Estimating dark matter distributions

Thanks to instrumental advances, new, very large kinematic data sets for nearby dwarf spheroidal (dSph) galaxies are on the horizon. A key aim of these data sets is to help determine the distribution of dark matter in these galaxies. Past analyses have generally relied on specifie dynamical models or highly restrictive dynamical assumptions. We describe a new, nonparametric analysis of the kinematics of nearby dSph galaxies designed to take full advantage of the future large data sets. The method takes as input the projected positions and radial velocities of stars known to be members of the galaxies but does not use any parametric dynamical model or the assumption that the mass distribution follows that of the visible matter. The problem of estimating the radial mass distribution M(r) (the mass within the true radius r) is converted into a problem of estimating a regression function nonparametrically. From the Jeans equation we show that the unknown regression function is subject to fundamental shape restrictions, which we exploit in our analysis using statistical techniques borrowed from isotonic estimation and spline smoothing. Simulations indicate that M(r) can be estimated to within a factor of 2 or better with samples as small as 1000 stars over almost the entire radial range sampled by the kinematic data. The technique is applied to a sample of 181 stars in the Fornax dSph galaxy. We show that the galaxy contains a significant, extended dark halo some 10 times more massive than its baryonic component. Although applied here to dSph kinematics, this approach can be used in the analysis of any kinematically hot stellar system in which the radial velocity field is discretely sampled.