Motion of halo compact objects in the gravitational potential of a low-mass model of the Galaxy

TL;DR

This paper tests the stability of a Milky Way mass estimate by simulating halo object motions in a realistic potential, confirming the robustness of previous point mass approximation results and deriving new kinematic relations.

Contribution

It demonstrates the structural stability of the Milky Way mass estimate using simulations in a realistic potential and derives new equations linking velocity dispersion to observable kinematics.

Findings

Radial velocity dispersion profile remains consistent under more realistic potential.

Mass estimate of the Milky Way is reliable within 150 kpc.

Derived new formula relating velocity dispersion to kinematic observables.

Abstract

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.