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Anisotropy of the Milky Way's stellar halo using K giants from LAMOST and $Gaia$

The anisotropy parameter $β$ characterizes the extent to which orbits in stellar systems are predominantly radial or tangential, and is likely to constrain, for the stellar halo of the Milky Way, scenarios for its formation and evolution. We have measured the anisotropy $β$ as a function of Galactocentric radius from $5-100$ kpc for over 8600 metal poor ([Fe/H] $<-1.3$) halo K giants from the LAMOST catalog with line-of-sight velocities and distances, matched to proper motions from the second $Gaia$ data release. We construct full 6-D positions and velocities for the K giants to directly measure the 3 components of the velocity dispersion $(σ_r, σ_θ, σ_ϕ)$ (in spherical coordinates). We find that the orbits in the halo are radial over our full Galactocentric distance range reaching over 100 kpc. The anisotropy remains remarkably unchanged with Galactocentric radius from approximately 5 to 25 kpc, with an amplitude that depends on the metallicity of the stars, dropping from $β\approx 0.9$ for $-1.8 \leq$ [Fe/H] $< -1.3$ (for the bulk of the stars) to $β\approx 0.6$ for the lowest metallicities ([Fe/H] $< -1.8$). Considering our sample as a whole, $β\approx0.8$ and, beyond 25 kpc, the orbits gradually become less radial and anisotropy decreases to $β<0.3$ past 100 kpc. Within 8 kpc, $β<0.8$. The measurement of anisotropy is affected by substructure and streams, particularly beyond a Galactocentric distance of approximately 25 kpc, where the Sagittarius stream is prominent in the data. These results are complimentary to recent analysis of simulations by Loebman et al. and of SDSS/$Gaia$ DR1 data by Belokurov et al.