Bayes versus the virial theorem: inferring the potential of a galaxy from a kinematical snapshot

TL;DR

This paper introduces a non-parametric Bayesian framework for inferring a galaxy's gravitational potential from stellar kinematics, outperforming traditional methods in complex scenarios and adaptable to observational errors.

Contribution

It develops a novel non-parametric Bayesian approach using Dirichlet process mixtures to estimate galaxy potentials from kinematic data, improving over existing methods.

Findings

Successfully recovers potentials of simple systems from perfect data

Outperforms traditional moment-based methods like the virial theorem in complex cases

Framework adaptable to observational errors and selection effects

Abstract

We present a new framework for estimating a galaxy's gravitational potential, Phi(x), from its stellar kinematics by adopting a fully non-parametric model for the galaxy's unknown action-space distribution function, f(J). Having an expression for the joint likelihood of Phi and f, the likelihood of Phi is calculated by using a Dirichlet process mixture to represent the prior on f and marginalising. We demonstrate that modelling machinery constructed using this framework is successful at recovering the potentials of some simple systems from perfect discrete kinematical data, a situation handled effortlessly by traditional moment-based methods, such as the virial theorem, but in which other, more modern, methods are less than satisfactory. We show how to generalise the machinery to account for realistic observational errors and selection functions. A practical implementation is likely to raise some interesting algorithmic and computational challenges.