Motion of halo compact objects in the gravitational potential of a
  low-mass model of the Galaxy
  Recently, we determined a lower bound for the Milky Way mass in a point mass
approximation. This result was obtained for most general spherically symmetric
phase-space distribution functions consistent with a measured radial velocity
dispersion. As a stability test of these predictions against a perturbation of
the point mass potential, in this paper we make use of a representative of
these functions to set the initial conditions for a simulation in a more
realistic potential of similar mass and accounting for other observations. The
predicted radial velocity dispersion profile evolves to forms still consistent
with the measured profile, proving structural stability of the point mass
approximation and the reliability of the resulting mass estimate of
$2.1\times10^{11}\mathrm{M}_{\odot}$ within $150\,\mathrm{kpc}$. We also find
an interesting coincidence with the recent estimates based on the kinematics of
the extended Orphan Stream. As a byproduct, we obtain the equations of motion
in axial symmetry from a nonstandard Hamiltonian, and derive a formula in the
spherical symmetry relating the radial velocity dispersion profile to a
directly measured kinematical observable.
