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

¹ Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskego 152, 31342 Kraków, Poland
e-mail: Lukasz.Bratek@ifj.edu.pl
² Astronomical Observatory, Jagiellonian University, Orla 171, 30244 Kraków, Poland
³ Institute of Physics, Jagiellonian University, Reymonta 4, 30059 Kraków, Poland

Received: 5 September 2013
Accepted: 4 December 2013

Abstract

We model the phase-space distribution 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 systematically construct a family of phase-space functions with the resulting radial velocity dispersion overlapping with the one obtained using data on radial motions of distant kinematic tracers, while making no assumptions about the density of the tracers and the velocity anisotropy parameter β regarded as a function of the radial variable. 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    ×    10¹¹  M_⊙, obtained in the past for lower and intermediate radii, 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.