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

Abstract

We analyze four epochs of Hubble Space Telescope imaging over 18 yr for the Draco dwarf spheroidal galaxy. We measure precise proper motions 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 $\bar{{\beta }_{{\rm{B}}}}=-{0.20}_{-0.53}^{+0.28}$ , (where 1 – ${\beta }_{{\rm{B}}}\equiv \langle {v}_{\tan }^{2}\rangle /\langle {v}_{\mathrm{rad}}^{2}\rangle $ in 3D). The logarithmic dark matter (DM) density slope over the observed radial range, Γ _dark , is $-{0.83}_{-0.37}^{+0.32}$ , consistent with the inner cusp predicted in ΛCDM 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, and 942 pc at 1 σ , 2 σ , and 3 σ confidence, respectively, 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 ${24.19}_{-2.97}^{+6.31}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ . We infer a dynamical distance of ${75.37}_{-4.00}^{+4.73}$ kpc and show that Draco has a modest LOS rotation, with $\left\langle v/\sigma \right\rangle =0.22\pm 0.09$ . Our results provide a new stringent test of the so-called “cusp–core” problem that can be readily extended to other dwarfs.

Keywords

• Dark matter
• Dwarf spheroidal galaxies
• Astronomy data analysis
• Proper motions
• Stellar kinematics
• Stellar dynamics