First-order mean motion resonances in two-planet systems: general analysis and observed systems
This paper focuses on two-planet systems in a first-order (q + 1): q mean motion resonance and undergoing type-Imigration in a disc.We present a detailed analysis of the resonance valid for any value of q. Expressions for the equilibrium eccentricities, mean motions, and departure from exact resonan...
| Κύριοι συγγραφείς: | , |
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| Μορφή: | Journal article |
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Oxford University Press
2018
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| _version_ | 1826273479452786688 |
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| author | Terquem, C Papaloizou, J |
| author_facet | Terquem, C Papaloizou, J |
| author_sort | Terquem, C |
| collection | OXFORD |
| description | This paper focuses on two-planet systems in a first-order (q + 1): q mean motion resonance and undergoing type-Imigration in a disc.We present a detailed analysis of the resonance valid for any value of q. Expressions for the equilibrium eccentricities, mean motions, and departure from exact resonance are derived in the case of smooth convergent migration. We show that this departure, not assumed to be small, is such that the period ratio normally exceeds but can also be less than (q + 1)/q. Departure from exact resonance as a function of time for systems starting in resonance and undergoing divergent migration is also calculated. We discuss observed systems in which two low-mass planets are close to a first-order resonance. We argue that the data are consistent with only a small fraction of the systems having been captured in resonance. Furthermore, when capture does happen, it is not in general during smooth convergent migration through the disc but after the planets reach the disc inner parts. We show that although resonances may be disrupted when the inner planet enters a central cavity, this alone cannot explain the spread of observed separations. Disruption is found to result in the system either moving interior to the resonance by a few per cent or attaining another resonance. We postulate two populations of low-mass planets: a small one for which extensive smooth migration has occurred and a larger one that formed approximately in situ with very limited migration. |
| first_indexed | 2024-03-06T22:28:48Z |
| format | Journal article |
| id | oxford-uuid:5795e559-732c-4f47-9c26-f7ee778a9d32 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:28:48Z |
| publishDate | 2018 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:5795e559-732c-4f47-9c26-f7ee778a9d322022-03-26T16:57:37ZFirst-order mean motion resonances in two-planet systems: general analysis and observed systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5795e559-732c-4f47-9c26-f7ee778a9d32Symplectic Elements at OxfordOxford University Press2018Terquem, CPapaloizou, JThis paper focuses on two-planet systems in a first-order (q + 1): q mean motion resonance and undergoing type-Imigration in a disc.We present a detailed analysis of the resonance valid for any value of q. Expressions for the equilibrium eccentricities, mean motions, and departure from exact resonance are derived in the case of smooth convergent migration. We show that this departure, not assumed to be small, is such that the period ratio normally exceeds but can also be less than (q + 1)/q. Departure from exact resonance as a function of time for systems starting in resonance and undergoing divergent migration is also calculated. We discuss observed systems in which two low-mass planets are close to a first-order resonance. We argue that the data are consistent with only a small fraction of the systems having been captured in resonance. Furthermore, when capture does happen, it is not in general during smooth convergent migration through the disc but after the planets reach the disc inner parts. We show that although resonances may be disrupted when the inner planet enters a central cavity, this alone cannot explain the spread of observed separations. Disruption is found to result in the system either moving interior to the resonance by a few per cent or attaining another resonance. We postulate two populations of low-mass planets: a small one for which extensive smooth migration has occurred and a larger one that formed approximately in situ with very limited migration. |
| spellingShingle | Terquem, C Papaloizou, J First-order mean motion resonances in two-planet systems: general analysis and observed systems |
| title | First-order mean motion resonances in two-planet systems: general analysis and observed systems |
| title_full | First-order mean motion resonances in two-planet systems: general analysis and observed systems |
| title_fullStr | First-order mean motion resonances in two-planet systems: general analysis and observed systems |
| title_full_unstemmed | First-order mean motion resonances in two-planet systems: general analysis and observed systems |
| title_short | First-order mean motion resonances in two-planet systems: general analysis and observed systems |
| title_sort | first order mean motion resonances in two planet systems general analysis and observed systems |
| work_keys_str_mv | AT terquemc firstordermeanmotionresonancesintwoplanetsystemsgeneralanalysisandobservedsystems AT papaloizouj firstordermeanmotionresonancesintwoplanetsystemsgeneralanalysisandobservedsystems |