A criterion for the stability of planets in chains of resonances

Goldberg, Max; Batygin, Konstantin; Morbidelli, Alessandro

doi:10.1016/j.icarus.2022.115206

Cited by 20 publications

(15 citation statements)

References 40 publications

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“…where λ is as given at the beginning of the section and the period ratio of the two planets is p/q (ex: Wang & Malhotra 2017). The composite two-body resonance angle, which reduces the full Hamiltonian to one degree of freedom (as used in Batygin 2015; Petit et al 2020;Goldberg et al 2022), is given by Equation (39) in Laune et al (2022) to be f e f e f e f e tan sin sin cos cos 4…”

Section: Two-body Resonancesmentioning

confidence: 99%

“…where coefficients f 1 and f 2 vary depending on the values of coefficients p and q (see Table 1 of Deck et al 2013). This angle is called the "mixed" resonant angle in Goldberg et al (2022). In multiplanet systems, libration of the angles given in Equations (2) and (3) denotes a two-body MMR.…”

Section: Two-body Resonancesmentioning

confidence: 99%

“…In multiplanet systems, libration of the angles given in Equations (2) and (3) denotes a two-body MMR. However, as discussed in Goldberg et al (2022), planets can still be in two- body resonance even if the angles given by Equations (2) and…”

Section: Two-body Resonancesmentioning

confidence: 99%

“…However, due to uncertainties in the TTV fit, it is possible that the phase space populated by the TTV solutions does not include the true orbits of the planets. Additionally, the formula given in Equation (4), which we used to check the resonant state of the system, was derived from the partial two-planet Hamiltonian (Equation (1) of Goldberg et al 2022). An interesting avenue for future work would be to derive the full mixed angle for a five-planet system and determine if that angle shows any evidence of libration for the Kepler-80 planets.…”

Section: Two-body Resonancesmentioning

confidence: 99%

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Kepler-80 Revisited: Assessing the Participation of a Newly Discovered Planet in the Resonant Chain

Weisserman

Becker

Vanderburg

2023

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In this paper, we consider the chain of resonances in the Kepler-80 system and evaluate the impact that the additional member of the resonant chain discovered by Shallue & Vanderburg has on the dynamics of the system and the physical parameters that can be recovered by a fit to the transit timing variations (TTVs). Ultimately, we calculate the mass of Kepler-80 g to be 0.8 ± 0.3M ⊕ when assuming all planets have zero eccentricity, and 1.0 ± 0.3 M ⊕ when relaxing that assumption. We show that the outer five planets are in successive three-body mean-motion resonances (MMRs). We assess the current state of two-body MMRs in the system and find that the planets do not appear to be in two-body MMRs. We find that while the existence of the additional member of the resonant chain does not significantly alter the character of the Kepler-80 three-body MMRs, it can alter the physical parameters derived from the TTVs, suggesting caution should be applied when drawing conclusions from TTVs for potentially incomplete systems. We also compare our results to those of MacDonald et al., who perform a similar analysis on the same system with a different method. Although the results of this work and MacDonald et al. show that different fit methodologies and underlying assumptions can result in different measured orbital parameters, the most secure conclusion is that which holds true across all lines of analysis: Kepler-80 contains a chain of planets in three-body MMRs but not in two-body MMRs.

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Section: Two-body Resonancesmentioning

confidence: 99%

Section: Two-body Resonancesmentioning

confidence: 99%

Section: Two-body Resonancesmentioning

confidence: 99%

Section: Two-body Resonancesmentioning

confidence: 99%

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Kepler-80 Revisited: Assessing the Participation of a Newly Discovered Planet in the Resonant Chain

Weisserman

Becker

Vanderburg

2023

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“…Despite their extant and inferred prevalence, mean-motion resonances do not arise as an innate byproduct of the planet formation process itself. Instead, they are established as a consequence of orbital convergence facilitated by dissipative effects (Goldreich 1965;Henrard 1982). Within protoplanetary nebulae, this occurs naturally due to planet-disk interactions (i.e., type I migration; Goldreich & Tremaine 1980;Ward 1997) -particularly in the inner regions of disks, where magnetospheric cavities create bona fide traps for planetary orbits (Masset et al 2006).…”

Section: Introductionmentioning

confidence: 99%

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

Batygin

Petit

2023

ApJL

Self Cite

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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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Dynamical stability of the Laplace resonance

Pucacco

2024

Celest Mech Dyn Astron

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A criterion for the stability of planets in chains of resonances

Cited by 20 publications

References 40 publications

Kepler-80 Revisited: Assessing the Participation of a Newly Discovered Planet in the Resonant Chain

Kepler-80 Revisited: Assessing the Participation of a Newly Discovered Planet in the Resonant Chain

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

Dynamical stability of the Laplace resonance

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