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1. Dynamics and Origins of the Near-resonant Kepler Planets

   https://doi.org/10.3847/1538-4357/acc9ae  

   Goldberg, Max; Batygin, Konstantin (April 2023, The Astrophysical Journal)

   Abstract Short-period super-Earths and mini-Neptunes encircle more than ∼50% of Sun-like stars and are relatively amenable to direct observational characterization. Despite this, environments in which these planets accrete are difficult to probe directly. Nevertheless, pairs of planets that are close to orbital resonances provide a unique window into the inner regions of protoplanetary disks, as they preserve the conditions of their formation, as well as the early evolution of their orbital architectures. In this work, we present a novel approach toward quantifying transit timing variations within multiplanetary systems and examine the near-resonant dynamics of over 100 planet pairs detected by Kepler. Using an integrable model for first-order resonances, we find a clear transition from libration to circulation of the resonant angle at a period ratio of ≈0.6% wide of exact resonance. The orbital properties of these systems indicate that they systematically lie far away from the resonant forced equilibrium. Cumulatively, our modeling indicates that while orbital architectures shaped by strong disk damping or tidal dissipation are inconsistent with observations, a scenario where stochastic stirring by turbulent eddies augments the dissipative effects of protoplanetary disks reproduces several features of the data. 

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2. Resonant cold scattering of highly vibrationally excited D2 with Ne

   https://doi.org/10.1063/5.0114349  

   Perreault, William E.; Zhou, Haowen; Mukherjee, Nandini; Zare, Richard N. (October 2022, The Journal of Chemical Physics)

   To accurately map weak D2–Ne long-range interactions, we have studied rotationally inelastic cold scattering of D2 prepared in the vibrationally excited (v = 4) and rotationally aligned (j = 2, m) quantum state within the moving frame of a supersonically expanded mixed molecular beam. In contrast to earlier high energy D2–Ne collision experiments, the (j = 2 → j′ = 0) cold scattering produced highly symmetric angular distributions that strongly suggest a resonant quasi-bound collision complex that lives long enough to make a few rotations. Our partial wave analysis indicates that the scattering dynamics is dominated by a single resonant l = 2 orbital, even in the presence of a broad temperature (0–5 K) distribution that allows incoming orbitals up to l = 5. The dominance of a single orbital suggests that the resonant complex stabilizes through the coupling of the internal (j = 2) and orbital (l = 2) angular momentum to produce a total angular momentum of J = 0 for the D2–Ne complex. 

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3. Dissipative Capture of Planets into First-order Mean-motion Resonances

   https://doi.org/10.3847/2041-8213/acc015  

   Batygin, Konstantin; Petit, Antoine C (March 2023, The Astrophysical Journal Letters)

   The emergence of orbital resonances among planets is a natural consequence of the early dynamical evolution of planetary systems. While it is well established that convergent migration is necessary for mean-motion commensurabilities to emerge, recent numerical experiments have shown that the existing adiabatic theory of resonant capture provides an incomplete description of the relevant physics, leading to an erroneous mass scaling in the regime of strong dissipation. In this work, we develop a new model for resonance capture that self-consistently accounts for migration and circularization of planetary orbits, and derive an analytic criterion based upon stability analysis that describes the conditions necessary for the formation of mean-motion resonances. We subsequently test our results against numerical simulations and find satisfactory agreement. Our results elucidate the critical role played by adiabaticity and resonant stability in shaping the orbital architectures of planetary systems during the nebular epoch, and provide a valuable tool for understanding their primordial dynamical evolution. 

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4. Chaotic tides as a solution to the Hyperion problem

   https://doi.org/10.1016/j.icarus.2024.116014  

   Goldberg, Max; Batygin, Konstantin (May 2024, Icarus)

   The dynamics of the outer regular satellites of Saturn are driven primarily by the outward migration of Titan, but several independent constraints on Titan's migration are difficult to reconcile with the current resonant orbit of the small satellite Hyperion. We argue that Hyperion's rapid irregular tumbling greatly increases tidal dissipation with a steep dependence on orbital eccentricity. Resonant excitation from a migrating Titan is then balanced by damping in a feedback mechanism that maintains Hyperion's eccentricity without fine-tuning. The inferred tidal parameters of Hyperion are most consistent with rapid Titan migration enabled by a resonance lock with an internal mode of Saturn, but a scenario with only equilibrium dissipation in Saturn is also possible. 

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5. On the divergence of first-order resonance widths at low eccentricities

   https://doi.org/10.1093/mnras/staa1751  

   Malhotra, Renu; Zhang, Nan (August 2020, Monthly Notices of the Royal Astronomical Society)

   null (Ed.)

   ABSTRACT Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first-order mean motion resonances diverge for nearly circular orbits. Here, we examine the nature of this divergence with a non-perturbative analysis of a few first-order resonances interior to a Jupiter-mass planet. We show that a first-order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centres of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of ‘bridges’ between adjacent first-order resonances: at low eccentricities, the apocentric libration zone of a first-order resonance smoothly connects with the pericentric libration zone of the neighbouring first-order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low-eccentricity regime. 

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