Massive ( stellar mass M _ { \star } \gtrsim 3 \times 10 ^ { 10 } M _ { \odot } ) , passively evolving galaxies at redshifts z \gtrsim 1 exhibit on the average physical sizes smaller by factors \approx 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 \lesssim 1 is limited to less than 40 \% , while most of the evolution occurs at z \gtrsim 1 , where both compact and already extended galaxies are observed and the scatter in size is remarkably larger than locally .
The presence at high redshift of a significant number of ETGs with the same size as their local counterparts as well as of ETGs with quite small size ( \lesssim 1 / 10 of the local one ) , points to a timescale to reach the new , expanded equilibrium configuration of less than the Hubble time t _ { H } ( 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 the average significantly denser .
This result suggests that the physical mechanism responsible for the size increase should also remove mass from central galaxy regions ( r \lesssim 1 kpc ) .
We propose that quasar activity , which peaks at redshift z \sim 2 , can remove large amounts of gas from central galaxy regions on a timescale shorter than , or of order of the dynamical one , triggering a puffing up of the stellar component at constant stellar mass ; in this case the size increase goes together with a decrease of 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 \gtrsim 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 _ { \star } \lesssim 3 \times 10 ^ { 10 } M _ { \odot } ) are expected to evolve less both in size and in velocity dispersion , because their evolution is ruled essentially by supernova feedback , which can not yield winds as powerful as those triggered by quasars .
The differential evolution is expected to leave imprints in the size vs. luminosity/mass , velocity dispersion vs. luminosity/mass , central black hole mass vs. velocity dispersion relationships , as observed in local ETGs .