Posterior distribution of values of M 31’s radial and tangential velocity for the Monte Carlo samples generated from the prior on the magnitude of v_tan from van der Marel et al. (2019) (purple). After compensating for the LMC perturbation, (Benisty et al. 2022) generates the corresponding v_rad and v_tan that used here as the modified effect of the LMC (green). The v_rad is increased by [25, 30 km/s] and v_rad is shifted to −75 ± 15 km/s.