The Fundamental Plane of Ellipticals: I. The Dark Matter Connection

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Abstract
We show that the small scatter around the Fundamental Plane (FP) of massive elliptical galaxies can be used to derive important properties of their dark and luminous matter. The central velocity dispersion sigma_0, appearing in (e.g.) 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 Lambda CDM 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. In order to agree with the FP, CDM halos must have concentrations parameters in the range of 5-9 (i.e. values significantly lower than the current predictions). Assuming a more heuristic approach and allowing for cored DM halos, we find that the small intrinsic scatter of the FP yields to i) an average value for the dark-to-light-traced mass ratio inside the length-scale of light R_e of about 0.3, ii) a mass-to-light ratio of the matter traced by the light increasing with spheroid luminosity as L^(0.2) in Gunn-r band, with a value of 5.3 at L = 2.7 x 10^{10} L_{sol}.

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