The Velocity Anisotropy of Distant Milky Way Halo Stars from Hubble
  Space Telescope Proper Motions
  Based on long baseline (5-7 years) multi-epoch HST/ACS photometry, used
previously to measure the proper motion of M31, we present the proper motions
(PMs) of 13 main-sequence Milky Way halo stars. The sample lies at an average
distance of r ~24 kpc from the Galactic center, with a root-mean-square spread
of 6 kpc. At this distance, the median PM accuracy is 5 km/s. We devise a
maximum likelihood routine to determine the tangential velocity ellipsoid of
the stellar halo. The velocity second moments in the directions of the Galactic
(l,b) system are < vl^2 >^{1/2} = 123 (+29, -23) km/s, and < vb^2 >^{1/2} = 83
(+24, -16) km/s. We combine these results with the known line-of-sight second
moment, < vlos^2 >^{1/2} = 105 \pm 5$ km/s, at this < r > to study the velocity
anisotropy of the halo. We find approximate isotropy between the radial and
tangential velocity distributions, with anisotropy parameter beta = 0.0 (+0.2,
-0.4). Our results suggest that the stellar halo velocity anisotropy out to r ~
30 kpc is less radially biased than solar neighborhood measurements. This is
opposite to what is expected from violent relaxation, and may indicate the
presence of a shell-type structure at r ~ 24 kpc. With additional multi-epoch
HST data, the method presented here has the ability to measure the transverse
kinematics of the halo for more stars, and to larger distances. This can yield
new improved constraints on the stellar halo formation mechanism, and the mass
of the Milky Way.
