Stability of coorbital planets around binaries

¹ Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
e-mail: stefan.adelbert@uni-tuebingen.de
² Astrophysics Group, Department of Physics, Imperial College London, Prince Consort Rd, London, SW7 2AZ, UK
e-mail: a.penzlin@imperial.ac.uk
³ Department of Applied Mathematics and Physics, Valdosta State University, Valdosta GA, 31698, USA
⁴ Grupo de Dinâmica Orbital e Planetologia, São Paulo State University, UNESP, Guaratinguetá, CEP 12516-410, São Paulo, Brazil

Received: 23 June 2022
Accepted: 10 October 2023

Abstract

In previous hydrodynamical simulations, we found a mechanism for nearly circular binary stars, such as Kepler-413, to trap two planets in a stable 1:1 resonance. Therefore, the stability of coorbital configurations becomes a relevant question for planet formation around binary stars. For this work, we investigated the coorbital planet stability using a Kepler-413 analogue as an example and then expanded the parameters to study a general n-body stability of planet pairs in eccentric horseshoe orbits around binaries. The stability was tested by evolving the planet orbits for 10⁵ binary periods with varying initial semi-major axes and planet eccentricities. The unstable region of a single circumbinary planet is used as a comparison to the investigated coorbital configurations in this work. We confirm previous findings on the stability of single planets and find a first order linear relation between the orbit eccentricity e_p and pericentre to identify stable orbits for various binary configurations. Such a linear relation is also found for the stability of 1:1 resonant planets around binaries. Stable orbits for eccentric horseshoe configurations exist with a pericentre closer than seven binary separations and, in the case of Kepler-413, the pericentre of the first stable orbit can be approximated by r_c,peri = (2.90 e_p + 2.46) a_bin.