Quantifying Scatter in Galaxy Formation at the Lowest Masses

We predict the stellar mass-halo mass (SMHM) relationship for dwarf galaxies, using simulated galaxies with peak halo masses of M _peak = 10¹¹ M _⊙ down into the ultra-faint dwarf range to M _peak = 10⁷ M _⊙. Our simulated dwarfs have stellar masses of M _star = 790 M _⊙ to 8.2 × 10⁸ M _⊙, with corresponding V-band magnitudes from -2 to -18.5. For M _peak > 10¹⁰ M _⊙, the simulated SMHM relationship agrees with literature determinations, including exhibiting a small scatter of 0.3 dex. However, the scatter in the SMHM relation increases for lower-mass halos. We first present results for well-resolved halos that contain a simulated stellar population, but recognize that whether a halo hosts a galaxy is inherently mass resolution dependent. We thus adopt a probabilistic model to populate "dark" halos below our resolution limit to predict an "intrinsic" slope and scatter for the SMHM relation. We fit linearly growing log-normal scatter in stellar mass, which grows to more than 1 dex at M _peak = 10⁸ M _⊙. At the faintest end of the SMHM relation probed by our simulations, a galaxy cannot be assigned a unique halo mass based solely on its luminosity. Instead, we provide a formula to stochastically populate low-mass halos following our results. Finally, we show that our growing log-normal scatter steepens the faint-end slope of the predicted stellar mass function.