1 research outputs found
Estimating Dark Matter Distributions
Thanks to instrumental advances, new, very large kinematic datasets for
nearby dwarf spheroidal (dSph) galaxies are on the horizon. A key aim of these
datasets is to help determine the distribution of dark matter in these
galaxies. Past analyses have generally relied on specific dynamical models or
highly restrictive dynamical assumptions. We describe a new, non-parametric
analysis of the kinematics of nearby dSph galaxies designed to take full
advantage of the future large datasets. 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, nor the assumption that the
mass distribution follows that of the visible matter. The problem of estimating
the radial mass distribution, M(r) (the mass interior to true radius r), is
converted into a problem of estimating a regression function
non-parametrically. 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 two 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 ten times more massive than its
baryonic component. Though 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.Comment: Accepted for publication in The Astrophysical Journa