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 { 3 D } } 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 = -2.193 \pm 0.016 ( 1 \sigma error ) with an observed rms scatter of only \sigma _ { \gamma ^ { \prime } } = 0.168 \pm 0.015 .
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 ) .