The velocity dispersion and mass profile of the Milky Way

We re-analyse the velocity-dispersion profile σ(r) at radii r > 10 kpc in the Galactic stellar halo, recently derived by Battaglia et al., who concluded that, for a constant velocity anisotropy of the tracers, these data rule out a flat circular-speed curve for the Milky Way. However, we demonstrate that if one makes the natural assumption that the tracer density is truncated at rt≳ 160 kpc and falls off significantly more steeply than r−3.5 at r≳ 80 kpc, then these data are consistent with a flat circular-speed curve and a constant velocity anisotropy comparable to that observed for halo stars in the solar neighbourhood. We also consider a more detailed mass model with an exponential stellar disc and an extended non-isothermal dark-matter halo. In this two-component model, the Milky Way's virial radius and mass are rvir≃ 200 kpc and Mvir≃ 1.5 × 1012 M⊙. Still assuming the tracers' velocity anisotropy to be constant (at β≃ 0.5), we again find good agreement with the observed σ(r), so long as the tracer density is truncated near the virial radius. These data by themselves do not allow to differentiate either between different dark-halo or total-mass models for the Milky Way, nor between different velocity-anisotropy profiles for the tracers.