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 \simeq 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 ^ { -1 } .
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 \langle v ^ { 2 } _ { l } \rangle ^ { 1 / 2 } = 123 ^ { +29 } _ { -23 } km s ^ { -1 } , and \langle v ^ { 2 } _ { b } \rangle ^ { 1 / 2 } = 83 ^ { +24 } _ { -16 } km s ^ { -1 } .
We combine these results with the known line-of-sight second moment , \langle v ^ { 2 } _ { los } \rangle ^ { 1 / 2 } = 105 \pm 5 km s ^ { -1 } , at this \langle r \rangle 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 \sim 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 \sim 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 .