Velocity Dispersion, Size, Sersic Index and Dn4000: The Scaling of Stellar Mass with Dynamical Mass for Quiescent Galaxies

H. Jabran Zahid, Margaret J. Geller

Published 2017-01-04Version 1

We examine the relation between stellar mass, velocity dispersion, size, Sersic index and Dn4000 for a volume limited sample of 40,000 quiescent galaxies in the SDSS. At a fixed stellar mass, galaxies with higher Dn4000 have larger velocity dispersions and smaller sizes. Dn4000 is a proxy for stellar population age, thus these trends suggest that older galaxies typically have larger velocity dispersions and smaller sizes. We combine velocity dispersion and size into a dynamical mass estimator, $\sigma^2 R$. At a fixed stellar mass, $\sigma^2 R$ depends on Dn4000. The Sersic index is also correlated with Dn4000. The dependence of $\sigma^2 R$ and Sersic index on Dn4000 suggests that quiescent galaxies are not structurally homologous systems. We derive an empirical correction for non-homology which is consistent with the analytical correction derived from the virial theorem. After accounting for non-homologous galactic structure, we measure M* ~ M_d^(0.997 +/- 0.004) where M* is the stellar mass and M_d is the dynamical mass derived from the velocity dispersion and size; stellar mass is directly proportional to dynamical mass. Quiescent galaxies appear to be in approximate virial equilibrium and deviations of the fundamental plane parameters from the expected virial relation may result from mass-to-light ratio variations, selection effects and the non-homology of quiescent galaxies. We infer the redshift evolution of velocity dispersion and size for galaxies in our sample assuming purely passive evolution. The inferred evolution is inconsistent with direct measurements at higher redshifts. Thus quiescent galaxies do not passively evolve. Quiescent galaxies have properties that are consistent with standard galaxy formation in LambdaCDM. They form at different epochs and evolve modestly increasing their size, velocity dispersion and Sersic index after they cease star formation.