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.