Haloes light and dark: Dynamical models of the stellar halo and constraints on the mass of the Galaxy

Abstract

We develop a flexible set of action-based distribution functions (DFs) for stellar haloes. The DFs have five free parameters, controlling the inner and outer density slope, break radius, flattening, and anisotropy, respectively. The DFs generate flattened stellar haloes with a rapidly varying logarithmic slope in density, as well as a spherically aligned velocity ellipsoid with a long axis that points towards the Galactic Centre - all attributes possessed by the stellar halo of the Milky Way. We use our action-based DF to model the blue horizontal branch stars extracted from the Sloan Digital Sky Survey as stellar halo tracers in a spherical Galactic potential. As the selection function is hard to model, we fix the density law from earlier studies and solve for the anisotropy and gravitational potential parameters. Our best-fitting model has a velocity anisotropy that becomes more radially anisotropic on moving outwards. It changes from β ≈0.4 at Galactocentric radius of 15 kpc to≈0.7 at 60 kpc. This is a gentler increase than is typically found in simulations of stellar haloes built from the multiple accretion of smaller systems. We find the potential corresponds to an almost flat rotation curve with amplitude of ≈200 km s-1 at these distances. This implies an enclosed mass of ≈4.5 × 1011M⊙ within a spherical shell of radius 50 kpc.