The 3D secular dynamics of radial-velocity-detected planetary systems

Abstract

Aims. To date, more than 600 multi-planetary systems have been discovered. Due to the limitations of the detection methods, our knowledge of the systems is usually far from complete. In particular, for planetary systems discovered with the radial velocity (RV) technique, the inclinations of the orbital planes, and thus the mutual inclinations and planetary masses, are unknown. Our work aims to constrain the spatial configuration of several RV-detected extrasolar systems that are not in a mean-motion resonance.Methods. Through an analytical study based on a first-order secular Hamiltonian expansion and numerical explorations performed with a chaos detector, we identified ranges of values for the orbital inclinations and the mutual inclinations, which ensure the long-term stability of the system. Our results were validated by comparison with n-body simulations, showing the accuracy of our analytical approach up to high mutual inclinations (∼ 70 • -80 • ).Results. We find that, given the current estimations for the parameters of the selected systems, long-term regular evolution of the spatial configurations is observed, for all the systems, i) at low mutual inclinations (typically less than 35 • ) and ii) at higher mutual inclinations, preferentially if the system is in a Lidov-Kozai resonance. Indeed, a rapid destabilisation of highly mutually inclined orbits is commonly observed, due to the significant chaos that develops around the stability islands of the Lidov-Kozai resonance.

Nodal Precession in Closely Spaced Planet Pairs

“…Additionally, studies that have included inclination effects (e.g. Volpi et al 2019) tend to be focused on the stability and dynamical effects and not on nodal precession itself.…”

Librational KAM tori in the secular dynamics of the $\upsilon$ Andromedæ planetary system

“…The characterization of the three dimensional architecture of extrasolar planetary systems is one of the very exciting problems that is currently investigated in Dynamical Astronomy. It has been studied within the framework of both complete and secular planetary Hamiltonians (see, e.g., [30], [24] and [40]). In [39], some of the Authors of this article introduced a reverse approach based on KAM theory: values of the mutual inclinations are considered to be acceptable if the subsequent construction of the Kolmogorov normal form is convergent.…”

Classification of orbits in three-dimensional exoplanetary systems

“…Recently, Schwarz et al (2012) investigated the linear stability of the libration point L 4 in the spatial restricted three-body problem (RTBP), which may have applications to exoplanetary systems. Moreover, Volpi et al (2019) studied the stability of three-dimensional exoplanetary systems. Antoniadou & Libert (2019) determined resonant threedimensional periodic solutions in the RTBP.…”