Stellar streams and dark substructure: the diffusion regime
  The cold dark matter picture predicts an abundance of substructure within the
Galactic halo. However, most substructures host no stars and can only be
detected indirectly. Stellar streams present a promising probe of this dark
substructure. These streams arise from tidally stripped star clusters or dwarf
galaxies, and their low dynamical temperature and negligible self-gravity give
them a sharp memory of gravitational perturbations caused by passing dark
substructures. For this reason, perturbed stellar streams have been the subject
of substantial study. While previous studies have been largely numerical, we
show here that in the diffusion regime -- where stream stars are subjected to
many small velocity kicks -- stream perturbations can be understood on a fully
analytic level. In particular, we derive how the (three-dimensional) power
spectrum of the substructure density field determines the power spectrum of the
(one-dimensional) density of a stellar stream. Our analytic description
supplies a clear picture of the behaviour of stream perturbations in response
to a perturbing environment, which may include contributions from both dark and
luminous substructure. In particular, stream perturbations grow in amplitude
initially, settle into a steady state, and ultimately decay. By directly
relating stellar stream perturbations to the surrounding matter distribution,
this analytic framework represents a versatile new tool for probing the nature
of dark matter through astrophysical observations.
