2015/05/07 by Konstantin Batygin, Batygin, Konstantin · 3 citations
Physics and Astronomy · #Astro and Planetary Science #Astrophysics and Star Formation Studies #Dynamical Systems (math.DS) #Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Mathematics #FOS: Physical sciences #Stellar, planetary, and galactic studies
paper · pdf · doi:10.48550/arxiv.1505.01778
openalex publication_date 2015/05/07 · openalex created_date 2022/08/05 · openalex updated_date 2026/07/28
The early stages of dynamical evolution of planetary systems are often shaped\nby dissipative processes that drive orbital migration. In multi-planet systems,\nconvergent amassing of orbits inevitably leads to encounters with rational\nperiod ratios, which may result in establishment of mean motion resonances. The\nsuccess or failure of resonant capture yields exceedingly different subsequent\nevolutions, and thus plays a central role in determining the ensuing orbital\narchitecture of planetary systems. In this work, we employ an integrable\nHamiltonian formalism for first order planetary resonances that allows both\nsecondary bodies to have finite masses and eccentricities, and construct a\ncomprehensive theory for resonant capture. Particularly, we derive conditions\nunder which orbital evolution lies within the adiabatic regime, and provide a\ngeneralized criterion for guaranteed resonant locking as well as a procedure\nfor calculating capture probabilities when capture is not certain.\nSubsequently, we utilize the developed analytical model to examine the\nevolution of Jupiter and Saturn within the protosolar nebula, and investigate\nthe origins of the dominantly non-resonant orbital distribution of sub-Jovian\nextrasolar planets. Our calculations show that the commonly observed extrasolar\norbital structure can be understood if planet pairs encounter mean motion\ncommensurabilities on slightly eccentric (e~0.02) orbits. Accordingly, we\nspeculate that resonant capture among low-mass planets is typically rendered\nunsuccessful due to subtle axial asymmetries inherent to the global structure\nof protoplanetary disks.\n