A quick method to identify secular resonances in multi-planet systems with a binary companion

TL;DR

This paper introduces a semi-analytical method to efficiently identify secular resonances in multi-planet systems with a binary star, demonstrated on the HD41004 AB system, highlighting the impact of binary perturbations.

Contribution

A new semi-analytical approach for locating secular resonances in binary star systems, reducing computational effort compared to traditional methods.

Findings

Perturbations cause high eccentricity and inclination in test planets.

Resonance locations depend on binary-planet architecture.

Method effectively identifies secular resonances in simulated systems.

Abstract

Gravitational perturbations in multi-planet systems caused by an accompanying star are the subject of this investigation. Our dynamical model is based on the binary star HD41004 AB where a giant planet orbits HD41004 A. We modify the orbital parameters of this system and analyze the motion of a hypothetical test-planet surrounding HD41004 A on an interior orbit to the detected giant planet. Our numerical computations indicate perturbations due to mean motion and secular resonances. The locations of these resonances are usually connected to high eccentricity and highly inclined motion depending strongly on the binary-planet architecture.As the positions of mean motion resonances can easily be determined, the main purpose of this study is to present a new semi-analytical method to determine the location of a secular resonance without huge computational effort.