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, Very Large Telescope, and Gemini for a sample of 36 secure strong gravitational lens systems and 17 candidates identified as part of the Strong Lensing Legacy Survey. The deflectors are massive early-type galaxies in the redshift range z= 0.2–0.8, while the lensed sources are at z = 1–3.5. We combine these data with photometric and lensing measurements presented in the companion paper III and with lenses from the Sloan Lens Advanced Camera for Surveys and Lenses Structure and Dynamics 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) ∝ r^−γ), on stellar mass, size, and redshift. We find that two parameters are sufficient to determine γ with less than 6% residual scatter. At fixed redshift, γ depends solely on the surface stellar mass density ∂γ/∂Σ∗ = 0.38±0.07, i.e., galaxies with denser stars also have steeper slopes. At fixed M∗ and Reff , γ depends on redshift, in the sense that galaxies at a lower redshift have steeper slopes (∂γ/∂z = −0.31±0.10). However, the mean redshift evolution of γ for an individual galaxy is consistent with zero dγ/dz = −0.10 ± 0.12. This result is obtained by combining our measured dependencies of γ on z,M∗,Reff with the evolution of the Reff–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.