HSTPROMO Internal Proper Motion Kinematics of Dwarf Spheroidal Galaxies: I. Velocity Anisotropy and Dark Matter Cusp Slope of Draco

TL;DR

This study uses multi-epoch HST data to measure 3D stellar kinematics in Draco, constraining its dark matter density profile and velocity anisotropy, and providing insights into the cusp-core problem in dwarf galaxies.

Contribution

First radially-resolved 3D velocity dispersion profiles for a dwarf galaxy, resolving the mass-anisotropy degeneracy and constraining dark matter cusp slope.

Findings

Dark matter density slope consistent with ΛCDM cusp prediction.

Rules out large cores, constraining self-interacting dark matter models.

Reveals velocity anisotropy varies with radius, affecting mass estimates.

Abstract

We analyze four epochs of HST imaging over 18 years for the Draco dwarf spheroidal galaxy. We measure precise proper motions (PMs) for hundreds of stars and combine these with existing line-of-sight (LOS) velocities. This provides the first radially-resolved 3D velocity dispersion profiles for any dwarf galaxy. These constrain the intrinsic velocity anisotropy and resolve the mass-anisotropy degeneracy. We solve the Jeans equations in oblate axisymmetric geometry to infer the mass profile. We find the velocity dispersion to be radially anisotropic along the symmetry axis and tangentially anisotropic in the equatorial plane, with a globally-averaged value $\overline{\beta_{\mathrm B}}=-0.20^{+ 0.28}_{- 0.53}$, (where $1 - \beta_{\mathrm B} \equiv \langle v_{\mathrm{ tan}}^2 \rangle / \langle v_{\mathrm{ rad}}^2 \rangle$ in 3D). The logarithmic dark matter (DM) density slope over the observed radial range, $\Gamma_{\mathrm{ dark}}$, is $-0.83^{+ 0.32}_{- 0.37}$, consistent with the inner cusp predicted in $\Lambda$CDM cosmology. As expected given Draco's low mass and ancient star formation history, it does not appear to have been dissolved by baryonic processes. We rule out cores larger than 487, 717, 942 pc at respective 1-, 2-, 3-$\sigma$ confidence, thus imposing important constraints on the self-interacting DM cross-section. Spherical models yield biased estimates for both the velocity anisotropy and the inferred slope. The circular velocity at our outermost data point (900 pc) is $24.19^{+ 6.31}_{- 2.97} \ \mathrm{km~s^{-1}}s$. We infer a dynamical distance of $75.37^{+ 4.73}_{- 4.00}$ kpc, and show that Draco has a modest LOS rotation, with $\left<v / \sigma \right> = 0.22 \pm 0.09$. Our results provide a new stringent test of the so-called `cusp-core' problem that can be readily extended to other dwarfs.