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
SL2S and SLACS surveys and combine the results with a hierarchical Bayesian
inference method to measure the distribution of dark matter mass and stellar
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 an NFW 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.
