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Abstract We predict the stellar mass–halo mass (SMHM) relationship for dwarf galaxies, using simulated galaxies with peak halo masses of M peak = 10 11 M ⊙ down into the ultra-faint dwarf range to M peak = 10 7 M ⊙ . Our simulated dwarfs have stellar masses of M star = 790 M ⊙ to 8.2 × 10 8 M ⊙ , with corresponding V -band magnitudes from −2 to −18.5. For M peak > 10 10 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 = 10 8 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. 

ABSTRACT Massive black holes often exist within dwarf galaxies, and both simulations and observations have shown that a substantial fraction of these may be off-centre with respect to their hosts. We trace the evolution of off-centre massive black holes (MBHs) in dwarf galaxies using cosmological hydrodynamical simulations, and show that the reason for off-centre locations is mainly due to galaxy–galaxy mergers. We calculate dynamical time-scales and show that off-centre MBHs are unlikely to sink to their galaxys’ centres within a Hubble time, due to the shape of the hosts’ potential wells and low stellar densities. These wandering MBHs are unlikely to be detected electromagnetically, nor is there a measurable dynamical effect on the galaxy’s stellar population. We conclude that off-centre MBHs may be common in dwarfs, especially if the mass of the MBH is small or the stellar mass of the host galaxy is large. However, detecting them is extremely challenging, because their accretion luminosities are very low and they do not measurably alter the dynamics of their host galaxies.