The number and size of subhalo-induced gaps in stellar streams

Abstract: Ample observational capabilities exist today to detect the small density perturbations that low-mass dark matter subhaloes impart on stellar streams from disrupting Galactic satellites. In anticipation of these observations, we investigate the expected number and size of gaps by combining an analytic prescription for gap evolution on circular orbits with the flux of subhaloes near the stream. We explore the distribution of gap sizes and depths for a typical cold stream around the Milky Way and find that for a given stream age and gap depth, each subhalo mass produces a characteristic gap size. For a stream with an age of a few Gyr, orbiting at a distance of 10-20 kpc from the Galactic center, even modest subhaloes with a mass of $10^6-10^7 M_\odot$ produce gaps with sizes that are on the order of several degrees. We consider the number and distribution of gap sizes created by subhaloes with masses $10^5-10^9 M_\odot$, accounting for the expected depletion of subhaloes by the Milky Way disk, and present predictions for six cold streams around the Milky Way. For Pal 5, we forecast 0.7 gaps with a density depletion of at least 25\% and a typical gap size of $8^\circ$. Thus, there appears to be {\it no tension} between the recent non-detection of density depletions in the Pal 5 tidal tails and $\Lambda$CDM expectations. These predictions can be used to guide the scale of future gap searches.