The fundamental plane of ellipticals - I. The dark matter connection

We show that the small scatter around the fundamental plane (FP) of massive elliptical galaxies can be used to derive important properties about their dark and luminous matter. The central velocity dispersion sigma(0) (appearing in the fundamental plane) is linked to photometric, dynamical and geometrical properties of (luminous and dark) matter. We find that, inside the effective radius R-e, the matter traced by the light must largely dominate over the dark matter (DM) in order to keep the ellipticals close enough to the FP. This recalls analogous findings for spiral galaxies. In particular we also find that cuspy DM distributions, as predicted by numerical simulations in LambdaCDM cosmology, are unable to explain the very existence of the FP; in fact, according to this theory, the structural properties of dark and luminous matter are so interwoven that a curved surface is predicted in the log-space (sigma(0) , R (e) , L ), rather than a plane. To agree with the FP implies that CDM haloes have values in the range of 5-9 for the concentration parameter c (i.e. values significantly lower than the current predictions). Assuming a more heuristic approach and allowing for cored DM haloes, we find that the small intrinsic scatter of the FP yields: (i) an average value of about 0.3 for the dark-to-light-traced mass ratio, (ii) a mass-to-light of the matter traced by the light increasing with spheroidal luminosity: M-sph /L-r proportional toL (0.2) (r) (Gunn-r band), with a value of 5.3 at L (*r) equivalent to 2.7 x 10(10) L (r circle dot).