Phase-space constraints on visible and dark matter distributions in elliptical galaxies

There are observational and theoretical indications that both the visible (stars) and the dark matter density distributions in elliptical galaxies increase significantly up to the galactic center. I present here some analytical results obtained with the aid of self-consistent, spherically symmetric two component galaxy models. These results suggest the possibility that this similar behavior could be a direct consequence of the structural and dynamical constraints imposed by the request of positivity of the phase-space distribution function of each density component.