Sweating the small stuff: solving small-scale challenges to $\Lambda$CDM with dwarf galaxy simulations at the high resolution limit

The currently favored cosmological paradigm — Lambda Cold Dark Matter Theory ($\Lambda$CDM) — has been widely successful in predicting the counts, clustering, colors, morphologies, and evolution of galaxies on large scales, as well as a variety of cosmological observables. Despite these successes, several challenges have arisen to this model in recent years, most of them occurring at the smallest scales — those of dwarf galaxies ($M_{\rm \star} < 10^9 M_{\odot}$), of which the lowest mass are observed almost exclusively within the Local Volume. I will review several of these small-scale challenges, including the Missing Satellites Problem, the Cusp-Core Controversy, and the tension between the regularity of galactic scaling relations and the diversity of rotation curves. In reviewing current attempts to rectify these issues — many of which rely on the inclusion of baryonic effects in simulations — I will introduce a new set of high resolution cosmological hydrodynamic zoom-in simulations (GIZMO/FIRE2) of isolated dwarf galaxies — the highest resolution ever run to z=0. This new generation of $m_{\rm bar} \sim 10 M_{\odot}$ simulations marks a transition point between simulations that treat star formation within a single stellar population in the aggregate, and simulations that model the individual collapse and fragmentation of a molecular clouds into individual stars, and will allow us to probe smaller physical scales than previously possible in a cosmological simulation.