Constraining the Milky Way potential with a 6-D phase-space map of the GD-1 stellar stream

The narrow GD-1 stream of stars, spanning 60 deg on the sky at a distance of ~10 kpc from the Sun and ~15 kpc from the Galactic center, is presumed to be debris from a tidally disrupted star cluster that traces out a test-particle orbit in the Milky Way halo. We combine SDSS photometry, USNO-B astrometry, and SDSS and Calar Alto spectroscopy to construct a complete, empirical 6-dimensional phase-space map of the stream. We find that an eccentric orbit in a flattened isothermal potential describes this phase-space map well. Even after marginalizing over the stream orbital parameters and the distance from the Sun to the Galactic center, the orbital fit to GD-1 places strong constraints on the circular velocity at the Sun's radius V_c=224 \pm 13 km/s and total potential flattening q_\Phi=0.87^{+0.07}_{-0.04}. When we drop any informative priors on V_c the GD-1 constraint becomes V_c=221 \pm 18 km/s. Our 6-D map of GD-1 therefore yields the best current constraint on V_c and the only strong constraint on q_\Phi at Galactocentric radii near R~15 kpc. Much, if not all, of the total potential flattening may be attributed to the mass in the stellar disk, so the GD-1 constraints on the flattening of the halo itself are weak: q_{\Phi,halo}>0.89 at 90% confidence. The greatest uncertainty in the 6-D map and the orbital analysis stems from the photometric distances, which will be obviated by Gaia.