Stellar Mass and Central Stellar Velocity Dispersion for Quiescent Galaxies at z<0.7

We examine the relation between stellar mass and central stellar velocity dispersion—the M_*σ 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_*σ relation and its scatter are independent of redshift with for M_* ≳ 10^10.3 M_⊙. The measured slope of the M_*σ 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, which may robustly connect galaxies to dark matter halos in N-body simulations. To interpret the results further in the context of ΛCDM, 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.