Model-Independent Estimates of Dark Matter Distributions

Abstract

A new nonparametric method is described to estimate the distribution of mass within spherical galaxies. The problem of estimating the mass, M ( r ), within radius r is converted into a problem of estimating a regression function nonparametrically, subject to shape restrictions. We represent the restrictions by the interception of quadratic cones and use the second-order cone programming to estimate the unknown parameters. We establish asymptotic results that are used to construct confidence intervals on M ( r ). We apply the technique to new kinematic data for four dwarf galaxies. Results indicate that dark matter dominates the stellar kinematics of these systems at all radii.