  Measurements of velocity and density perturbations along stellar streams in
the Milky Way provide a time integrated measure of dark matter substructure at
larger galactic radius than the complementary instantaneous inner halo strong
lensing detections of dark matter sub-halos in distant galaxies. An interesting
case to consider is the proposed Phoenix-Hermus star stream, which is long,
thin and on a nearly circular orbit, making it a particular good target to
study for velocity variations along its length. In the presence of dark matter
sub-halos the distribution of velocities is significantly perturbed in a manner
that is readily understood with the impulse approximation. A set of simulations
show that only sub-halos above a few 10^7 M_sun lead to reasonably long lived
observationally detectable velocity variations of amplitude of order 1 kms,
with an average of about one visible hit per (two-armed) stream. An implication
is that globular clusters themselves will not have a visible impact on the
stream. Radial velocities have the benefit that they are completely insensitive
to distance errors. Distance errors scatter individual star velocities
perpendicular and tangential to the mean orbit but their mean values remain
unbiased. Calculations like these help build the quantitative case to acquire
large, fairly deep, velocity samples of stream stars.
