Dependence of Galactic Halo Kinematics on the Adopted Galactic Potential
  We explore differences in Galactic halo kinematic properties derived from two
commonly employed Galactic potentials: the St$\ddot{a}$ckel potential and the
default Milky Way-like potential used in the "Galpy" package (MWPotential2014),
making use of stars with available metallicities, radial velocities, and proper
motions from Sloan Digital Sky Survey Data Release 12. Adopting the
St$\ddot{a}$ckel potential, we find that the shape of the metallicity
distribution function (MDF) and the distribution of orbital rotation abruptly
change at $Z_{\rm max}$ = 15 kpc and $r_{\rm max}$ = 30 kpc (where $Z_{\rm
max}$ and $r_{\rm max}$ are the maximum distances reached by a stellar orbit
from the Galactic plane and from the Galactic center, respectively), indicating
that the transition from dominance by the inner-halo stellar population to the
outer-halo population occurs at those distances. Stars with $Z_{\rm max}$ $>$
15 kpc show an average retrograde motion of $V_{\rm \phi}$ = $-$60 km s$^{-1}$,
while stars with $r_{\rm max}$ $>$ 30 kpc exhibit an even larger retrograde
value, $V_{\rm \phi}$ = $-$150 km s$^{-1}$. This retrograde signal is also
confirmed using the sample of stars with radial velocities obtained by $Gaia$
Data Release 2, assuming the St$\ddot{a}$ckel potential. In comparison, when
using the shallower Galpy potential, a noticeable change in the MDF occurs only
at $Z_{\rm max}$ = 25 kpc, and a much less extreme retrograde motion is
derived. This difference arises because stars with highly retrograde motions in
the St$\ddot{a}$ckel potential are unbound in the shallower Galpy potential,
and stars with lower rotation velocities reach larger $Z_{\rm max}$ and $r_{\rm
max}$. The different kinematic characteristics derived from the two potentials
suggest that the nature of the adopted Galactic potential can strongly
influence interpretation of the properties of the Galactic halo.
