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 in the streams , but does not require identification of any specific stream , nor determination of stream membership for any star .
We exploit the principle that the action distribution of stream stars is most clustered—that is , most informative—when the potential used to calculate the actions is closest to the true potential .
We measure the amount of clustering with the Kullback-Leibler Divergence ( KLD ) or relative entropy , a statistical measure of information 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 and type of streams in the sample ; we find that with the phase-space structure and observational uncertainties expected in the Gaia red-giant-star data set , 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 both 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 ) , the bias in the scale radius measurement is eliminated and all parameters can be determined with \sim 10 % accuracy and 20 % precision ( 1.3 % accuracy in the case of the enclosed mass ) .
This finding underlines the need for ground-based spectroscopic follow-up to complete the radial velocity catalog for faint halo stars ( V > 17 ) observed by Gaia .