Action-space Clustering of Tidal Streams to Infer the Galactic Potential

We present a new method for constraining the Milky Way halo gravitational potential by simultaneously fitting multiple tidal streams. This method requires three-dimensional positions and velocities for all stars to be fit, but does not require identification of any specific stream or determination of stream membership for any star. We exploit the principle that the action distribution of stream stars is most clustered when the potential used to calculate the actions is closest to the true potential. Clustering is quantified with the Kullback-Leibler Divergence (KLD), which also provides conditional uncertainties for our parameter estimates. We show, for toy Gaia-like data in a spherical isochrone potential, that maximizing the KLD of the action distribution relative to a smoother distribution recovers the input potential. The precision depends on the observational errors and number of streams; using K III giants as tracers, we measure the enclosed mass at the average radius of the sample stars accurate to 3% and precise to 20%-40%. Recovery of the scale radius is precise to 25%, biased 50% high by the small galactocentric distance range of stars in our mock sample (1-25 kpc, or about three scale radii, with mean 6.5 kpc). 20-25 streams with at least 100 stars each are required for a stable confidence interval. With radial velocities (RVs) to 100 kpc, all parameters are determined with ~10% accuracy and 20% precision (1.3% accuracy for the enclosed mass), underlining the need to complete the RV catalog for faint halo stars observed by Gaia.