A Universal Mass Profile for Dwarf Spheroidal Galaxies?
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 modelindependent constraint on the maximum circular velocity, V _{max} = 20^{+4} _{3} km s^{1}. Although we obtain only lower limits of V _{max} >~ 10 km s^{1} for the remaining dSphs, we find that in all cases the enclosed mass at the projected halflight 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}) vprop r ^{1.4±0.4} _{half}, or in terms of the mean density interior to the halflight radius, langρrang vprop 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 halflight 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 lsim2 in normalization (V _{max} ~ 1020 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 vprop r ^{1.4}, viable candidates include a cuspy "NavarroFrenkWhite" halo with V _{max} ~ 15 km s^{1} and scale radius r _{0} ~ 800 pc, as well as a cored halo with V _{max} ~ 13 km s^{1} 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 langρrang <~ 5 M _{sun} pc^{3} (lsim200 GeV cm^{3}).
This paper presents data gathered with the Magellan Telescopes at Las Campanas Observatory, Chile, and the MMT Observatory at Mt. Hopkins, AZ, USA.
 Publication:

The Astrophysical Journal
 Pub Date:
 October 2009
 DOI:
 10.1088/0004637X/704/2/1274
 arXiv:
 arXiv:0906.0341
 Bibcode:
 2009ApJ...704.1274W
 Keywords:

 galaxies: dwarf;
 galaxies: kinematics and dynamics;
 Local Group;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 Astrophysics  Galaxy Astrophysics
 EPrint:
 Replacement provides corrections to values of halflight radii adopted for eight classical dSphs, including revised tables and figures (conclusions are unchanged). Erratum submitted to ApJ and posted at http://www.ast.cam.ac.uk/~walker/erratum.pdf