2012ApJ...753....8V

We determine the velocity vector of M31 with respect to the Milky Way and use this to constrain the mass of the Local Group, based on Hubble Space Telescope proper-motion measurements of three fields presented in Paper I. We construct N-body models for M31 to correct the measurements for the contributions from stellar motions internal to M31. This yields an unbiased estimate for the M31 center-of-mass motion. We also estimate the center-of-mass motion independently, using the kinematics of satellite galaxies of M31 and the Local Group, following previous work but with an expanded satellite sample. All estimates are mutually consistent, and imply a weighted average M31 heliocentric transverse velocity of (v_W, v_N) = (- 125.2±30.8, -73.8±28.4) km/s. We correct for the reflex motion of the Sun using the most recent insights into the solar motion within the Milky Way, which imply a larger azimuthal velocity than previously believed. This implies a radial velocity of M31 with respect to the Milky Way of V_rad, M31_= -109.3±4.4 km/s, and a tangential velocity of V_tan, M31_= 17.0 km/s, with a 1σ confidence region of V_tan, M31_ ≤ 34.3 km/s. Hence, the velocity vector of M31 is statistically consistent with a radial (head-on collision) orbit toward the Milky Way. We revise prior estimates for the Local Group timing mass, including corrections for cosmic bias and scatter, and obtain M_LG≡ M_MW, vir_+ M_M31, vir_= (4.93±1.63)x10¹² M_☉. Summing known estimates for the individual masses of M31 and the Milky Way obtained from other dynamical methods yields smaller uncertainties. Bayesian combination of the different estimates demonstrates that the timing argument has too much (cosmic) scatter to help much in reducing uncertainties on the Local Group mass, but its inclusion does tend to increase other estimates by ∼10%. We derive a final estimate for the Local Group mass from literature and new considerations of M_LG= (3.17±0.57)x10¹² M_☉. The velocity and mass results at 95% confidence imply that M33 is bound to M31, consistent with expectation from observed tidal deformations.