The M31 Velocity Vector. Iii. Future Milky Way M31–m33 Orbital Evolution, Merging, and Fate of the Sun

We study the future orbital evolution and merging of the Milky Way (MW)-M31-M33 system, using a combination of collisionless N-body simulations and semi-analytic orbit integrations. Monte-Carlo simulations are used to explore the consequences of varying all relevant initial phase-space and mass parameters within their observational uncertainties. The observed M31 transverse velocity from Papers I and II implies that the MW and M31 will merge t = 5.86+1.61 −0.72 Gyr from now. The first pericenter occurs at t = 3.87+0.42 −0.32Gyr, at a pericenter distance r = 31.0+38.0 −19.8 kpc. In 41 % of Monte-Carlo orbits M31 makes a direct hit with the MW, defined here as a first-pericenter distance less than 25 kpc. For the M31-M33 system, the first-pericenter time and distance are t = 0.85+0.18 −0.13Gyr and