Mass density slope of elliptical galaxies from strong lensing and resolved stellar kinematics

TL;DR

This paper presents a method to constrain the mass density slope of elliptical galaxies using strong lensing and stellar kinematics at two specific radii, verified on simulations and real galaxy data, achieving accurate results with simplified calculations.

Contribution

Introduces a two-pinch-radii approach to determine galaxy density slopes that is simpler and relies on fewer calculations than previous methods.

Findings

Accurately recovers density slope with ~13% error in simulations.

Finds a mean density slope of 2.1±0.05 in SLACS galaxies.

Method simplifies analysis using only observable quantities.

Abstract

We discuss constraints on the mass density distribution (parameterized as $\rho\propto r^{-\gamma}$) 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 $r_1=2.2 R_{Einst}$ is defined such that the Einstein (i.e. aperture) mass can be converted to the spherical mass almost independently of the mass-model. Another `pinch' radius $r_2=R_{opt}$ 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 $0.01 \leq z \leq 0.35$, which have already been analysed in Barnabe et al. (2011) by the self-consistent joint lensing and kinematic code. For massive simulated galaxies the density slope $\gamma$ is recovered with an accuracy of $\sim 13\%$, unless $r_1$ and $r_2$ happen to be close to each other. For SLACS galaxies, we found good overall agreement with the results of Barnabe et al. (2011) with a sample-averaged slope $\gamma=2.1\pm0.05$. While the two-pinch-radii approach has larger statistical uncertainties, it is much simpler and uses only few arithmetic operations with directly observable quantities.