Title: Reliability of the measured velocity anisotropy of the Milky Way stellar halo,
Abstract: Determining the velocity distribution of halo stars is essential for
estimating the mass of the Milky Way and for inferring its formation history.
Since the stellar halo is a dynamically hot system, the velocity distribution
of halo stars is well described by the 3-dimensional velocity dispersions
$(\sigma_r, \sigma_\theta, \sigma_\phi)$, or by the velocity anisotropy
parameter $\beta=1-(\sigma_\theta^2+\sigma_\phi^2)/(2\sigma_r^2)$. Direct
measurements of $(\sigma_r, \sigma_\theta, \sigma_\phi)$ consistently suggest
$\beta =0.5$-$0.7$ for nearby halo stars. In contrast, the value of $\beta$ at
large Galactocentric radius $r$ is still controversial, since reliable proper
motion data are available for only a handful of stars. In the last decade,
several authors have tried to estimate $\beta$ for distant halo stars by
fitting the observed line-of-sight velocities at each radius with simple
velocity distribution models (local fitting methods). Some results of local
fitting methods imply $\beta<0$ at $r \gtrsim 20 \;\rm{kpc}$, which is
inconsistent with recent predictions from cosmological simulations. Here we
perform mock-catalogue analyses to show that the estimates of $\beta$ based on
local fitting methods are reliable only at $r \leq 15 \;\rm{kpc}$ with the
current sample size ($\sim10^3$ stars at a given radius). As $r$ increases, the
line-of-sight velocity (corrected for the Solar reflex motion) becomes
increasingly closer to the Galactocentric radial velocity, so that it becomes
increasingly more difficult to estimate tangential velocity dispersion
$(\sigma_\theta, \sigma_\phi)$ from line-of-sight velocity distribution. Our
results suggest that the forthcoming Gaia data will be crucial for
understanding the velocity distribution of halo stars at $r \geq 20\;\rm{kpc}$.