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-boolean OR, in a typical cold dark matter (CDM) galactic halo at 100 kpc is R-boolean OR similar or equal to 0.0066 (M) over cap (-0.35)(8) kpc(-1) Gyr(-1), where (M) over cap (8)(equivalent to (M) over cap /10(8) M-circle dot) is the minimum mass halo that creates a visible gap. The relation can be recast entirely in terms of observables, as R-boolean OR similar or equal to 0.059w(-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 requires a total halo population of 10(5) sub-halos above a minimum mass of 10(5) M-circle dot.