http://arxiv.org/abs/1404.6534
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 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 a factor two. Recovery of the scale radius is also precise to roughly a factor two, 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). About 15 streams with at least 100 stars, including 2-3 large streams, are needed to place limits on the enclosed mass; about 40 are required to obtain bounds on the scale radius, primarily to get sufficient distance range. This finding underlines the need for ground-based spectroscopic follow-up to complete the radial velocity catalog for faint stars ($V>17$) observed by Gaia.
R. Sanderson, A. Helmi and D. Hogg
Tue, 29 Apr 14
32/69
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