We show that the observed velocity dispersion function of E/S0 galaxies matches strikingly well the distribution function of virial velocities of massive halos virializing at z >= 1.5, as predicted by the standard hierarchical clustering scenario in a Lambda CDM cosmology, for a constant ratio sigma/V-vir similar or equal to 0.55 +/- 0.05, which is close to the value expected at virialization if it typically occurred at z greater than or similar to 3. This strongly suggests that dissipative processes and later merging events had little impact on the matter density profile. Adopting the above sigma V-vir ratio, the observed relationships between photometric and dynamical properties that define the fundamental plane of elliptical galaxies, such as the luminosity-sigma ( Faber-Jackson) and the luminosity-effective radius relations, as well as the M-BH-sigma relation, are nicely reproduced. Their shapes turn out to be determined by the mutual feedback of star formation (and supernova explosions) and nuclear activity, along the lines discussed by Granato and coworkers. To our knowledge, this is the first semianalytic model for which simultaneous fits of the fundamental plane relations and of the epochdependent luminosity function of spheroidal galaxies have been presented.
