The radio galaxy K-z relation: the 10^12 Msol mass limit; masses of galaxies from the L_K luminosity, up to z >4

The narrow K-z relation of powerful radio galaxies in the Hubble K diagram is often attributed to the stellar populations of massive elliptical galaxies. Extended over a large range of redshifts (0<z<4), it is difficult to estimate masses at high z from galaxy evolution. In the present paper, we propose to estimate the stellar masses of galaxies using the galaxy evolution model PEGASE. We use star formation scenarios that successfully fit faint galaxy counts and z=0 galaxy templates. They also allow to estimate valid photometric redshifts. The baryonic mass of the initial gas cloud M_bar is then derived. The K-z relation is remarkably reproduced by our scenario for elliptical galaxies of baryonic mass M_(bar,max)=10^12 Msol, at all z up to z=4. M_(bar,max) is also the maximum mass limit of all types of galaxies. Using another IMF, even a top-heavy one, does not alter our conclusions. The high value of M_(bar,max) observed at z > 4 implies that massive clouds were already formed at early epochs. We also find that the M_(bar,max) limit is similar to the critical mass M_crit of a self-gravitating cloud regulated by cooling (Rees & Ostriker, 1977; Silk, 1977). Moreover, the critical size r_crit = 75 Kpc is remarkably close to the typical diameter of Ly_alpha haloes surrounding distant radio galaxies. This confirms the validity of the method of baryonic mass determination based on the K-band luminosity. A puzzling question that remains to be answered is the short time-scale of mass-accumulation required to form such massive galaxies at z=4. We discuss the dispersion of the K-z relation and the link between the active nucleus and a large stellar mass.