2009ApJ...704.1274W

We apply the Jeans equation to estimate masses for eight of the brightest dwarf spheroidal (dSph) galaxies. For Fornax, the dSph with the largest kinematic data set, we obtain a model-independent constraint on the maximum circular velocity, V_max= 20⁺⁴_–3 km/s. Although we obtain only lower limits of V_max≳ 10 km/s for the remaining dSphs, we find that in all cases the enclosed mass at the projected half-light radius is well constrained and robust to a wide range of halo models and velocity anisotropies. We derive a simple analytic formula that estimates M(r_half) accurately with respect to results from the full Jeans analysis. Applying this formula to the entire population of Local Group dSphs with published kinematic data, we demonstrate a correlation such that M(r_half) ∝ r ^1.4±0.4_half, or in terms of the mean density interior to the half-light radius, #961; ∝ r^–1.6±0.4_half. This relation is driven by the fact that the dSph data exhibit a correlation between global velocity dispersion and half-light radius. We argue that tidal forces are unlikely to have introduced this relation, but tides may have increased the scatter and/or altered the slope. While the data are well described by mass profiles ranging over a factor of ≲2 in normalization (V_max∼ 10-20 km/s), we consider the hypothesis that all dSphs are embedded within a "universal" dark matter halo. We show that in addition to the power law M ∝ r ^1.4, viable candidates include a cuspy "Navarro-Frenk-White" halo with V_max∼ 15 km/s and scale radius r₀∼ 800 pc, as well as a cored halo with V_max∼ 13 km/s and r ₀∼ 150 pc. Finally, assuming that their measured velocity dispersions accurately reflect their masses, the smallest dSphs now allow us to resolve dSph densities at radii as small as a few tens of pc. At these small scales, we find mean densities as large as #961; ≲ 5 M_☉/pc3 (≲200 GeV/cm3).