A large local rotational speed for the Galaxy found from proper-motions: Implications for the mass of the Milky-Way

Abstract

Predictions from a Galactic Structure and Kinematic model are compared to the absolute proper-motions of about 30,000 randomly selected stars with $9 < B_{\rm J} \le 19$ derived from the Southern Proper-Motion Program (SPM) toward the South Galactic Pole. The absolute nature of the SPM proper-motions allow us to measure not only the relative motion of the Sun with respect to the local disk, but also, and most importantly, the overall state of rotation of the local disk with respect to galaxies. The SPM data are best fit by models having a solar peculiar motion of +5 km~s$^{-1}$ in the V-component (pointing in the direction of Galactic rotation), a large LSR speed of 270 km~s$^{-1}$, and a disk velocity ellipsoid that points towards the Galactic center. We stress, however, that these results rest crucially on the assumptions of both axisymmetry and equilibrium dynamics. The absolute proper-motions in the U-component indicate a solar peculiar motion of $11.0 \pm 1.5$ km~s$^{-1}$, with no need for a local expansion or contraction term. The implications of the large LSR speed are discussed in terms of gravitational mass of the Galaxy inferred from the most recent and accurate determination for the proper-motion of the LMC. We find that our derived value for the LSR is consistent both with the mass of the Galaxy inferred from the motion of the Clouds ($3 - 4 \times 10^{12} M_\odot$ to $\sim 50$ kpc), as well as the timing argument, based on the binary motion of M31 and the Milky Way, and Leo I and the Milky Way ($\ge 1.2 \times 10^{12} M_\odot$ to $\sim 200$ kpc).