Resolving the mass-anisotropy degeneracy of the spherically symmetric jeans equation - II. Optimum smoothing and model validation

Abstract

The spherical Jeans equation iswidely used to estimate the mass content of stellar systems with apparent spherical symmetry. However, this method suffers from a degeneracy between the assumed mass density and the kinematic anisotropy profile, β(r). In a previous work, we laid the theoretical foundations for an algorithm that combines smoothing B splines with equations from dynamics to remove this degeneracy. Specifically, our method reconstructs a unique kinematic profile of σ2rr and σ2tt for an assumed free functional form of the potential and mass density (Φ, ρ) and given a set of observed line-of-sight velocity dispersion measurements, σ2los. In Paper I, we demonstrated the efficiency of our algorithm with a very simple example and we commented on the need for optimum smoothing of the B-spline representation; this is in order to avoid unphysical variational behaviour when we have large uncertainty in our data. In the current contribution, we present a process of finding the optimum smoothing for a given data set by using information of the behaviour from known ideal theoretical models. Markov Chain Monte Carlo methods are used to explore the degeneracy in the dynamical modelling process. We validate our model through applications to synthetic data for systems with constant or variable mass-to-light ratio Υ. In all cases, we recover excellent fits of theoretical functions to observables and unique solutions. Our algorithm is a robust method for the removal of the mass-anisotropy degeneracy of the spherically symmetric Jeans equation for an assumed functional form of the mass density. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.