Dancing in the Dark: Uncertainty in ultra-faint dwarf galaxy predictions from cosmological simulations

The existence of ultra-faint dwarf (UFD) galaxies highlights the need to push our theoretical understanding of galaxies to extremely low mass. We examine the formation of UFDs by twice running a fully cosmological simulations of dwarf galaxies, but varying star formation. One run uses a temperature-density threshold for star formation, while the other uses an H$_{2}$-based sub-grid star formation model. The total number of dwarf galaxies that forms is different by a factor of 2 between the two runs, but most of these are satellites, leading to a factor of 5 difference in the number of luminous UFD companions around more massive, isolated dwarfs. The first run yields a 47\% chance of finding a satellite around a M$_{halo}$ $\sim 10^{10}$ M$_{\odot}$ host, while the H$_2$ run predicts only a 16\% chance. Metallicity is the primary physical parameter that creates this difference. As metallicity decreases, the formation of H$_2$ is slowed and relegated to higher-density material. Thus, our H$_2$ run is unable to form many (and often, any) stars before reionization removes gas. These results emphasize that predictions for UFD properties made using hydrodynamic simulations, in particular regarding the frequency of satellites around dwarf galaxies, the slope of the stellar mass function at low masses, as well as the properties of ultra-faint galaxies occupying the smallest halos, are extremely sensitive to the subgrid physics of star formation contained within the simulation. However, upcoming discoveries of ultra-faint dwarfs will provide invaluable constraining power on the physics of the first star formation.