The Cold Dark Matter Halos of Local Group Dwarf Spheroidals

We examine the dynamics of stellar systems embedded within cold dark matter (CDM) halos in order to assess observational constraints on the dark matter content of Local Group dwarf spheroidals (dSphs). Our analysis shows that the total mass within the luminous radius is reasonably well constrained and approximately independent of the luminosity of the dwarf, highlighting the poor correspondence between luminosity and halo mass. This result implies that the average density of dark matter is substantially higher in physically small systems such as Draco and Sculptor than in larger systems such as Fornax. For example, our results imply that Draco formed in a halo 5 times more massive than Fornax's despite being roughly 70 times fainter. Stellar velocity dispersion profiles, sigmaₚ (R), provide further constraints; flat sigmaₚ (R) profiles imply that stars are deeply embedded within their cold dark matter halos and so quite resilient to tidal disruption. We estimate that halos would need to lose more than 90% of their original mass before tides begin affecting the kinematics of stars. We estimate that Vₘax is about 3 times higher than the central velocity dispersion of the stars, which alleviates significantly the CDM ``substructure crisis''. We use these results to interpret the size differences between the M31 and Milky Way (MW) dSph population. Our modeling indicates that this difference should be reflected in their kinematics, and predicts that M31 dwarfs should have velocity dispersions up to a factor of ~ 2 higher than their MW counterparts. This CDM-motivated prediction may be verified with present observational capabilities.