Early-type Galaxies in the Hubble Deep Field. The <mu_e>-r_e relation and the lack of large galaxies at high redshift

We present the results of the detailed surface photometry of a sample of early-type galaxies in the Hubble Deep Field. Effective radii, surface brightnesses and total V_606 magnitudes have been obtained, as well as U_300, B_450, I_814, J, H and K colors, which are compared with the predictions of chemical-spectrophotometric models of population synthesis. Spectroscopic redshifts are available for 23 objects. For other 25 photometric redshifts are given. In the <mu_e>-r_e plane the early-type galaxies of the HDF, once the appropriate K+E corrections are applied, turn out to follow the `rest frame' Kormendy relation. This evidence, linked to the dynamical information gathered by Steidel et al.(1996), indicates that these galaxies, even at z~2-3, lie in the Fundamental Plane, in a virial equilibrium condition. At the same redshifts a statistically significant lack of large galaxies [i.e. with Log r_e(kpc) > 0.2] is observed.