Filling in the Blanks: A Method to Infer the Substructure Membership and Dynamics of 5D Stars

We present and test a method to infer a probability density function (PDF) for the missing vlos of a star with 5D information within 2.5 kpc. We use stars from the Gaia DR3 RVS catalogue to describe the local orbital structure in action space. This technique also allows us to infer the probability that a 5D star is associated with the Milky Way's stellar Disc or the stellar Halo, which can be further decomposed into known stellar substructures. The method is tested on a 6D Gaia DR3 RVS sample and a 6D Gaia sample crossmatched to groundbased spectroscopic surveys, stripped of their true vlos. The stars predicted vlos, membership probabilities, and inferred structure properties are then compared to the true 6D equivalents, allowing the method's accuracy and limitations to be studied in detail. Our predicted vlos PDFs are statistically consistent with the true vlos, with accurate uncertainties. We find that the vlos of Disc stars can be well constrained, with a median uncertainty of 26 kms. Halo stars are typically less well constrained with a median uncertainty of 72 kms, but those found likely to belong to Halo substructures can be better constrained. The dynamical properties of the total sample and subgroups, such as distributions of integrals of motion and velocities, are also accurately recovered. The group membership probabilities are statistically consistent with our initial labelling, allowing high quality sets to be selected from 5D samples by choosing a trade off between higher expected purity and decreasing expected completeness.