The Tilt of the Halo Velocity Ellipsoid and the Shape of the Milky Way
  Halo
  A sample of roughly 1,800 halo subdwarf stars with radial velocities and
proper motions is assembled, using the repeated multi-band Sloan Digital Sky
Survey photometric measurements in Stripe 82. Our sample of halo subdwarfs is
extracted via a reduced proper motion diagram and distances are obtained using
photometric parallaxes, thus giving full phase space information. The tilt of
the velocity ellipsoid with respect to the spherical polar coordinate system is
computed and found to be consistent with zero for two of the three tilt angles,
and very small for the third. We prove that if the inner halo is in a
steady-state and the triaxial velocity ellipsoid is everywhere aligned in
spherical polar coordinates, then the potential must be spherically symmetric.
The detectable, but very mild, misalignment with spherical polars is consistent
with the perturbative effects of the Galactic disk on a spherical dark halo.
Banana orbits are generated at the 1:1 resonance (in horizontal and vertical
frequency) by the disk. They populate Galactic potentials at the typical radii
of our subdwarf sample, along with the much more dominant short-axis tubes.
However, on geometric grounds alone, the tilt cannot vanish for the banana
orbits and this leads to a slight, but detectable, misalignment. We argue that
the tilt of the stellar halo velocity ellipsoid therefore provides a hitherto
largely neglected but important line of argument that the Milky Way's dark
halo, which dominates the potential, must be nearly spherical.
