Statistical strong lensing. I. Constraints on the inner structure of
  galaxies from samples of a thousand lenses
  Context: The number of known strong gravitational lenses is expected to grow
substantially in the next few years. The statistical combination of large
samples of lenses has the potential of providing strong constraints on the
inner structure of galaxies. Aims: We investigate to what extent we can
calibrate stellar mass measurements and constrain the average dark matter
density profile of galaxies by statistically combining strong lensing data from
thousands of lenses. Methods: We generate mock samples of axisymmetric lenses.
We assume that, for each lens, we have measurements of two image positions of a
strongly lensed background source, as well as magnification information from
full surface brightness modelling, and a stellar population synthesis-based
estimate of the lens stellar mass. We then fit models describing the
distribution of the stellar population synthesis mismatch parameter
$\alpha_{sps}$ (the ratio between the true stellar mass and the stellar
population synthesis-based estimate) and dark matter density profile of the
population of lenses to an ensemble of 1000 mock lenses. Results: The average
$\alpha_{sps}$, projected dark matter mass and dark matter density slope can be
obtained with great precision and accuracy, compared with current constraints.
A flexible model and the knowledge of the lens detection efficiency as a
function of image configuration are required in order to avoid a biased
inference. Conclusions: Statistical strong lensing inferences from upcoming
surveys have the potential to calibrate stellar mass measurements and to
constrain the inner dark matter density profile of massive galaxies.
