The K20 survey. V. The evolution of the near-IR Luminosity Function

We present the galaxy rest-frame near-IR Luminosity Function (LF) and its cosmic evolution to $z\sim1.5$ based on a spectroscopic survey of a magnitude limited sample of galaxies with $K_{\rm s}<20$ (the K20 survey, Cimatti et al. 2002b). The LFs have been derived in the rest-frame J and Ks bands. Their evolution is traced using three different redshift bins ($z_{\rm mean}\simeq 0.5, 1, 1.5$) and comparing them to the Local near-IR Luminosity Function. The luminosity functions at different redshifts are fairly well fitted by Schechter functions at $z<1.3$. The faint-end of the LFs ($L<L^*$) is consistent with the local estimates, with no evidence for a change either in the slope or normalization up to $z<1.3$. At higher redshift this part of the luminosity function is not well sampled by our data. Viceversa, the density of luminous galaxies ($M_{K_{\rm s}}-5~\log~h_{70}<-25.5$) is higher than locally at all redshifts and relatively constant or mildly increasing with redshift within our sample. The data are consistent with a mild luminosity evolution both in the J- and Ks-band up to $z\simeq1.5$, with an amplitude of about $\Delta M_J \simeq -0.69\pm0.12$ and $\Delta M_K \simeq -0.54\pm0.12$ at $z\sim1$. Pure density evolution is not consistent with the observed LF at $z\le1$. Moreover, we find that red and early-type galaxies dominate the bright-end of the LF, and that their number density shows at most a small decrease (< $30\%$) up to $z\simeq 1$, thus suggesting that massive elliptical galaxies were already in place at $z\simeq 1$ and they should have formed their stars and assembled their mass at higher redshift. There appears to be a correlation of the optical/near-IR colors with near-IR luminosities, the most luminous/massive galaxies being red/old, the low-luminous galaxies being instead dominated by blue young stellar populations. We also investigate the evolution of the near-IR comoving luminosity density to $z\simeq1.5$, finding a slow evolution with redshift ($\rho_\lambda(z)= \rho_\lambda(z=0) (1+z)^{\beta(\lambda)}$ with $\beta(J)\simeq0.70$ and $\beta(K_{\rm s})\simeq0.37$). Finally, we compare the observed LFs with the predictions of a set of the most updated hierarchical merging models. Such a comparison shows that the current versions of hierarchical models overpredict significantly the density of low luminosity galaxies at $z\le1$ and underpredict the density of luminous galaxies at $z\ge1$, whereas passive evolution models are more consistent with the data up to $z\sim1.5$. The GIF model (Kaufmann et al. 1999) shows a clear deficiency of red luminous galaxies at $z\sim1$ compared to our observations and predicts a decrease of luminous galaxies with redshift not observed in our sample