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 similar to 2 orders of magnitude in virial mass. We find the total mass distributions from similar to 0.2 to 10R(e), where R(e) is the optical effective radius of the central galaxy, are remarkably similar to power-law density profiles. The negative logarithmic slope of the mass density profiles, alpha, systematically varies with R(e), from alpha similar or equal to 2, for systems with R(e) similar to 4 kpc to alpha similar or equal to 1.2 for systems with R(e) greater than or similar to 30 kpc. 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 (Navarro-Frenk-White/Einasto) components required to maintain a power-law total mass distribution naturally predicts an anti-correlation between alpha and R(e) that is very close to what is observed. The systematic variation of alpha with R(e) implies a dark matter fraction within R(e) 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 power-law total mass distribution is therefore a fundamental feature of galaxy formation and the primary factor which determines the tilt of the Fundamental Plane.