Dynamical analysis and constraints for the HD 196885 system

TL;DR

This study analyzes the orbital configurations of the HD 196885 system, identifying likely planetary inclinations and stable regions through dynamical analysis, with implications for understanding planet stability in binary star systems.

Contribution

It provides a comprehensive dynamical analysis of the HD 196885 system, exploring unknown orbital parameters and identifying stable configurations and regions for the planet.

Findings

Most likely planetary orbits are nearly coplanar or highly inclined near Lidov-Kozai points.

Retrograde coplanar orbits are less chaotic than prograde.

Stable observational regions are identified in specific inclination and longitude of ascending node ranges.

Abstract

The HD\,196885 system is composed of a binary star and a planet orbiting the primary. The orbit of the binary is fully constrained by astrometry, but for the planet the inclination with respect to the plane of the sky and the longitude of the node are unknown. Here we perform a full analysis of the HD\,196885 system by exploring the two free parameters of the planet and choosing different sets of angular variables. We find that the most likely configurations for the planet is either nearly coplanar orbits (prograde and retrograde), or highly inclined orbits near the Lidov-Kozai equilibrium points, i = 44^{\circ} or i = 137^{\circ} . Among coplanar orbits, the retrograde ones appear to be less chaotic, while for the orbits near the Lidov-Kozai equilibria, those around \omega= 270^{\circ} are more reliable, where \omega_k is the argument of pericenter of the planet's orbit with respect to the binary's orbit. From the observer's point of view (plane of the sky) stable areas are restricted to (I1, \Omega_1) \sim (65^{\circ}, 80^{\circ}), (65^{\circ},260^{\circ}), (115^{\circ},80^{\circ}), and (115^{\circ},260^{\circ}), where I1 is the inclination of the planet and \Omega_1 is the longitude of ascending node.