An intriguing coincidence between the majority of vast polar structure dwarfs and a recent major merger at the M31 position

A significant part of the Milky Way (MW) dwarf galaxies orbit within a Vast POlar Structure (VPOS), which is perpendicular to the Galactic disc and whose origin has not yet been identified. It includes the Large Magellanic Cloud (LMC) and its six dynamically associated dwarf galaxies. Andromeda Galaxy (M31) experienced a major merger two to three billion years ago, and its accurate modelling predicts that an associated tidal tail is pointing towards the Galaxy. Here, we tested a possible association between M31 tidal tail particles and MW dwarf galaxies, focusing first on the LMC and its associated dwarfs since they are less affected by ram pressure. We traced back these dwarf galaxy orbits by one billion years and calculated their association with the tidal tail particles in the 6D phase space, based on their proper motion from \textit{Gaia} DR3. We find that for low-mass MW models (total mass less than 5 $\times 10^{11} M_{\odot}$), the separation in the 6D space can be less than 1$σ$ for most of the M31 modelling, albeit with a significant degree of freedom due to the still unknown proper motion of M31. We further discover that many other dwarfs could also be associated with the M31 tidal tails if their motions had been radially slowed, as expected from the ram pressure exerted by the MW corona. This intriguing coincidence could explain the origin of the VPOS, which resulted from a matter exchange between M31 and MW.