Secondary resonances and the boundary of effective stability of Trojan motions

Abstract

One of the most interesting features in the libration domain of co-orbital motions is the existence of secondary resonances. For some combinations of physical parameters, these resonances occupy a large fraction of the domain of stability and rule the dynamics within the stable tadpole region. In this work, we present an application of a recently introduced `basic Hamiltonian model' Hb for Trojan dynamics, in Paez and Efthymiopoulos (2015), Paez, Locatelli and Efthymiopoulos (2016): we show that the inner border of the secondary resonance of lowermost order, as defined by Hb, provides a good estimation of the region in phase-space for which the orbits remain regular regardless the orbital parameters of the system. The computation of this boundary is straightforward by combining a resonant normal form calculation in conjunction with an `asymmetric expansion' of the Hamiltonian around the libration points, which speeds up convergence. Applications to the determination of the effective stability domain for exoplanetary Trojans (planet-sized objects or asteroids) which may accompany giant exoplanets are discussed.

21 pages, 9 figures. Accepted for publication in Celestial Mechanics and Dynamical Astronomy

References in corpus (11)

• Secondary resonances of co-orbital motions
• Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systems
• On the growth and stability of Trojan planets
• Detectability of quasi-circular co-orbital planets. Application to the radial velocity technique
• Detection of co-orbital planets by combining transit and radial-velocity measurements
• Disruption of co-orbital (1:1) planetary resonances during gas-driven orbital migration
• Trojan dynamics well approximated by a new Hamiltonian normal form
• Dynamics of Jupiter Trojans during the 2:1 mean motion resonance crossing of Jupiter and Saturn
• New Hamiltonian expansions adapted to the Trojan problem
• Dynamics of co-orbital exoplanets
• New normal form approaches adapted to the Trojan problem

Cited by in corpus (3)

• Co-orbital exoplanets from close period candidates: The TOI-178 case
• A systematic survey of the dynamics of Uranus Trojans
• A new radial, natural, higher order intermediary of the main problem four decades after the elimination of the parallax