Secular chaos in white-dwarf planetary systems

The overlap of non-linear secular resonances in planetary systems drives chaotic secular evolution of test particles. Over long time-scales, this “secular chaos” can excite a particle’s eccentricity to a value near unity, leading to tidal interactions or collisions with the system’s central star. We present a semi-analytic study of secular chaos in systems containing two massive planets and an inner test particle. We use Gauss’ ring-averaging method to study the relationship between the properties and orbital configuration of the perturbing bodies and the rate of tidal disruption events (TDEs) driven by secular chaos over a Hubble time of evolution. We also characterize the role of short-range forces in preventing tidal disruption. Our results are relevant to the dynamical evolution of planetary systems around white dwarfs (WDs): we find that secular chaos can drive TDEs of planetesimals at a steady rate over a Hubble time, consistent with observations of atmospheric metal pollution in WDs with cooling ages ranging from ~30 Myr to several Gyr. The cooling age at which the TDE rate is greatest (in an individual system) is sensitive to the masses and eccentricities of the perturbing planets. We suggest that a population of giant planets driving secular chaos in these systems would produce microlensing events observable by the Roman Space Telescope.