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.
