Effects of non-Kozai mutual inclinations on two-planet system stability through all phases of stellar evolution

TL;DR

This study investigates how small to moderate non-Kozai mutual inclinations affect the long-term stability of two-planet systems through all stellar evolution phases, challenging the common coplanar orbit assumption.

Contribution

It provides comprehensive simulations showing that near-coplanar assumptions are generally valid for stability predictions, except near mean-motion resonances, and highlights late instabilities after stellar evolution.

Findings

Near-coplanar assumption approximates stability frequencies well.

Late instabilities occur across all mutual inclinations.

Non-Kozai inclinations are not reliable predictors for white dwarf system stability.

Abstract

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 (<40 degrees) relative inclinations. We run nearly 10^4 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.