2018/09/26 by Caroline Terquem, J. C. B. Papaloizou, John Papaloizou · 30 citations
Physics and Astronomy · #Astro and Planetary Science #Astrophysics #Astrophysics and Star Formation Studies #Atomic physics #Celestial mechanics #Function (biology) #Mean motion #Order (exchange) #Physics #Planet #Planetary system #Resonance (particle physics) #Stellar, planetary, and galactic studies #astro-ph.EP
paper · pdf · open access · doi:10.1093/mnras/sty2693
published in Monthly Notices of the Royal Astronomical Society 482(1), 530-549 (Oxford University Press) · Accepted for publication in MNRAS
arxiv created 2018/09/26 · openalex publication_date 2018/10/03 · arxiv updated 2018/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper focuses on two-planet systems in a first-order (q + 1)|\colon|q mean motion resonance and undergoing type-I migration 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.