The Sloan Lens ACS Survey. X. Stellar, Dynamical, and Total Mass
  Correlations of Massive Early-type Galaxies
  We use stellar masses, photometry, lensing, and velocity dispersions to
investigate empirical correlations for the final sample of 73 early-type lens
galaxies (ETGs) from the SLACS survey. The traditional correlations
(Fundamental Plane [FP] and its projections) are consistent with those found
for non-lens galaxies, supporting the thesis that SLACS lens galaxies are
representative of massive ETGs. The addition of strong lensing estimates of the
total mass allows us to gain further insights into their internal structure: i)
the mean slope of the total mass density profile is <gamma'> = 2.078+/-0.027
with an intrinsic scatter of 0.16+/-0.02; ii) gamma' correlates with effective
radius and central mass density, in the sense that denser galaxies have steeper
profiles; iii) the dark matter fraction within reff/2 is a monotonically
increasing function of galaxy mass and size; iv) the dimensional mass M_dim is
proportional to the total mass, and both increase more rapidly than stellar
mass M*; v) the Mass Plane (MP), obtained by replacing surface brightness with
surface mass density in the FP, is found to be tighter and closer to the virial
relation than the FP and the M*P, indicating that the scatter of those
relations is dominated by stellar population effects; vi) we construct the
Fundamental Hyper-Plane by adding stellar masses to the MP and find the M*
coefficient to be consistent with zero and no residual intrinsic scatter. Our
results demonstrate that the dynamical structure of ETGs is not scale invariant
and that it is fully specified by the total mass, r_eff, and sigma. Although
the basic trends can be explained qualitatively in terms of varying star
formation efficiency as a function of halo mass and as the result of dry and
wet mergers, reproducing quantitatively the observed correlations and their
tightness may be a significant challenge for galaxy formation models.
