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{sub U}, in a typical cold dark matter (CDM) galactic halo at 100 kpc is R{sub U}{approx_equal}0.0066 M-hat{sub 8}{sup -0.35}kpc{sup -1}Gyr{sup -1}, where M-hat{sub 8}({identical_to} M-hat /10{sup 8} M{sub Sun }) is the minimum mass halo that creates a visible gap. The relation can be recast entirely in terms of observables, as R{sub U}{approx_equal}0.059w{sup -0.85}kpc{sup -1}Gyr{sup -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{sup 5} sub-halos above a minimum mass of 10{sup 5} M{sub Sun }.