The slope of the mass profile and the tilt of the fundamental plane in early-type galaxies

We present a survey, using the Chandra X-ray observatory, of the central gravitating mass profiles in a sample of 10 galaxies, groups and clusters, spanning ~2 orders of magnitude in virial mass. We find the total mass distributions from ~0.2--10Re, where Re is the optical effective radius of the central galaxy, are remarkably similar to powerlaw density profiles. The negative logarithmic slope of the mass density profiles, alpha, systematically varies with Re, from alpha=2, for systems with Re~4kpc to alpha=1.2 for systems with Re>30kpc. Departures from hydrostatic equilibrium are likely to be small and cannot easily explain this trend. We show that the conspiracy between the baryonic (Sersic) and dark matter (NFW/ Einasto) components required to maintain a powerlaw total mass distribution naturally predicts an anti-correlation between alpha and Re that is very close to what is observed. The systematic variation of alpha with Re implies a dark matter fraction within Re that varies systematically with the properties of the galaxy in such a manner as to reproduce, without fine tuning, the observed tilt of the fundamental plane. We speculate that establishing a nearly powerlaw total mass distribution is therefore a fundamental feature of galaxy formation and the primary factor which determines the tilt of the fundamental plane.