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 full 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 true
values of the potential parameters. The precision depends on the observational
errors and the number of streams in the sample; using KIII 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%,
and is 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).
About 15 streams, with at least 100 stars per stream, are needed to obtain
upper and lower bounds on the enclosed mass and scale radius when observational
errors are taken into account; 20-25 streams are required to stabilize the size
of the confidence interval. If radial velocities are provided for stars out to
100 kpc (10 scale radii), all parameters can be determined with 10% accuracy
and 20% precision (1.3% accuracy in the case of the enclosed mass), underlining
the need for ground-based spectroscopic follow-up to complete the radial
velocity catalog for faint halo stars observed by Gaia.
