Secondary resonances and the boundary of effective stability of Trojan motions

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.