Action-based Dynamical Modelling for the Milky Way Disk

Abstract

We present RoadMapping, a full-likelihood dynamical modelling machinery that aims to recover the Milky Way's (MW) gravitational potential from large samples of stars in the Galactic disk. RoadMapping models the observed positions and velocities of stars with a parametrized, three-integral distribution function (DF) in a parametrized axisymmetric potential. We investigate through differential test cases with idealized mock data how the breakdown of model assumptions and data properties affect constraints on the potential and DF. Our key results are: (i) If the MW's true potential is not included in the assumed model potential family, we can - in the axisymmetric case - still find a robust estimate for the potential, with only <~ 10% difference in surface density within |z| <= 1.1 kpc inside the observed volume. (ii) Modest systematic differences between the true and model DF are inconsequential. E.g, when binning stars to define sub-populations with simple DFs, binning errors do not affect the modelling as long as the DF parameters of neighbouring bins differ by < 20%. In addition, RoadMapping ensures unbiased potential estimates for either (iii) small misjudgements of the spatial selection function (i.e., <~ 15% at the survey volume's edge), (iv) if distances are known to within 10%, or (v) if proper motion uncertainties are known within 10% or are smaller than delta mu <~ 1 mas/yr. Challenges are the rapidly increasing computational costs for large sample sizes. Overall, RoadMapping is well suited to making precise new measurements of the MW's potential with data from the upcoming Gaia releases.