Forged in FIRE: cusps, cores, and baryons in low-mass dwarf galaxies

We present ultra-high resolution cosmological hydrodynamic simulations of $M_*\simeq10^{4-6.3}M_{\odot}$ dwarf galaxies that form within $M_{v}=10^{9.5-10}M_{\odot}$ dark matter halos. Our simulations rely on the FIRE implementation of star formation feedback and were run with high enough force and mass resolution to directly resolve stellar and dark matter structure on the ~200 pc scales of interest for classical and ultra-faint dwarfs in the Local Group. The resultant galaxies sit on the $M_*$ vs. $M_{v}$ relation required to match the Local Group stellar mass function. They have bursty star formation histories and also form with half-light radii and metallicities that broadly match those observed for local dwarfs at the same stellar mass. We demonstrate that it is possible to create a large (~1 kpc) dark matter core in a cosmological simulation of an $M_*\simeq10^{6.5}M_{\odot}$ dwarf galaxy that resides within an $M_{v}=10^{10}M_{\odot}$ halo -- precisely the scale of interest for resolving the Too Big to Fail problem. However, these large cores are not ubiquitous and appear to correlate closely with the star formation histories of the dwarfs: dark matter cores are largest in systems that form their stars late ($z\lesssim2$), after the early epoch of cusp building mergers has ended. Our $M_*\simeq10^4M_{\odot}$ dwarf retains a cuspy dark matter halo density profile that matches almost identically that of a dark-matter only run of the same system. Despite forming in a field environment, this very low mass dwarf has observable properties that match closely to those of ultra-faint satellite galaxies of the Milky Way, including a uniformly old stellar population (>10 Gyr). Though ancient, most of the stars in our ultra-faint form after reionization; the UV field acts mainly to suppress fresh gas accretion, not to boil away gas that is already present in the proto-dwarf.