HALO7D II: The Halo Velocity Ellipsoid and Velocity Anisotropy with
  Distant Main Sequence Stars
  The Halo Assembly in Lambda-CDM: Observations in 7 Dimensions (HALO7D)
dataset consists of Keck II/DEIMOS spectroscopy and Hubble Space
Telescope-measured proper motions of Milky Way (MW) halo main sequence turnoff
stars in the CANDELS fields. In this paper, the second in the HALO7D series, we
present the proper motions for the HALO7D sample. We discuss our measurement
methodology, which makes use of a Bayesian mixture modeling approach for
creating the stationary reference frame of distant galaxies. Using the 3D
kinematic HALO7D sample, we estimate the parameters of the halo velocity
ellipsoid, $\langle v_{\phi} \rangle, \sigma_r, \sigma_{\phi},
\sigma_{\theta}$, and the velocity anisotropy $\beta$. Using the full HALO7D
sample, we find $\beta=0.63 \pm 0.05$ at $\langle r \rangle =24$ kpc. We also
estimate the ellipsoid parameters for our sample split into three apparent
magnitude bins; the posterior medians for these estimates of $\beta$, while
consistent with one another, increase as a function of mean sample distance.
Finally, we estimate $\beta$ in each of the individual HALO7D fields. We find
that the velocity anisotropy $\beta$ can vary from field to field, which
suggests that the halo is not phase mixed at $\langle r \rangle =24$ kpc. We
explore the $\beta$ variation across the skies of two stellar halos from the
\textit{Latte} suite of FIRE-2 simulations, finding that both simulated
galaxies show $\beta$ variation over a similar range to the variation observed
across the four HALO7D fields. The accretion histories of the two simulated
galaxies result in different $\beta$ variation patterns; spatially mapping
$\beta$ is thus a way forward in characterizing the accretion history of the
Galaxy.
