Scaling Relationships between the Dark Matter Halo and Optical Parameters of Milky Way Dwarf Spheroidal Galaxies

Based on surface brightness (SB) data, velocity dispersion data, Jeans analysis, and constraints from virial shape parameters, we determine the best-fit cored (Burkert) and cuspy (NFW) dark matter (DM) density profiles for 10 Milky Way dwarf spheroidal galaxies (dSphs). Using likelihood analysis, we determine if each dSph is better fit by a DM core or cusp and if the cuspiness of the DM halo is correlated with the cuspiness of the baryonic matter density, as constrained via SB data. We also show that there are strong correlations between the optical half-light radii of the dSphs and the scale radii and scale densities of their best-fit DM halos. If these relationships hold beyond this small sample, it could enable astronomers to estimate the properties of a galaxy's dark matter halo simply by measuring its half-light radius.