Mass density slope of elliptical galaxies from strong lensing and resolved stellar kinematics
We discuss constraints on the mass density distribution (parametrized as ρ ∝ r−γ) in early-type galaxies provided by strong lensing and stellar kinematics data. The constraints come from mass measurements at two ‘pinch’ radii. One ‘pinch’ radius r1 = 2.2REinst is defined such that the Einstein (i.e. aperture) mass can be converted into the spherical mass almost independently of the mass-model. Another ‘pinch’ radius r2 = Ropt is chosen so that the dynamical mass, derived from the line-of-sight velocity dispersion, is least sensitive to the anisotropy of stellar orbits. We verified the performance of this approach on a sample of simulated elliptical galaxies and on a sample of 15 SLACS lens galaxies at 0.01 ≤ z ≤ 0.35, which have already been analysed in Barnabè et al. by the self-consistent joint lensing and kinematic code. For massive simulated galaxies, the density slope γ is recovered with an accuracy of ∼13 per cent, unless r1 and r2 happen to be close to each other. For SLACS galaxies, we found good overall agreement with the results of Barnabè et al. with a sample-averaged slope γ = 2.1 ± 0.05. Although the two-pinch-radii approach has larger statistical uncertainties, it is much simpler and uses only few arithmetic operations with directly observable quantities.