Abstract

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, Vmax = 20+4−3 km s−1. Although we obtain only lower limits of Vmax ≳ 10 km s−1 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(rhalf) 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(rhalf) ∝ r1.4±0.4half, or in terms of the mean density interior to the half-light radius, 〈ρ〉 ∝ r−1.6±0.4half. 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 (Vmax ∼ 10–20 km s−1), 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 ∝ r1.4, viable candidates include a cuspy "Navarro–Frenk–White" halo with Vmax ∼ 15 km s−1 and scale radius r0 ∼ 800 pc, as well as a cored halo with Vmax ∼ 13 km s−1 and r0 ∼ 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 〈ρ〉 ≲ 5 M☉ pc−3 (≲200 GeV cm−3).