  Perturbations to stellar systems can reflect the gravitational influence of
dark matter substructures. On scales much smaller than the size of a stellar
system, we point out analytic connections between the stellar and dark matter
distributions. In particular, the density and velocity power spectra of the
stars are proportional to the density power spectrum of the perturbing dark
matter, scaled by $k^{-4}$. This relationship allows easy evaluation of the
suitability of a stellar system for detecting dark substructure. As examples,
we show that the Galactic stellar halo is expected to be sensitive to cold dark
matter substructure at wavenumbers $k\lesssim 0.3$ kpc$^{-1}$, and the Galactic
disk might be sensitive to substructure at wavenumbers $k\sim 4$ kpc$^{-1}$.
The perturbations considered in this work are short-lived, being rapidly erased
by the stellar velocity dispersion, so it may be possible to attribute a
detection to dark matter substructure without ambiguity.
