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.
