The mass distribution of dwarf spheroidal galaxies from stellar kinematics: Draco, Ursa Minor and Fornax

Abstract

We model three dSph galaxies, Draco, Ursa Minor and Fornax, as axisymmetric stellar systems embedded in spherical dark-matter potentials, which are in dynamical equilibrium without significant external tidal forces. We construct non-parametric two- and three-integral models that match the observed surface-density profiles and the current kinematic samples of $\sim150-200$ stars per galaxy; these models naturally produce the so-called ``extra-tidal extensions", which had previously been suggested as evidence of tidal stripping. Isochrone, NFW and power-law models fit the data, but we strongly rule out any centrally condensed mass distribution like a dominant central black hole, as well as constant-density and (for Draco and Fornax) constant mass-to-light ratio models. The average V-band mass-to-light ratio is $400\pm80$ \ml within 0.75 kpc for Draco, $580^{+140}_{-100}$ \ml within 1.1 kpc for Ursa Minor and $25^{+7}_{-5}$ \ml within 2.5 kpc for Fornax. Two-integral models fit the data almost as well as three-integral models; in contrast to previous suggestions we do not find that anisotropy contributes substantially to the high mass-to-light ratios in these dSph galaxies.