2018MNRAS.481.2180V

Previous full-lifetime simulations of single-star multi-planet systems across all phases of stellar evolution have predominately assumed coplanar or nearly coplanar orbits. Here we assess the consequences of this assumption by removing it and exploring the effect of giant branch mass loss on the stability of two-planet systems with small to moderate non-Kozai (<40o) relative inclinations. We run nearly 10⁴ simulations over 14 Gyr for F-star, A-star and B-star planet hosts, incorporating main-sequence stellar masses of 1.5, 2.0, 2.5, 3.0 and 5.0 solar masses, and initial planetary semimajor axis ratios that straddle their three-dimensional Hill stability limits. We find that the near-coplanar assumption can approximate well the stability frequencies and critical separations found for higher inclinations, except around strong mean-motion commensurabilities. Late instabilities - after the star has become a white dwarf - occur throughout the explored mutual inclination range. Consequently, non-Kozai mutual inclination should not be used as a predictive orbital proxy for determining which white dwarf multi-planet systems discovered by Gaia should represent high-priority follow-up targets for the detection of metal pollution and planetary debris discs.