2012ApJ...748...20C

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∪, in a typical cold dark matter (CDM) galactic halo at 100 kpc is R∪≃ 0.00661₈^–0.35/kpc, where 1₈ (≡1/10⁸M_☉) is the minimum mass halo that creates a visible gap. The relation can be recast entirely in terms of observables, as R∪≃ 0.059ω^–0.85/kpc/Gyr, 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 10⁵ sub-halos above a minimum mass of 10⁵ M_☉.