Semi-analytic Inference of Satellite Densities in the Cold Dark Matter Model Part I. Comparison to Ultra-faint Dwarf Kinematics

Ultra-faint dwarf galaxies are critical testing grounds for probing the limits of galaxy formation in the cold dark matter (CDM) paradigm. Employing a semi-analytic cosmological satellite generator that captures the expected CDM halo population, we estimate Milky Way dwarf density profiles through two methods: a kinematic approach using stellar velocity dispersions and a separate method based on dwarf stellar masses. The kinematic approach yields a larger diversity in central dark matter densities than expected from the CDM population, as inferred from the stellar-to-halo mass relation, with compact ultra-faints appearing overdense and larger systems appearing underdense. For the ultra-faint dwarfs with at least 10 stars with spectroscopic measurements, this discrepancy persists at the 2.4 sigma level across all considered systematic variations on the semi-analytic modeling. Our framework introduces a novel, robust procedure for testing the consistency of the observed population of Milky Way satellites with cosmological expectations. As future surveys discover new dwarf satellites and refine stellar velocity measurements, updating this analysis will provide an increasingly stringent test of the CDM paradigm.