The Fate of the Milky Way--Andromeda System: To Merge or Not?

It has long been predicted that the Milky Way (MW) will eventually merge with Andromeda (M31), a view reinforced by $\mathit{\text{HST}}$ measurements indicating a small M31 transverse velocity. However, using updated $\mathit{\text{Gaia}}$-based proper motions (PMs) and including the dynamical influence of the Large Magellanic Cloud (LMC) and M33, Sawala et al. reported an MW–M31 merger probability of $\sim$50% within 10 Gyr, leaving the fate of the Local Group (LG) uncertain. Adopting their semi-analytic framework, we revisit this problem with the latest and most precise $\mathit{\text{Gaia}}$-based PMs for M31 and M33, corrected for systematic offsets in $\mathit{\text{Gaia}}$ astrometry. In our fiducial model, the MW–M31 merger probability rises to 90%, with a median merger time of $6.5_{-1.5}^{+1.3}$ Gyr, broadly restoring the classical picture. A sensitivity analysis shows that the merger probability depends strongly on the adopted M31 PM through two channels: a direct effect via the radial-tangential balance of the MW-M31 orbit, and a satellite-mediated effect, where the M31 PM fixes the orbital plane and determines how satellite-induced barycentric reflex motions project onto it, either promoting or suppressing a merger. Given this sensitivity, current measurements, while favoring a high merger probability, remain inconclusive, spanning from 64.7% to 100% across the 2$\sigma$ PM region. Future PM measurements with uncertainty of $\lesssim 2\text{upmu}\mathrm{a}\mathrm{s}\mathrm{y}{\mathrm{r}}^{-1}$ will be required to reach a firm conclusion, i.e., to constrain the probability range within 10% at the 2$\sigma$ level.