Breaking beta: A comparison of mass modelling methods for spherical systems

Abstract

We apply four different mass modelling methods to a suite of publicly available mock data for spherical stellar systems. We focus on the recovery of the density and velocity anisotropy as a function of radius, either using line-of-sight velocity data only or adding proper motion data. All methods perform well on isotropic and tangentially anisotropic mock data, recovering the density and velocity anisotropy within their 95 per cent confidence intervals over the radial range 0.25 < 4, where R1/2 is the half-light radius. However, radially anisotropic mocks are more challenging. For line-of-sight data alone, only methods that use information about the shape of the velocity distribution function are able to break the degeneracy between the density profile and the velocity anisotropy, β, to obtain an unbiased estimate of both. This shape information can be obtained through directly fitting a global phase-space distribution function, by using higher order 'virial shape parameters' or by assuming a Gaussian velocity distribution function locally, but projecting it self-consistently along the line of sight. Including proper motion data yields further improvements, and in this case, all methods give a good recovery of both the radial density and velocity anisotropy profiles.