Dark Matter Sub-Halo Counts via Star Stream Crossings
  Dark matter sub-halos create gaps in the stellar streams orbiting in the
halos of galaxies. We evaluate the sub-halo stream crossing integral with the
guidance of simulations to find that the linear rate of gap creation, R_gap, in
a typical Cold Dark Matter (CDM) galactic halo at 100 kpc is R_gap = 0.0066
M_8^-0.35 kpc^-1 Gyr^-1$, where M_8 = M/10^8 M_sun, is the minimum mass halo
that creates a visible gap. The relation can be recast entirely in terms of
observables, as R_gap= 0.059 w^-0.85 kpc^-1 Gyr^-1, for w in kpc, normalized at
100 kpc. Using published data, the density of gaps is estimated for M31's NW
stream and the Milky Way Pal 5 stream, Orphan stream, and Eastern Banded
Structure. The estimated rates of gap creation all have errors of 50% or more
due to uncertain dynamical ages and the relatively noisy stream density
measurements. The gap rate-width data are in good agreement with the CDM
predicted relation. The high density of gaps in the narrow streams require a
total halo population of 10^5 sub-halos above a minimum mass of 10^5 M_sun.
