Rapid dynamical chaos in an exoplanetary system

TL;DR

This study reveals that the Kepler-36 exoplanet system exhibits rapid chaotic orbital evolution driven by specific resonances, with most initial conditions leading to instability within hundreds of millions of years.

Contribution

The paper identifies the specific resonances causing rapid chaos in Kepler-36 and quantifies the fraction of stable initial conditions, highlighting the importance of Hill stability margins.

Findings

Chaos arises from 34:29 and 6:7 orbital resonances.

Only ~4.5% of initial conditions are stable over 200 million years.

Stable orbits are associated with maximum Hill stability margin.

Abstract

We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which we studied through numerical integrations of initial conditions that are consistent with observations of the system. The orbits are chaotic with a Lyapunov time of only ~10 years. The chaos is a consequence of a particular set of orbital resonances, with the inner planet orbiting 34 times for every 29 orbits of the outer planet. The rapidity of the chaos is due to the interaction of the 29:34 resonance with the nearby first order 6:7 resonance, in contrast to the usual case in which secular terms in the Hamiltonian play a dominant role. Only one contiguous region of phase space, accounting for ~4.5% of the sample of initial conditions studied, corresponds to planetary orbits that do not show large scale orbital instabilities on the timescale of our integrations (~200 million years). The long-lived subset of the allowed initial conditions are those that satisfy the Hill stability criterion by the largest margin. Any successful theory for the formation of this system will need to account for why its current state is so close to unstable regions of phase space.