Dynamical evolution of two-planet systems and its connection with white dwarf atmospheric pollution

Asteroid material is detected in white dwarfs (WDs) as atmospheric pollution by metals, in the form of gas/dust discs, or in photometric transits. Within the current paradigm, minor bodies need to be scattered, most likely by planets, into highly eccentric orbits where the material gets disrupted by tidal forces and then accreted on to the star. This can occur through a planet-planet scattering process triggered by the stellar mass-loss during the post main-sequence (MS) evolution of planetary systems. So far, studies of the N-body dynamics of this process have used artificial planetary system architectures built ad hoc. In this work, we attempt to go a step further and study the dynamical instability provided by more restrictive systems that, at the same time, allow us an exploration of a wider parameter space: the hundreds of multiple planetary systems found around MS stars. We find that most of our simulated systems remain stable during the MS, Red, and Asymptotic Giant Branch and for several Gyr into the WD phases of the host star. Overall, only ≈2.3 ${{\ \rm per\ cent}}$ of the simulated systems lose a planet on the WD as a result of dynamical instability. If the instabilities take place during the WD phase most of them result in planet ejections with just five planetary configurations ending as a collision of a planet with the WD. Finally 3.2 ${{\ \rm per\ cent}}$ of the simulated systems experience some form of orbital scattering or orbit crossing that could contribute to the pollution at a sustained rate if planetesimals are present in the same system.