Secular chaos in white-dwarf planetary systems: origins of metal pollution and short-period planetary companions

Secular oscillations in multi-planet systems can drive chaotic evolution through non-linear resonant perturbations. Secular chaos tends to excite the eccentricity of the innermost planet or small body to an extreme value, triggering tidal interactions or collision with the central star. We have conducted a numerical study of secular chaos in systems with two outer planets and an inner test particle, with emphasis on the relationship between the planets’ properties and the time-scale of the particle’s chaotic evolution. Our results are relevant to the evolution of planetary systems around white dwarfs (WDs), where secular chaos may drive tidal disruption or high-eccentricity migration of surviving planets or planetesimals. This may explain the origins of atmospheric metal pollution in WDs. We find that secular chaos driven by planets with masses > 10 M_⊕ and semi-major axes > 10 AU can sustain pollution of the WD over Gyr time-scales. Our simulations predict a trend of metal accretion rate vs. cooling age that is broadly consistent with observations of polluted WDs across the cooling sequence (cooling ages >10 Myr and <8 Gyr). Thus, we are able to constrain the mass of a surviving planetesimal belt that is the source of pollution in our scenario. Based on the occurrence rates of long-period giant exoplanets, we find that secular chaos could explain a large fraction of solitary polluted WDs, provided that inner planetesimal belts are also common. Secular chaos may also explain the surviving short-period planets and planetesimals discovered around WDs in recent years, in concert with various circularization mechanisms. The long-period exoplanets driving secular chaos around WDs could be detected soon by direct imaging or microlensing surveys.