One of the primary hurdles in pushing dark matter constraints to dwarf scales the uncertainty in the stellar-mass--halo-mass (SMHM) relation. Results from simulations differ by two orders of magnitude at halo masses < 10^10 solar masses, and none can match observations. Moreover, there is no consensus on the amount of scatter. To address these uncertainties, I used high-resolution simulations of dwarfs from the Engineering Dwarfs at Galaxy formation's Edge (EDGE) Project to investigate the SMHM at < 10^10 solar masses. Based on these simulations, I created a new galaxy-halo model, DarkLight, that can accurately predict the stellar masses of dwarfs, uniquely including its dependence on accretion history. We find that a ~1 dex scatter in the SMHM relation for halos with a mass of 10^9 solar masses is due predominantly to the scatter in the accretion histories. Differences between previous simulations results and their inability to reproduce observations can be explained by an increase in scatter in the SMHM at low masses, the limited sample sizes and resolution of simulations, and the incompleteness of observational searches. We discuss the implications this has for constraining dark matter models with assembly history statistics that differ from cold dark matter, such as warm dark matter.
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