Anisotropy of the Milky Way's stellar halo using K giants from LAMOST
  and $Gaia$
  The anisotropy parameter $\beta$ 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 $\beta$ 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 $(\sigma_r, \sigma_\theta,
\sigma_\phi)$ (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 $\beta \approx 0.9$ for $-1.8 \leq$ [Fe/H] $< -1.3$
(for the bulk of the stars) to $\beta \approx 0.6$ for the lowest metallicities
([Fe/H] $< -1.8$). Considering our sample as a whole, $\beta\approx0.8$ and,
beyond 25 kpc, the orbits gradually become less radial and anisotropy decreases
to $\beta<0.3$ past 100 kpc. Within 8 kpc, $\beta<0.8$. 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.
