Isotropic at the Break? 3D Kinematics of Milky Way Halo Stars in the Foreground of M31

Abstract: 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.