A Dark Census: Statistically Detecting the Satellite Populations of
  Distant Galaxies
  In the standard structure formation scenario based on the cold dark matter
paradigm, galactic halos are predicted to contain a large population of dark
matter subhalos. While the most massive members of the subhalo population can
appear as luminous satellites and be detected in optical surveys, establishing
the existence of the low mass and mostly dark subhalos has proven to be a
daunting task. Galaxy-scale strong gravitational lenses have been successfully
used to study mass substructures lying close to lensed images of bright
background sources. However, in typical galaxy-scale lenses, the strong lensing
region only covers a small projected area of the lens's dark matter halo,
implying that the vast majority of subhalos cannot be directly detected in
lensing observations. In this paper, we point out that this large population of
dark satellites can collectively affect gravitational lensing observables,
hence possibly allowing their statistical detection. Focusing on the region of
the galactic halo outside the strong lensing area, we compute from first
principles the statistical properties of perturbations to the gravitational
time delay and position of lensed images in the presence of a mass substructure
population. We find that in the standard cosmological scenario, the statistics
of these lensing observables are well approximated by Gaussian distributions.
The formalism developed as part of this calculation is very general and can be
applied to any halo geometry and choice of subhalo mass function. Our results
significantly reduce the computational cost of including a large substructure
population in lens models and enable the use of Bayesian inference techniques
to detect and characterize the distributed satellite population of distant lens
galaxies.
