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

TL;DR

This paper develops action-based models for the Milky Way's stellar halo, constraining the galaxy's mass distribution and anisotropy profile using SDSS data, revealing a gradually increasing radial anisotropy and a nearly flat rotation curve.

Contribution

The authors introduce a flexible action-based distribution function for stellar haloes and apply it to SDSS data to derive the Galaxy's mass profile and velocity anisotropy.

Findings

Velocity anisotropy increases from 0.4 to 0.7 between 15 and 60 kpc.

Galaxy's rotation curve is nearly flat at ~200 km/s.

Enclosed mass within 50 kpc is approximately 4.5 x 10^11 solar masses.

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 distribution function 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 fit model has a velocity anisotropy that becomes more radially anisotropic on moving outwards. It changes from $\beta \approx 0.4$ at Galactocentric radius of 15 kpc to $\approx 0.7$ at 60 kpc. This is a gentler increase than is typically found in simulations of stellar haloes built from the mutiple accretion of smaller systems. We find the potential corresponds to an almost flat rotation curve with amplitude of $\approx 200$ kms$^{-1}$ at these distances. This implies an enclosed mass of $\approx 4.5 \times 10^{11} M_\odot$ within a spherical shell of radius 50 kpc.