Isotropic at the Break? 3D Kinematics of Milky Way Halo Stars in the
  Foreground of M31
  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,
$\langle v^2_b \rangle^{1/2} = 88^{+28}_{-17}$ km/s, and $\langle
v^2_{\rm{LOS}} \rangle^{1/2} = 91^{+27}_{-14}$ km/s. 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 program.
