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A Large Local Rotational Speed for the Galaxy Found from Proper Motions: Implications for the Mass of the Milky Way

Predictions from a Galactic structure and kinematic model are compared with the absolute proper motions of about 30,000 randomly selected stars with 9 < BJ ≤ 19 derived from the Southern Proper-Motion (SPM) program toward the south Galactic pole. The absolute nature of the SPM proper motions allows 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 fitted 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 toward 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 ± 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 the 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) × 1012 M☉ to ~50 kpc] and with the timing argument, based on the binary motion of M31 and the Milky Way and on that of Leo I and the Milky Way (≥1.2 × 1012 M☉ to ~200 kpc).