The M31 Velocity Vector. II. Radial Orbit Towards 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 (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. This implies a radial velocity of M31 with respect to the
Milky Way of V_rad = -109.3+/-4.4 km/s, and a tangential velocity V_tan = 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 M_LG = M_MW(vir) + M_M31(vir) = (3.17 +/- 0.57) x 10^12 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)
