We present the line-of-sight ( LOS ) velocities for 13 distant main sequence Milky Way halo stars with published proper motions .
The proper motions were measured using long baseline ( 5–7 years ) multi-epoch HST /ACS photometry , and the LOS velocities were extracted from deep ( 5–6 hour integrations ) Keck II/DEIMOS spectra .
We estimate the parameters of the velocity ellipsoid of the stellar halo using a Markov chain Monte Carlo ensembler sampler method .
The velocity second moments in the directions of the Galactic ( l,b, LOS ) coordinate system are \langle v ^ { 2 } _ { l } \rangle ^ { 1 / 2 } = 138 ^ { +43 } _ { -26 } km s ^ { -1 } , \langle v ^ { 2 } _ { b } \rangle ^ { 1 / 2 } = 88 ^ { +28 } _ { -17 } \mbox { km s } ^ { -1 } , and \langle v ^ { 2 } _ { LOS } \rangle ^ { 1 / 2 } = 91 ^ { +27 } _ { -14 } \mbox { km s } ^ { -1 } .
We use these ellipsoid parameters to constrain the velocity anisotropy of the stellar halo .
Ours is the first measurement of the anisotropy parameter \beta using 3D kinematics outside of the solar neighborhood .
We find \beta = -0.3 ^ { +0.4 } _ { -0.9 } , consistent with isotropy and lower than solar neighborhood \beta measurements by 2 \sigma ( \beta _ { SN } \sim 0.5 - 0.7 ) .
We identify two stars in our sample that are likely members of the known TriAnd substructure , and excluding these objects from our sample increases our estimate of the anisotropy to \beta = 0.1 ^ { +0.4 } _ { -1.0 } , which is still lower than solar neighborhood measurements by 1 \sigma .
The potential decrease in \beta with Galactocentric radius is inconsistent with theoretical predictions , though consistent with recent observational studies , and may indicate the presence of large , shell-type structure ( or structures ) at r \sim 25 kpc .
The methods described in this paper will be applied to a much larger sample of stars with 3D kinematics observed through the ongoing HALO7D Halo Assembly in Lambda-CDM : Observations in 7-Dimensions ( HALO7D ) is a spectroscopic survey of distant , Milky Way halo stars with Keck II/DEIMOS .
The 7 dimensions are the 6 dimensions of phase space plus chemical abundances . program .