Cosmic Evolution of Size and Velocity Dispersion for Early-type Galaxies

Massive (stellar mass M sstarf >~ 3 × 1010 M sun), passively evolving galaxies at redshifts z >~ 1 exhibit on average physical sizes smaller, by factors ≈3, than local early-type galaxies (ETGs) endowed with the same stellar mass. Small sizes are in fact expected on theoretical grounds, if dissipative collapse occurs. Recent results show that the size evolution at z <~ 1 is limited to less than 40%, while most of the evolution occurs at z >~ 1, where both compact and already extended galaxies are observed and the scatter in size is remarkably larger than it is locally. The presence at high redshift of a significant number of ETGs with the same size as their local counterparts, as well as ETGs with quite small size (lsim1/10 of the local one), points to a timescale for reaching the new, expanded equilibrium configuration of less than the Hubble time tH (z). We demonstrate that the projected mass of compact, high-redshift galaxies and that of local ETGs within the same physical radius, the nominal half-luminosity radius of high-redshift ETGs, differ substantially in that the high-redshift ETGs are on average significantly denser. This result suggests that the physical mechanism responsible for the size increase should also remove mass from central galaxy regions (r <~ 1 kpc). We propose that quasar activity, which peaks at redshift z ~ 2, can remove large amounts of gas from central galaxy regions on a timescale shorter than the triggering a puffing up of the stellar component at constant stellar mass (or a timescale on the order of the dynamical one); in this case, the size increase goes together with a decrease in the central mass. The size evolution is expected to parallel that of the quasars and the inverse hierarchy, or downsizing, seen in the quasar evolution is mirrored in the size evolution. Exploiting the virial theorem, we derive the relation between the stellar velocity dispersion of ETGs and the characteristic velocity of their hosting halos at the time of formation and collapse. By combining this relation with the halo formation rate at z >~ 1, we predict the local velocity dispersion distribution function. On comparing it to the observed one, we show that velocity dispersion evolution of massive ETGs is fully compatible with the observed average evolution in size at constant stellar mass. Less massive ETGs (with stellar masses M sstarf <~ 3 × 1010 M sun) are expected to evolve less both in size and in velocity dispersion, because their evolution is essentially determined by supernova feedback, which cannot yield winds as powerful as those triggered by quasars. The differential evolution is expected to leave imprints in the size versus luminosity/mass, velocity dispersion versus luminosity/mass, and central black hole mass versus velocity dispersion relationships, as observed in local ETGs.