Constraining the Galactic potential via action-based distribution functions for mono-abundance stellar populations

We present a rigorous and practical way of constraining the Galactic potential based on the phase-space information for many individual stars. Such an approach is needed to dynamically model the data from ongoing spectroscopic surveys of the Galaxy and in the future Gaia. This approach describes the orbit distribution of stars by a family of parametrized distribution function (DF) proposed by McMillan and Binney, which are based on actions. We find that these parametrized DFs are flexible enough to capture well the observed phase-space distributions of individual abundance-selected Galactic subpopulations of stars ('mono-abundance populations') for a disc-like gravitational potential, which enables independent dynamical constraints from each of the Galactic mono-abundance populations. We lay out a statistically rigorous way to constrain the Galactic potential parameters by constructing the joint likelihood of potential and DF parameters, and subsequently marginalizing over the DF parameters. This approach explicitly incorporates the spatial selection function inherent to all Galactic surveys, and can account for the uncertainties of the individual position-velocity observations. On that basis, we study the precision of the parameters of the Galactic potential that can be reached with various sample sizes and realistic spatial selection functions. By creating mock samples from the DF, we show that, even under a restrictive and realistic spatial selection function, given a two-parameter gravitational potential, one can recover the true potential parameters to a few per cent with sample sizes of a few thousands. The assumptions of axisymmetry, of DFs that are smooth in the actions and of no time variation remain important limitations in our current study.