Secular Orbital Evolution of Compact Planet Systems

TL;DR

This paper investigates how gravitational interactions with distant companions can sustain eccentric orbits in close-in exoplanets despite tidal damping, revealing long-term orbital behaviors and constraints on unseen companions.

Contribution

It introduces a model for the secular evolution of two-planet systems with tidal damping, explaining eccentricity persistence and providing criteria to infer unseen companions from observed eccentricities.

Findings

Eccentricities can be maintained longer than expected due to apsidal locking.

The model constrains properties of potential unseen companions based on orbital configurations.

Most close-in single planets show no evidence of unseen companions, suggesting alternative explanations for eccentricities.

Abstract

Recent observations have shown that at least some close-in exoplanets maintain eccentric orbits despite tidal circularization timescales that are typically shorter than stellar ages. We explore gravitational interactions with a distant planetary companion as a possible cause of these non-zero eccentricities. For simplicity, we focus on the evolution of a planar two-planet system subject to slow eccentricity damping and provide an intuitive interpretation of the resulting long-term orbital evolution. We show that dissipation shifts the two normal eigenmode frequencies and eccentricity ratios of the standard secular theory slightly, and that each mode decays at its own rate. Tidal damping of the eccentricities drives orbits to transition between periods of pericenter circulation and libration, and the planetary system settles into a locked state where the pericenters are nearly aligned or anti-aligned. Once in the locked state, the eccentricities of the two orbits decrease very slowly due to tides rather than at the much more rapid single-planet rate, and thus eccentric orbits, even for close-in planets, can often survive much longer than the age of the system. Assuming that an observed close-in planet on an elliptical orbit is apsidally-locked to a more distant, and perhaps unseen companion, we provide a constraint on the mass, semi-major axis, and eccentricity of the companion. We find the observed two-planet system HAT-P-13 might be in just such an apsidally-locked state, with parameters that obey our constraint well. We also survey close-in single planets, and found that none provide compelling evidence for unseen companions. Instead, we suspect that (1) orbits are circular, (2) tidal damping rates are slower than our assumption, or (3) a recent event has excited these eccentricities. Our method should prove useful for interpreting the results of current and future planet searches.