  The dark matter subhalos orbiting in a galactic halo perturb the orbits of
stars in thin stellar streams. Over time the random velocities in the streams
develop non-Gaussian wings. The rate of velocity increase is approximately a
random walk at a rate proportional to the number of subhalos, primarily those
in the mass range $\approx 10^{6-7} M_\odot$. The distribution of random
velocities in long, thin, streams is measured in simulated Milky Way-like halos
that develop in representative WDM and CDM cosmologies. The radial velocity
distributions are well modeled as the sum of a Gaussian and an exponential. The
resulting MCMC fits find Gaussian cores of 1-2 km/sec and exponential wings
that increase from 3 km/sec for 5.5 keV WDM, 4 km/sec for 7 keV WDM, to 6
km/sec for a CDM halo. The observational prospects to use stream measurements
to constrain the nature of galactic dark matter are discussed.
