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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 γ' (ρ(r)\propto r^{-γ'}) on stellar mass, size, and redshift. We find that two parameters are sufficent to determine γ' with less than 6% residual scatter. At fixed redshift, γ' depends solely on the surface stellar mass density \partial γ'/ \partial Σ_*=0.38\pm 0.07, i.e. galaxies with denser stars also have steeper slopes. At fixed M_* and R_{eff}, γ' depends on redshift, in the sense that galaxies at a lower redshift have steeper slopes (\partial γ' / \partial z = -0.31\pm 0.10). However, the mean redshift evolution of γ' for an individual galaxy is consistent with zero dγ'/dz=-0.10\pm0.12. This result is obtained by combining our measured dependencies of γ' 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.