Measuring Dark Matter Profiles Non-Parametrically in Dwarf Spheroidals: An Application to Draco

We introduce a novel implementation of orbit-based (or Schwarzschild) modeling that allows dark matter density profiles to be calculated non-parametrically in nearby galaxies. Our models require no assumptions to be made about velocity anisotropy or the dark matter profile. The technique can be applied to any dispersion-supported stellar system, and we demonstrate its use by studying the Local Group dwarf spheroidal (dSph) galaxy Draco. We use existing kinematic data at larger radii and also present 12 new radial velocities within the central 13 pc obtained with the VIRUS-W integral field spectrograph on the 2.7m telescope at McDonald Observatory. Our non-parametric Schwarzschild models find strong evidence that the dark matter profile in Draco is cuspy for 20 < r < 700 pc. The profile for r > 20 pc is well-fit by a power law with slope \alpha=-1.0 +/- 0.2, consistent with predictions from Cold Dark Matter (CDM) simulations. Our models confirm that, despite its low baryon content relative to other dSphs, Draco lives in a massive halo.