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

TL;DR

This study measures the 3D kinematics of distant Milky Way halo stars to estimate the velocity anisotropy parameter, revealing a more isotropic halo at large radii than previously observed near the Sun.

Contribution

First measurement of the velocity anisotropy parameter using 3D kinematics of halo stars outside the solar neighborhood, employing a novel MCMC method.

Findings

Velocity ellipsoid parameters estimated with MCMC.

Anisotropy parameter β consistent with isotropy at large radii.

Potential large shell structures at ~25 kpc.

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.