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The existence of ultra-faint dwarf (UFD) galaxies highlights the need to pushour theoretical understanding of galaxies to extremely low mass. We examine theformation of UFDs by twice running a fully cosmological simulations of dwarfgalaxies, but varying star formation. One run uses a temperature-densitythreshold for star formation, while the other uses an H$_{2}$-based sub-gridstar formation model. The total number of dwarf galaxies that forms isdifferent by a factor of 2 between the two runs, but most of these aresatellites, leading to a factor of 5 difference in the number of luminous UFDcompanions 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 theprimary physical parameter that creates this difference. As metallicitydecreases, the formation of H$_2$ is slowed and relegated to higher-densitymaterial. Thus, our H$_2$ run is unable to form many (and often, any) starsbefore reionization removes gas. These results emphasize that predictions forUFD properties made using hydrodynamic simulations, in particular regarding thefrequency of satellites around dwarf galaxies, the slope of the stellar massfunction at low masses, as well as the properties of ultra-faint galaxiesoccupying the smallest halos, are extremely sensitive to the subgrid physics ofstar formation contained within the simulation. However, upcoming discoveriesof ultra-faint dwarfs will provide invaluable constraining power on the physicsof the first star formation.

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