The M31 Velocity Vector. Ii. Radial Orbit Toward the Milky Way and Implied Local Group Mass

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 HST proper-motion measurements presented in Paper I. We construct N-body models for M31 to correct the measurements for the contributions from stellar motions internal to M31. We also estimate the center-of-mass motion independently, using the kinematics of satellite galaxies of M31 and the Local Group. All estimates are mutually consistent, and imply a weighted average M31 heliocentric transverse velocity of (vW, vN) = (-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. This implies a radial velocity of M31 with respect to the Milky Way of Vᵣad = -109. 3+/-4. 4 km/s, and a tangential velocity Vₜan = 17. 0 km/s (<34. 3 km/s at 1-sigma confidence). Hence, the velocity vector of M31 is statistically consistent with a radial (head-on collision) orbit towards the Milky Way. We revise prior estimates for the Local Group timing mass, including corrections for cosmic bias and scatter. Bayesian combination with other mass estimates yields MLG = MMW (vir) + MM31 (vir) = (3. 17 +/- 0. 57) x 10¹2 solar masses. The velocity and mass results imply at 95% confidence that M33 is bound to M31, consistent with expectation from observed tidal deformations. (Abridged)