Dissipative Divergence of Resonant Orbits

TL;DR

This paper demonstrates that many near-resonant exoplanet systems are likely still resonant, with their divergence from exact resonance explained by dissipative processes, supported by analytical theory and numerical confirmation.

Contribution

It introduces an analytical framework showing how dissipative effects can cause divergence from resonance while maintaining libration of critical angles.

Findings

Many near-resonant systems are actually resonant with dissipative divergence.

Libration of critical angles can persist tens of percent away from resonance.

Analytical theory matches numerical simulations of long-term evolution.

Abstract

A considerable fraction of multi-planet systems discovered by the observational surveys of extrasolar planets reside in mild proximity to first-order mean motion resonances. However, the relative remoteness of such systems from nominal resonant period ratios (e.g. 2:1, 3:2, 4:3) has been interpreted as evidence for lack of resonant interactions. Here we show that a slow divergence away from exact commensurability is a natural outcome of dissipative evolution and demonstrate that libration of critical angles can be maintained tens of percent away from nominal resonance. We construct an analytical theory for the long-term dynamical evolution of dissipated resonant planetary pairs and confirm our calculations numerically. Collectively, our results suggest that a significant fraction of the near-commensurate extrasolar planets are in fact resonant and have undergone significant dissipative evolution.