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

TL;DR

This study compares four mass modelling methods on mock data of spherical stellar systems, highlighting the importance of velocity distribution shape information and proper motion data for accurate density and anisotropy recovery.

Contribution

It systematically evaluates the performance of different mass modelling techniques, emphasizing the role of velocity distribution shape information and proper motions in breaking degeneracies.

Findings

Methods recover density and anisotropy within 95% confidence for isotropic/tangential mocks.

Shape information is crucial for unbiased estimates in radially-anisotropic cases.

Proper motion data significantly improves recovery accuracy.

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, using either 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% confidence intervals over the radial range 0.25 < R/Rhalf < 4, where Rhalf 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 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.