Dark Matter in Draco and Boötes I: Hints of a Core in an Ultra-Faint Dwarf from Simulation-Based Inference

Abstract

The density profiles of dwarf spheroidal galaxies are among the most sensitive probes of dark matter physics, yet extracting them from noisy stellar kinematics remains a fundamental obstacle. We present GraphNPE, a simulation-based inference method for dynamical mass modeling that incorporates measurement uncertainties and spectroscopic selection functions in the forward model. Using mock data, we show that methods relying solely on line-of-sight velocity dispersion are biased toward cuspy density profiles, even in the absence of the mass-anisotropy degeneracy. By accessing higher-order velocity moments, particularly line-of-sight kurtosis, GraphNPE breaks key degeneracies and recovers density profiles with substantially less bias. We apply GraphNPE to Draco and Boötes I using MMT/Hectochelle and DESI for Draco, and the S5 survey for Boötes I. For each, we report density profiles and dark matter $J$- and $D$-factors. For Draco, GraphNPE yields consistent results across datasets, marginally preferring a cuspy inner profile ($ρ_{150} \sim 1.6-1.9 \times 10^8\,\mathrm{M}_\odot\,\mathrm{kpc}^{-3}$) in agreement with literature. On DESI, however, second-order Jeans modeling fits the dispersion but fails to reproduce the kurtosis, demonstrating higher-order moments are essential. For Boötes I, limited statistical power prevents definitive determination of the inner slope. GraphNPE recovers $ρ_{150} = 0.36^{+0.15}_{-0.11} \times 10^8\,\mathrm{M}_\odot\,\mathrm{kpc}^{-3}$, significantly lower than literature and consistent with a cored inner profile. This places Boötes I among the lowest density dwarfs at comparable stellar masses.