Measuring the power spectrum of dark matter substructure using strong
  gravitational lensing
  In recent years, it has become possible to detect individual dark matter
subhalos near images of strongly lensed extended background galaxies.
Typically, only the most massive subhalos in the strong lensing region may be
detected this way. In this work, we show that strong lenses may also be used to
constrain the much more numerous population of lower mass subhalos that are too
small to be detected individually. In particular, we show that the power
spectrum of projected density fluctuations in galaxy halos can be measured
using strong gravitational lensing. We develop the mathematical framework of
power spectrum estimation, and test our method on mock observations. We use our
results to determine the types of observations required to measure the
substructure power spectrum with high significance. We predict that deep
observations ($\sim10$ hours on a single target) with current facilities can
measure this power spectrum at the $3\sigma$ level, with no apparent degeneracy
with unknown clumpiness in the background source structure or fluctuations from
detector noise. Upcoming ALMA measurements of strong lenses are capable of
placing strong constraints on the abundance of dark matter subhalos and the
underlying particle nature of dark matter.
