The SL2S Galaxy-scale Lens Sample. IV. The dependence of the total mass
  density profile of early-type galaxies on redshift, stellar mass, and size
  We present optical and near infrared spectroscopy obtained at Keck, VLT, and
Gemini for a sample of 36 secure strong gravitational lens systems and 17
candidates identified as part of the SL2S survey. The deflectors are massive
early-type galaxies in the redshift range z_d=0.2-0.8, while the lensed sources
are at z_s=1-3.5. We combine this data with photometric and lensing
measurements presented in the companion paper III and with lenses from the
SLACS and LSD surveys to investigate the cosmic evolution of the internal
structure of massive early-type galaxies over half the age of the universe. We
study the dependence of the slope of the total mass density profile \gamma'
(\rho(r)\propto r^{-\gamma'}) on stellar mass, size, and redshift. We find that
two parameters are sufficent to determine \gamma' with less than 6% residual
scatter. At fixed redshift, \gamma' depends solely on the surface stellar mass
density \partial \gamma'/ \partial \Sigma_*=0.38\pm 0.07, i.e. galaxies with
denser stars also have steeper slopes. At fixed M_* and R_{eff}, \gamma'
depends on redshift, in the sense that galaxies at a lower redshift have
steeper slopes (\partial \gamma' / \partial z = -0.31\pm 0.10). However, the
mean redshift evolution of \gamma' for an individual galaxy is consistent with
zero d\gamma'/dz=-0.10\pm0.12. This result is obtained by combining our
measured dependencies of \gamma' on z,M_*,R_{eff} with the evolution of the
R_{eff}-M_* taken from the literature, and is broadly consistent with current
models of the formation and evolution of massive early-type galaxies. Detailed
quantitative comparisons of our results with theory will provide qualitatively
new information on the detailed physical processes at work.
