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1. 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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2. Kepler-discovered Multiple-planet Systems near Period Ratios Suggestive of Mean-motion Resonances Are Young

   https://doi.org/10.3847/1538-3881/ad110e  

   Hamer, Jacob H.; Schlaufman, Kevin C. (January 2024, The Astronomical Journal)

   Abstract Before the launch of the Kepler Space Telescope, models of low-mass planet formation predicted that convergent type I migration would often produce systems of low-mass planets in low-order mean-motion resonances. Instead, Kepler discovered that systems of small planets frequently have period ratios larger than those associated with mean-motion resonances and rarely have period ratios smaller than those associated with mean-motion resonances. Both short-timescale processes related to the formation or early evolution of planetary systems and long-timescale secular processes have been proposed as explanations for these observations. Using a thin disk stellar population’s Galactic velocity dispersion as a relative age proxy, we find that Kepler-discovered multiple-planet systems with at least one planet pair near a period ratio suggestive of a second-order mean-motion resonance have a colder Galactic velocity dispersion and are therefore younger than both single-transiting and multiple-planet systems that lack planet pairs consistent with mean-motion resonances. We argue that a nontidal secular process with a characteristic timescale no less than a few hundred Myr is responsible for moving systems of low-mass planets away from second-order mean-motion resonances. Among systems with at least one planet pair near a period ratio suggestive of a first-order mean-motion resonance, only the population of systems likely affected by tidal dissipation inside their innermost planets has a small Galactic velocity dispersion and is therefore young. We predict that period ratios suggestive of mean-motion resonances are more common in young systems with 10 Myr ≲τ≲ 100 Myr and become less common as planetary systems age. 

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3. Non-perturbative investigation of low-eccentricity exterior mean motion resonances

   https://doi.org/10.1093/mnras/stad483  

   Malhotra, Renu; Chen, Zherui (March 2023, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT Mean motion resonances are important in the analysis and understanding of the dynamics of planetary systems. While perturbative approaches have been dominant in many previous studies, recent non-perturbative approaches have revealed novel properties in the low-eccentricity regime for interior mean motion resonances of Jupiter in the fundamental model of the circular planar restricted three-body model. Here, we extend the non-perturbative investigation to exterior mean motion resonances in the low-eccentricity regime (up to about 0.1) and for perturber mass in the range of ∼5 × 10−5 to 1 × 10−3 (in units of the central mass). Our results demonstrate that first-order exterior resonances have two branches at low eccentricity as well as low-eccentricity bridges connecting neighbouring first-order resonances. With increasing perturber mass, higher order resonances dissolve into chaos, whereas low-order resonances persist with larger widths in their radial extent but smaller azimuthal widths. For low-order resonances, we also detect secondary resonances arising from small-integer commensurabilities between resonant librations and the synodic frequency. These secondary resonances contribute significantly to generating the chaotic sea that typically occurs near mean motion resonances of higher mass perturbers. 

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4. New results on orbital resonances

   https://doi.org/10.48550/arXiv.2111.09289  

   Malhotra, Renu (September 2022, Proceedings of the International Astronomical Union)

   Celletti, Alessandra; Beaugé, Cristian; Galeş, Cătălin; Lemaître, Anne (Ed.)

   Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called ``low-eccentricity resonant bridges" connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some -- though not necessarily entire -- resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase space structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances. 

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5. An In-Situ Formation Model for Systems of Tightly-Packed Inner Planets

   Wallace, S.; Quinn, T. (April 2022, Bulletin of the American Astronomical Society)

   Using high-resolution N-body simulations, we investigate the outcome of terrestrial planet formation at short (< 100 day) orbital periods under a migration-free model. The collisional and dynamical evolution of systems of nearly 106 self-interacting planetesimals are directly followed through the final planet assembly phase. This is done by first modeling the planetesimal evolution with the tree-based N-body code ChaNGa, and then passing the results to the hybrid-symplectic N-body code genga, once the particle count has dropped sufficiently. Previously, we showed that oligarchic growth fails to operate at arbitrarily short orbital periods. This leaves a distinct feature in the mass and orbital distribution of the planetary embryos. In this most recent work, we explore whether this boundary between oligarchic and non-oligarchic growth leaves any kind of imprint on the terrestrial planets that form. If so, this would provide an important clue to evaluate whether migration played a significant role in shaping the architecture systems of tightly-packed inner planets. 

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