Could the Magellanic Clouds be tidal dwarves expelled from a past-merger event occurring in Andromeda?

The Magellanic Clouds are often considered as outliers in the satellite system of the Milky Way because they are irregular and gas-rich galaxies. From their large relative motion, they are likely from their first pass near the Milky Way, possibly originating from another region of the Local Group or its outskirts. M31 could have been in a merger stage in its past and we investigate whether or not the Large Magellanic Cloud could have been a tidal dwarf expelled during this event. Such an hypothesis is tested in the frame of present-day measurements and uncertainties of the relative motions of LMC and M31. Our method is to trace back the LMC trajectory using several thousands of different configurations that sample the corresponding parameter space. We find several configurations that let LMC at 50 kpc from M31, 4.3 to 8 Gyrs ago, depending on the adopted shape of the Milky Way halo. For all configurations, the LMC velocity at such a location is invariably slightly larger than the escape velocity at such a radius. The preferred solutions correspond to a spherical to prolate Milky Way halo, predicting a transversal motion of M31 of less than 107 km/s and down to values that are close to zero. We conclude that from present-day measurements, Magellanic Clouds could well be tidal dwarves expelled from a former merger events occurring in M31.