Stability of multiplanet systems in binaries

TL;DR

This study evaluates the stability criteria for multiplanet systems in binary star systems, revealing limitations of existing parameters and proposing a new semiempirical formula to predict stability boundaries more accurately.

Contribution

The paper tests the applicability of the critical semimajor axis and Hill stability limit in binary systems and introduces a semiempirical formula for minimum binary separation for stable two-planet systems.

Findings

The empirical formula for ac underestimates stability limits by 10-20%.

Chaotic behaviour increases with higher binary eccentricity and smaller semimajor axes.

A new semiempirical formula predicts the minimum binary separation for stability.

Abstract

When exploring the stability of multiplanet systems in binaries, two parameters are normally exploited: the critical semimajor axis ac computed by Holman and Wiegert (1999) within which planets are stable against the binary perturbations, and the Hill stability limit Delta determining the minimum separation beyond which two planets will avoid mutual close encounters. Our aim is to test whether these two parameters can be safely applied in multiplanet systems in binaries or if their predictions fail for particular binary orbital configurations. We have used the frequency map analysis (FMA) to measure the diffusion of orbits in the phase space as an indicator of chaotic behaviour. First we revisited the reliability of the empirical formula computing ac in the case of single planets in binaries and we find that, in some cases, it underestimates by 10-20% the real outer limit of stability. For two planet systems, the value of Delta is close to that computed for planets around single stars, but the level of chaoticity close to it substantially increases for smaller semimajor axes and higher eccentricities of the binary orbit. In these configurations ac also begins to be unreliable and non linear secular resonances with the stellar companion lead to chaotic behaviour well within ac, even for single planet systems. For two planet systems, the superposition of mean motion resonances, either mutual or with the binary companion, and non linear secular resonances may lead to chaotic behaviour in all cases. We have developed a parametric semiempirical formula determining the minimum value of the binary semimajor axis, for a given eccentricity of the binary orbit, below which stable two planet systems cannot exist.