THE SL2S GALAXY-SCALE LENS SAMPLE. V. DARK MATTER HALOS AND STELLAR IMF OF MASSIVE EARLY-TYPE GALAXIES OUT TO REDSHIFT 0.8

We investigate the cosmic evolution of the internal structure of massive early-type galaxies over half of the age of the universe. We perform a joint lensing and stellar dynamics analysis of a sample of 81 strong lenses from the Strong Lensing Legacy Survey and Sloan ACS Lens Survey and combine the results with a hierarchical Bayesian inference method to measure the distribution of dark matter mass and stellar initial mass function (IMF) across the population of massive early-type galaxies. Lensing selection effects are taken into account. We find that the dark matter mass projected within the inner 5 kpc increases for increasing redshift, decreases for increasing stellar mass density, but is roughly constant along the evolutionary tracks of early-type galaxies. The average dark matter slope is consistent with that of a Navarro-Frenk-White profile, but is not well constrained. The stellar IMF normalization is close to a Salpeter IMF at log M ∗ = 11.5 and scales strongly with increasing stellar mass. No dependence of the IMF on redshift or stellar mass density is detected. The anti-correlation between dark matter mass and stellar mass density supports the idea of mergers being more frequent in more massive dark matter halos.