A lower bound on the Milky Way mass from general phase-space distribution function models

TL;DR

This paper derives a conservative lower bound on the Milky Way's mass using phase-space distribution functions, highlighting the strong dependence of mass estimates on the modeling approach.

Contribution

The authors introduce a method using general phase-space models to establish a lower bound on the Milky Way's mass without assuming specific tracer densities or velocity anisotropy profiles.

Findings

A lower bound of approximately 2.4 x 10^{11} solar masses is consistent with observed velocity dispersions.

Mass estimates are highly model-dependent, with no apparent upper bound based solely on radial motions.

The approach allows for calculating moments like orbital anisotropy without restrictive assumptions.

Abstract

We model the phase-space of the kinematic tracers using general, smooth distribution functions to derive a conservative lower bound on the total mass within 150-200 kpc. By approximating the potential as Keplerian, the phase-space distribution can be simplified to that of a smooth distribution of energies and eccentricities. Our approach naturally allows for calculating moments of the distribution function, such as the radial profile of the orbital anisotropy. We construct a family of phase-spaces with the resulting radial velocity dispersion overlapping with that of distant kinematic tracers, while making no assumptions about the density of the tracers and the radial profile of the velocity anisotropy (beta). While there is no apparent upper bound for the Milky Way mass, at least as long as only the radial motions are concerned, we find a sharp lower bound for the mass that is small. In particular, a mass value of $2.4 \times 10^{11}$ of solar masses, is still consistent with the dispersion profile at larger radii. Compared with much greater mass values in the literature, this result shows that determining the Milky Way mass is strongly model dependent. We expect a similar reduction of mass estimates in models assuming more realistic mass profiles.