Dynamical and Secular Stability of Mutually Inclined Planetary Systems

Fuente: arXiv
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Autores principales: Bhaskar, Hareesh Gautham, Perets, Hagai
Formato: Preprint
Publicado: 2024
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author Bhaskar, Hareesh Gautham
Perets, Hagai
author_facet Bhaskar, Hareesh Gautham
Perets, Hagai
contents Multiple analytical and empirical stability criteria have been derived in the literature for two planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well modeled by previous stability criteria. Here, we derive a semi-analytical stability criteria for two planet systems, at arbitrary inclinations, in which the inner planet is a test particle. Using perturbation theory we calculate the characteristic fractional change in the semi-major axis of the inner binary $β=δa_1/a_1$ caused by perturbations from the companion. A stability criteria can be derived by setting a threshold on $β$ Focusing initially on circular orbits, we derive an analytical expression for $β$ for co-planar prograde and retrograde orbits. For non-coplanar configurations, we evaluate a semi-analytical expression. We then generalize to orbits with arbitrary eccentricities and account for the secular effects. Our analytical and semi-analytical results are in excellent agreement with direct N-body simulations. In addition, we show that contours of $β\sim0.01$ can serve as criteria for stability. More specifically, we show that (1) retrograde orbits are generally more stable than prograde ones; (2) systems with intermediate mutual inclination are less stable due to vZLK dynamics; and (3) mean-motion resonances (MMRs) can stabilize intermediate inclination secularly unstable regions in phase space, by quenching vZLK secular processes (4) MMRs can destabilize some of the dynamically stable regions. We also point out that these stability criteria can be used to constrain the orbital properties of observed systems and their age. We also point out that these stability criteria can be used to constrain the orbital properties of observed systems (in particular inclination) and their age.
format Preprint
id arxiv_https___arxiv_org_abs_2404_07264
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Dynamical and Secular Stability of Mutually Inclined Planetary Systems
Bhaskar, Hareesh Gautham
Perets, Hagai
Earth and Planetary Astrophysics
Multiple analytical and empirical stability criteria have been derived in the literature for two planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well modeled by previous stability criteria. Here, we derive a semi-analytical stability criteria for two planet systems, at arbitrary inclinations, in which the inner planet is a test particle. Using perturbation theory we calculate the characteristic fractional change in the semi-major axis of the inner binary $β=δa_1/a_1$ caused by perturbations from the companion. A stability criteria can be derived by setting a threshold on $β$ Focusing initially on circular orbits, we derive an analytical expression for $β$ for co-planar prograde and retrograde orbits. For non-coplanar configurations, we evaluate a semi-analytical expression. We then generalize to orbits with arbitrary eccentricities and account for the secular effects. Our analytical and semi-analytical results are in excellent agreement with direct N-body simulations. In addition, we show that contours of $β\sim0.01$ can serve as criteria for stability. More specifically, we show that (1) retrograde orbits are generally more stable than prograde ones; (2) systems with intermediate mutual inclination are less stable due to vZLK dynamics; and (3) mean-motion resonances (MMRs) can stabilize intermediate inclination secularly unstable regions in phase space, by quenching vZLK secular processes (4) MMRs can destabilize some of the dynamically stable regions. We also point out that these stability criteria can be used to constrain the orbital properties of observed systems and their age. We also point out that these stability criteria can be used to constrain the orbital properties of observed systems (in particular inclination) and their age.
title Dynamical and Secular Stability of Mutually Inclined Planetary Systems
topic Earth and Planetary Astrophysics
url https://arxiv.org/abs/2404.07264