Organized chaos: scatter in the relation between stellar mass and halo mass in small galaxies

We use Local Group galaxy counts together with the ELVIS N-body simulations to explore the relationship between the scatter and slope in the stellar mass versus halo mass relation at low masses, M-star similar or equal to 10(5)-10(8)M(circle dot). Assuming models with lognormal scatter about a median relation of the form M-star alpha M-halo(alpha), the preferred log-slope steepens from alpha similar or equal to 1.8 in the limit of zero scatter to alpha similar or equal to 2.6 in the case of 2 dex of scatter in M-star at fixed halo mass. We provide fitting functions for the best-fitting relations as a function of scatter, including cases where the relation becomes increasingly stochastic with decreasing mass. We show that if the scatter at fixed halo mass is large enough (greater than or similar to 1 dex) and if the median relation is steep enough (alpha greater than or similar to 2), then the ` too-big-to-fail' problem seen in the Local Group can be self-consistently eliminated in about similar to 5-10 per cent of realizations. This scenario requires that the most massive subhaloes host unobservable ultra-faint dwarfs fairly often; we discuss potentially observable signatures of these systems. Finally, we compare our derived constraints to recent high-resolution simulations of dwarf galaxy formation in the literature. Though simulation-to-simulation scatter in M-star at fixed M-halo is large among different authors (similar to 2 dex), individual codes produce relations with much less scatter and usually give relations that would overproduce local galaxy counts.