Multi-component, axisymmetric dynamical models of dSphs based on distribution functions: inferences on dark matter and intermediate-mass black holes in Draco and Ursa Minor

Abstract

Dwarf spheroidal galaxies (dSphs) are prime laboratories for studying dark matter (DM) and the black hole demographics in the low-mass regime. These systems are also often flattened; nevertheless most studies rely on spherical models, potentially affecting dynamical inferences. We introduce the first multi-component, axisymmetric dynamical models of dSphs based on distribution functions and apply them to the Milky Way dSphs Draco and Ursa Minor. The stellar distribution is described by chemo-dynamically distinct axisymmetric populations tracing a spherical potential generated by a dominant DM halo and a central intermediate-mass BH (IMBH). The models are fitted to discrete stellar data from a Gaia-based astrometric sample and two spectroscopic datasets providing line-of-sight velocities and metallicities, testing robustness across samples. We compare the DM properties under different modelling assumptions, including flattened one- and spherical two-component models. Both galaxies are better described by two stellar populations: a metal-rich, kinematically colder and concentrated component, and a more extended metal-poor one with hotter kinematics. We detect weak rotation, dynamically unimportant and ignored in the models. We measure a cuspy DM density profile in Draco ($γ=0.98_{-0.26}^{+0.28}$), and a more cored distribution ($γ=0.37_{-0.24}^{+0.31}$) for Ursa Minor. The DM halo of Draco remains stable across all models and datasets, making it the most robustly determined in the Local Group and highly relevant for indirect DM searches. We show that modelling flattened systems with spherical models can bias the DM inner slope towards cuspier values, while we find no degeneracy between inner halo density and inclination. We find no evidence for IMBHs and place upper limits on their masses, $\log M_{\rm BH}[M_{\odot}] < 5.2$ for Draco and $< 3.33$ for Ursa Minor (95% confidence).