Conditions for Convergent Migration of N-Planet Systems

Beaugé, C.; Cerioni, M.

doi:10.1007/s10569-022-10113-4

Cited by 4 publications

(2 citation statements)

References 37 publications

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“…( 21) leads to a slope of 1.34. We excluded the 2:1 resonance from the trend analysis due to its unique dynamics (Beauge 1994). We fitted Σ (k+1:k) tr as described in Sect.…”

Section: Transition Surface Density σ Tr As a Function Of The Resonan...mentioning

confidence: 99%

Mean motion resonance capture in the context of type I migration

Kajtazi

Petit

Johansen

2023

A&A

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Capture into mean motion resonance (MMR) is an important dynamical mechanism as it shapes the final architecture of a planetary system. We simulate systems of two or three planets undergoing migration with varied initial parameters such as planetary mass and disk surface density and analyse the resulting resonant chains. In contrast to previous studies, our results show that the disk properties have the dominant impact on capture into mean motion resonance, while the total planetary mass barely affects the final system configuration as long as the planet does not open a gap in the disk. We confirm that the adiabatic resonant capture is the correct framework to understand the conditions leading to MMR formation, since its predictions are qualitatively similar to the numerical results. However, we find that the eccentricity damping can facilitate the capture in a given resonance. We find that under typical disk conditions, planets tend to be captured into 2:1 or 3:2 MMRs, which agrees well with the observed exoplanet MMRs. Our results predict two categories of systems: those that have uniform chains of wide resonances (2:1 or 3:2 MMRs) and those that have a more compact inner pair than the outer pair such as 4:3:2 chains. Both categories of resonant chains are present in observed exoplanet systems. On the other hand, chains with a wider inner pair than the outer one are very rare and emerge from stochastic capture. Our work here can be used to link current configuration of exoplanetary systems to the formation conditions within protoplanetary disks.

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“…( 21) leads to a slope of 1.34. We excluded the 2:1 resonance from the trend analysis due to its unique dynamics (Beauge 1994). We fitted Σ (k+1:k) tr as described in Sect.…”

Section: Transition Surface Density σ Tr As a Function Of The Resonan...mentioning

confidence: 99%

Mean motion resonance capture in the context of type I migration

Kajtazi

Petit

Johansen

2023

A&A

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“…For instance, a new resonance island may emerge at very high eccentricity in the planar circular restricted three-body model (e.g. Beauge 1994;Lan & Malhotra 2019), while in the non-planar case, very high inclination may introduce significant distortion to asymmetric islands (e.g. Gallardo 2006Gallardo , 2020Saillenfest et al 2016;Efimov & Sidorenko 2020).…”

Section: Introductionmentioning

confidence: 99%

Asymmetric capture into Neptunian 1:2 resonance

Li,

Zhou

2023

A&A

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The asymmetric resonance configuration characterised by the critical angle librating around centres other than 0° or 180° is found in the 1:N mean motion resonance. The asymmetric 1:2 resonance with Neptune is of particular interest because the two asymmetric islands seem to host different populations, and this might be a direct clue to understanding the early evolution of the Solar System. The asymmetry has been investigated from both observational and theoretical perspectives, but conclusions among studies vary widely. In this paper, using toy models, we carefully designed a series of tests to systematically study the capture of planetesimals into the leading and trailing resonance islands. Although these tests may not exactly reproduce the real processes the Solar System experienced, they reveal some typical dynamics in the resonance capture. Since the real Twotinos have small to moderate inclinations, as a first attempt, we adopted planar models in this paper in order to investigate the mechanisms that may lead to asymmetric capture by the leading and trailing islands, including their size variation during the outward migration of Neptune, the stickiness of the leading island, and the migration slowdown effect. We find that the ratio between the populations of the leading and trailing islands can be easily tuned by introducing the slowdown effect into the migration model, and thus it may not be a good tracer of the migration history. However, the eccentricity of objects trapped in two asymmetric islands may conserve some valuable information of the early evolution of the Solar System.

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Resonant chains in triple-planet systems

Wang,

Zhou,

Beaugé

2024

A&A

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The mean motion resonance is the most important mechanism that may dominate the dynamics of a planetary system. In a multi-planetary system consisting of $N planets, the planets may form a resonant chain when the ratios of orbital periods of planets can be expressed as the ratios of small integers $T_1: T_2: :T_N=k_1: k_2: k_N$. Due to the high degree of freedom, the motion in such systems could be complex and difficult to depict. In this paper, we investigate the dynamics and possible formation of the resonant chain in a triple-planet system. We defined the appropriate Hamiltonian for a three-planet resonant chain and numerically averaged it over the synodic period. The stable stationary solutions -- apsidal corotational resonances (ACRs) -- of this averaged system, corresponding to the local extrema of the Hamiltonian function, can be searched out numerically. The topology of the Hamiltonian around these ACRs reveals their stabilities. We further constructed the dynamical maps on different representative planes to study the dynamics around the stable ACRs, and we calculated the deviation ($ of the resonant angle in the evolution from the uniformly distributed values, by which we distinguished the behaviour of critical angles. Finally, the formation of the resonant chain via convergent planetary migration was simulated and the stable configurations associated with ACRs were verified. We find that the stable ACR families arising from circular orbits always exist for any resonant chain, and they may extend to a high eccentricity region. Around these ACR solutions, regular motion can be found, typically in two types of resonant configurations. One is characterised by libration of both the two-body resonant angles and the three-body Laplace resonant angle, and the other by libration of only two-body resonant angles. The three-body Laplace resonance does not seem to contribute to the stability of the resonant chain much. The resonant chain can be formed via convergent migration, and the resonant configuration evolves along the ACR families to eccentric orbits once the planets are captured into the chain. Ideally, our methods introduced in this paper can be applied to any resonant chain of any number of planets at any eccentricity.

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Conditions for Convergent Migration of N-Planet Systems

Cited by 4 publications

References 37 publications

Mean motion resonance capture in the context of type I migration

Mean motion resonance capture in the context of type I migration

Asymmetric capture into Neptunian 1:2 resonance

Resonant chains in triple-planet systems

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