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

Abstract

We present a new framework for estimating a galaxy's gravitational potential, φ, from its stellar kinematics by adopting a fully non-parametric model for the galaxy's unknown actionspace distribution function, f ( J). Having an expression for the joint likelihood of φ and f, the likelihood of φ is calculated by using a Dirichlet process mixture to represent the prior on f and marginalizing. 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 generalize the machinery to account for realistic observational errors and selection functions. A practical implementation is likely to raise some interesting algorithmic and computational challenges. © 2013 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.