Chemo-dynamics of the stellar component of the Sculptor dwarf galaxy: II. Dynamical properties and dark matter halo density

Dwarf galaxy satellites of the Milky Way are excellent laboratories for testing dark matter (DM) models and baryonic feedback implementation in simulations. The Sculptor "classical" dwarf spheroidal galaxy, a system with two distinct stellar populations and high-quality data, offers a remarkable opportunity to study DM distributions in these galaxies. However, inferences from dynamical modeling in the literature have led to discrepant results. In this work, we infer the DM halo density distribution of Sculptor, applying a method based on spherically symmetric distribution functions depending on actions to fit the stellar structural and kinematic properties of Sculptor. The galaxy is represented via four components: two distinct stellar populations based on distribution functions, tracers within a fixed and dominant DM potential, and the contribution of a third stellar component that accounts for possible sources of contamination. The model-data comparison accounts for the kinematics and metallicities of individual stars rather than relying on binned profiles, allowing us to assign probabilities of membership to each star. This is the most general approach employed to date to model Sculptor, and we applied it on the largest available set of spectroscopic data, which have not been previously analyzed with this objective. We find the DM distribution of Sculptor to have a logarithmic inner slope of γ = 0.39- 0.26+0.23 and a scale radius of rs = 0.79- 0.17+0.38kpc at a 1Ï confidence level. Our results show that the Sculptor DM density profile deviates from predictions of DM-only simulations at a 3Ï level over a large range of radii. The dynamical-to-luminous mass ratio is around 13 at the 3D half-light radius and 154 at 2 kpc, the outermost radius with observed stars in our dataset. Our analysis suggests that the velocity distribution of Sculptor's two main stellar components is isotropic in the center and becomes radially anisotropic in the outskirts. Additionally, we provide predictions for the projected radial and tangential velocity dispersion profiles. We also present updated DM annihilation and decay J and D-factors, for which we find J = 18.15- 0.12+0.11 and D = 18.07- 0.10+0.10 for an angular aperture of 0.5 degrees.