The Stability and Dynamics of Planets in Tight Binary Systems

TL;DR

This paper investigates the stability and dynamical behavior of planets in tight binary systems, focusing on how Kozai oscillations and mutual gravitational interactions influence planetary stability and eccentricity evolution.

Contribution

It introduces the concept of a Kozai-stable zone and analyzes how weak planetary coupling can induce Kozai oscillations, explaining observed eccentricity trends in binary systems.

Findings

Stable at low inclinations ($\, extless 40^\u00b0$), but high inclinations lead to instability.

A Kozai-stable zone exists where mutual perturbations suppress oscillations.

Inducing Kozai oscillations is more likely in binaries with separations less than a certain threshold.

Abstract

Planets have been observed in tight binary systems with separations less than 20 AU. A likely formation scenario for such systems involves a dynamical capture, after which high relative inclinations are likely and may lead to Kozai oscillations. We numerically investigate the fate of an initially coplanar double-planet system in a class of binaries with separation ranging between $12 - 20 $ AU. Dynamical integrations of representative four-body systems are performed, each including a hot Jupiter and a second planet on a wider orbit. We find that, although such systems can remain stable at low relative inclinations ($\lesssim 40^\circ$), high relative inclinations are likely to lead to instabilities. This can be avoided if the planets are placed in a \emph{Kozai-stable zone} within which mutual gravitational perturbations can suppress the Kozai mechanism. We investigate the possibility of inducing Kozai oscillations in the inner orbit by a weak coupling mechanism between the planets in which the coplanarity is broken due to a differential nodal precession. Propagating perturbations from the stellar companion through a planetary system in this manner can have dramatic effects on the dynamical evolution of planetary systems, especially in tight binaries and can offer a reasonable explanation for eccentricity trends among planets observed in binary systems. We find that inducing such oscillations into the orbit of a hot Jupiter is more likely in tight binaries and an upper limit can be set on the binary separation above which these oscillations are not observed.