  We study trends in the slope of the total mass profiles and dark matter
fractions within the central half-light radius of 258 early-type galaxies,
using data from the volume-limited ATLAS$^{\mathrm{3D}}$ survey. We use three
distinct sets of dynamical models, which vary in their assumptions and also
allow for spatial variations in the stellar mass-to-light ratio, to test the
robustness of our results. We confirm that the slopes of the total mass
profiles are approximately isothermal, and investigate how the total-mass slope
depends on various galactic properties. The most statistically-significant
correlations we find are a function of either surface density, \(\Sigma_e\), or
velocity dispersion, \(\sigma_e\). However there is evidence for a break in the
latter relation, with a nearly universal logarithmic slope above
\(\log_{10}[\sigma_e/(\si{km~s^{-1}})]\sim 2.1\) and a steeper trend below this
value. For the 142 galaxies above that critical \(\sigma_e\) value, the total
mass-density logarithmic slopes have a mean value
\(\left\langle\gamma^\prime\right\rangle = -2.192 \pm 0.016\) (\(1\sigma\)
error) with an observed rms scatter of only \(\sigma_{\gamma^\prime}=0.167 \pm
0.016\). Considering the observational errors, we estimate an intrinsic scatter
of \(\sigma_{\gamma^\prime}^\mathrm{intr} \approx 0.15\). These values are
broadly consistent with those found by strong lensing studies at similar radii
and agree, within the tight errors, with values recently found at much larger
radii via stellar dynamics or HI rotation curves (using significantly smaller
samples than this work).
