Dynamical and Secular Stability of Mutually Inclined Planetary Systems
Multiple analytical, semi-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,...
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IOP Publishing
2024-01-01
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| Series: | The Astrophysical Journal |
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| Online Access: | https://doi.org/10.3847/1538-4357/ad62f9 |
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| author | Hareesh Gautham Bhaskar Hagai Perets |
| author_facet | Hareesh Gautham Bhaskar Hagai Perets |
| author_sort | Hareesh Gautham Bhaskar |
| collection | DOAJ |
| description | Multiple analytical, semi-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 semimajor axis of the inner binary β = δ a _1 / a _1 caused by perturbations from the companion. Stability criteria can be derived by setting a threshold on β. Focusing initially on circular orbits, we derive an analytical expression for β for coplanar prograde and retrograde orbits. For noncoplanar 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 ∼ 0.01 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 von Ziepel–Lidov–Kozai (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. |
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| id | doaj-art-947b27746f764605a1ff80ea7ad0b4d9 |
| institution | OA Journals |
| issn | 1538-4357 |
| language | English |
| publishDate | 2024-01-01 |
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| spelling | doaj-art-947b27746f764605a1ff80ea7ad0b4d92025-08-20T01:54:34ZengIOP PublishingThe Astrophysical Journal1538-43572024-01-01973210810.3847/1538-4357/ad62f9Dynamical and Secular Stability of Mutually Inclined Planetary SystemsHareesh Gautham Bhaskar0Hagai Perets1Technion-Israel Institute of Technology , Haifa, IsraelTechnion-Israel Institute of Technology , Haifa, IsraelMultiple analytical, semi-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 semimajor axis of the inner binary β = δ a _1 / a _1 caused by perturbations from the companion. Stability criteria can be derived by setting a threshold on β. Focusing initially on circular orbits, we derive an analytical expression for β for coplanar prograde and retrograde orbits. For noncoplanar 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 ∼ 0.01 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 von Ziepel–Lidov–Kozai (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.https://doi.org/10.3847/1538-4357/ad62f9Exoplanet dynamicsExoplanet evolutionThree-body problemN-body simulations |
| spellingShingle | Hareesh Gautham Bhaskar Hagai Perets Dynamical and Secular Stability of Mutually Inclined Planetary Systems The Astrophysical Journal Exoplanet dynamics Exoplanet evolution Three-body problem N-body simulations |
| title | Dynamical and Secular Stability of Mutually Inclined Planetary Systems |
| title_full | Dynamical and Secular Stability of Mutually Inclined Planetary Systems |
| title_fullStr | Dynamical and Secular Stability of Mutually Inclined Planetary Systems |
| title_full_unstemmed | Dynamical and Secular Stability of Mutually Inclined Planetary Systems |
| title_short | Dynamical and Secular Stability of Mutually Inclined Planetary Systems |
| title_sort | dynamical and secular stability of mutually inclined planetary systems |
| topic | Exoplanet dynamics Exoplanet evolution Three-body problem N-body simulations |
| url | https://doi.org/10.3847/1538-4357/ad62f9 |
| work_keys_str_mv | AT hareeshgauthambhaskar dynamicalandsecularstabilityofmutuallyinclinedplanetarysystems AT hagaiperets dynamicalandsecularstabilityofmutuallyinclinedplanetarysystems |