Dynamics of co-orbital exoplanets

TL;DR

This paper investigates the dynamics of co-orbital exoplanets, analyzing their orbital configurations, how they evolve with eccentricity, and discusses detection methods, especially radial velocity and transit techniques, including effects of perturbations.

Contribution

It provides a detailed analysis of the phase space topology of eccentric co-orbital exoplanets and explores detection strategies, extending understanding of their orbital dynamics and observational signatures.

Findings

Geometry of orbital families varies with eccentricity

Detection methods are adapted for co-orbital configurations

Orbital perturbations influence spin-orbit resonances

Abstract

This work focuses on the dynamics and the detection methods of co-orbital exoplanets. We call "co-orbital" any configuration in which two planets orbit with the same mean mean-motion around the same star. First, we revisit the results of the circular coplanar case. We also recall that the manifold associated to the coplanar case and the manifold corresponding to the circular case are both invariant by the flow of the averaged Hamiltonian. We hence study these two particular cases. We focus mainly on the coplanar case (eccentric), where we study the evolution of families of non-maximal quasi-periodic orbits parametrized by the eccentricity of the planets. We show that the geometry of these families is highly dependent on the eccentricity, which causes significant topology changes across the space of phases as the latter increases. A chapter is dedicated to the detection of co-orbital exoplanets. We recall the different detection methods adapted to the co-orbital case. We focus on the radial velocity technique, and the combination of radial velocity and transit measurements. Finally, we describe a method to study the effect of orbital perturbations on the spin-orbit resonances for a rigid body. We apply this method in two cases: the eccentric co-orbital case and the circumbinary case.