### 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±0.4 half , or in terms of the mean density interior to the half-light radius, ρ 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 (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).

Original language | English (US) |
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Pages (from-to) | 1274-1287 |

Number of pages | 14 |

Journal | Astrophysical Journal |

Volume | 704 |

Issue number | 2 |

DOIs | |

State | Published - Oct 20 2009 |

### Keywords

- Dwarf
- Galaxies
- Galaxies
- Kinematics and dynamics
- Local Group

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astrophysical Journal*,

*704*(2), 1274-1287. https://doi.org/10.1088/0004-637X/704/2/1274