Quantifying scatter in galaxy formation at the lowest masses

Abstract

We predict the stellar mass -- halo mass (SMHM) relationship for dwarf galaxies, using simulated galaxies with peak halo masses of M${}_{\mathrm{peak}}=10^{11}$ M${}_{\odot }$ down into the ultra-faint dwarf range to M${}_{\mathrm{peak}}=$ 10${}^7$ M${}_{\odot }$. Our simulated dwarfs have stellar masses of M${}_{\mathrm{star}}=$ 790 M${}_{\odot }$ to $8.2\times 10^8$ M${}_{\odot }$, with corresponding $V$-band magnitudes from $-2$ to $-18.5$. For M${}_{\mathrm{peak}}>10^{10}$ M${}_{\odot }$, 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${}_{\mathrm{peak}}$ $=$ 10${}^8$ M${}_{\odot }$. 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.

16 pages, 5 figures; submitted to ApJ. arXiv admin note: text overlap with arXiv:1705.06286

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