Measuring the dark matter scale of Local Group dwarf spheroidals

We reanalyze published Draco and Ursa Minor dwarf spheroidal (dSph) stellar velocity data. Previous studies of dSph stellar distributions have concent rated principally on the spatial distribution of stars or on computation of a global velocity dispersion. A detailed understanding of the spatial beha vior of the velocity distribution, however, is necessary to distinguish amo ng competing theories of dSph dynamics. Here we apply a maximum-likelihood technique to fit the set of individual v elocity measurements to a global distribution. Rather than calculating mean local velocity dispersions in regions where the data are sparse, this tech nique has the advantage of using the velocity measurements individually. We confirm earlier findings of a radial falloff in the velocity distribution of UMi, which is consistent with a mass-follows-light (MFL) King model. We also confirm an apparent radial rise in the velocity dispersion of Draco. H owever, these data do not suffice to distinguish among extended halo and MF L models. Finally, we perform simulations to determine the number of additi onal observations required to clearly differentiate between different dynam ical models. Only similar to 10-20 additional observations at 0.75 times th e tidal radius would be required to distinguish clearly between an MFL dist ribution and an extended halo or disrupted remnant model with a flat or rad ially rising velocity dispersion. We describe a method for treating the eff ect of binary stars, which may be a source of contamination.