2014MNRAS.439.2442F

A significant fraction of white dwarfs are observed to be polluted with metals despite high surface gravities and short settling times. The current theoretical model for this pollution is accretion of rocky bodies, which are delivered to the white dwarf through perturbations by orbiting planets. Using N-body simulations, we examine the possibility of a single planet as the source of pollution. We determine the stability of test particles on circular orbits in systems with a single planet located at 4 au for a range of masses and eccentricities, comparing the fractions that are ejected and accreted by the star. In particular, we compare the instabilities that develop before and after the star loses mass to form a white dwarf, a process which causes the semimajor axes of orbiting bodies to expand adiabatically. We determine that a planet must be eccentric (e > 0.02) to deliver significant (>0.5 percent) amounts of material to the central body, and that the amount increases with the planetary eccentricity. This result is robust with respect to the initial eccentricities of the scattered particles in the case of planetary eccentricity above ∼ 0.4 and the case of randomly distributed particle longitude of pericentre. We also find that the efficiency of the pollution is enhanced as planetary mass is reduced. We demonstrate that a 0.03 MJup planet with substantial eccentricity (e > 0.4) can account for the observed levels of pollution for initial disc masses of the order of 1 M⊕. Such discs are well within the range estimated for initial planetesimals discs and well below that estimated for our own Solar system within the context of the Nice model. However, their long-term survival to the white dwarf stage is uncertain as estimates for the collisional evolution of planetesimal discs suggest they should be ground down below the required levels on Gyr time-scales. Thus, planetary scattering by eccentric, sub-Jovian planets can explain the observed levels of pollution in white dwarfs, but only if current estimates of the collisional erosion of planetesimal discs are in error.