Limits on the power-law mass and luminosity density profiles of
  elliptical galaxies from gravitational lensing systems
  We use 118 strong gravitational lenses observed by the SLACS, BELLS, LSD and
SL2S surveys to constrain the total mass profile and the profile of luminosity
density of stars (light-tracers) in elliptical galaxies up to redshift $z \sim
1$. Assuming power-law density profiles for the total mass density,
$\rho=\rho_0(r/r_0)^{-\alpha}$, and luminosity density,
$\nu=\nu_0(r/r_0)^{-\delta}$, we investigate the power law index and its first
derivative with respect to the redshift. Using Monte Carlo simulations of the
posterior likelihood taking the Planck's best-fitted cosmology as a prior, we
find $\gamma= 2.132\pm0.055$ with a mild trend $\partial \gamma/\partial z_l=
-0.067\pm0.119$ when $\alpha=\delta=\gamma$, suggesting that the total density
profile of massive galaxies could have become slightly steeper over cosmic
time. Furthermore, similar analyses performed on sub-samples defined by
different lens redshifts and velocity dispersions, indicate the need of
treating low, intermediate and high-mass galaxies separately. Allowing $\delta$
to be a free parameter, we obtain $\alpha=2.070\pm0.031$, $\partial
\alpha/\partial z_l= -0.121\pm0.078$, and $\delta= 2.710\pm0.143$. The model in
which mass traces light is rejected at $>95\%$ confidence and our analysis
robustly indicates the presence of dark matter in the form of a mass component
that is differently spatially extended than the light. In this case,
intermediate-mass elliptical galaxies ($200$ km/s $ < \sigma_{ap} \leq 300$
km/s) show the best consistency with the singular isothermal sphere as an
effective model of galactic lenses.
