Semianalytical model for planetary resonances

Gallardo, Tabaré; Beaugé, C.; Giuppone, C. A.

doi:10.1051/0004-6361/202039764

“…a p ∼ 0.35 AU). Radius, period, and coplanarity values are affected by observational biases (Martin E-mail: egianuzzi@mi.unc.edu There is some evidence that the N/1 mean motion resonances (MMRs) are related to the planetary parking location and their evolution in the disc, as they lead to strong regions of chaos around the binaries (Gallardo et al 2021). For example, Zoppetti et al (2018) applied a simplified model to Kepler-38 and suggested a capture in 5/1 MMR with subsequent tidal evolution of the planet outside MMRs.…”

Section: Introductionmentioning

confidence: 99%

Circumbinary planets: migration, trapping in mean-motion resonances, and ejection

Gianuzzi

¹

,

Giuppone

²

,

Cuello

³

2023

A&A

View full text Add to dashboard Cite

Context. Most of the planetary systems discovered around binary stars are located at approximately three semi-major axes from the barycentre of their system, curiously close to low-order mean-motion resonances (MMRs). The formation mechanism of these circumbinary planets is not yet fully understood. In situ formation is extremely challenging because of the strong interaction with the binary. One possible explanation is that, after their formation, the interactions between these planets and the surrounding protoplanetary disc cause them to migrate at velocities dependent on the nature of the disc and the mass of the exoplanet. Although extensive data can be obtained with direct hydrodynamical simulations, their computational cost remains too high. On the other hand, the direct n-body simulations approach allows us to model a large variety of parameters at much lower cost. Aims. We analyse the planetary migration around a wide variety of binary stars using Stokes-like forces that mimic planetary migration at a constant rate. Our goal is to identify the main parameters responsible for the ejection of planets at different resonances with the inner binary. Methods. We performed 4200 n-body simulations with Stokes-like forces and analysed their evolution and outcome as a function of the properties of each system. For each simulated exoplanet, we applied an ensemble learning method for classification in order to clarify the relationship between the inspected parameters and the process of MMR capture. Results. We identify the capture probability for different N/1 MMRs, 4/1 being the most prone to capture exoplanets, with 37% probability, followed by MMR 5/1 with ∼ 23% of probability. The eccentricity of the binary is found to be the most important parameter in determining the MMR capture of each circumbinary exoplanet, followed by the mass ratio of the binary and the initial eccentricity of the planet.

show abstract

“…Lithwick & Wu 2008a;Cheng et al 2014b;Woo & Lee 2018;Kenyon & Bromley 2021), which are considered to be strongest around binaries (e.g. Cuello & Giuppone 2019;Gallardo et al 2021). However, Lithwick & Wu (2008b) found some difficulties in adjusting the values of Charon's eccentricity, e C : in order to safely transport Nix to the 4/1 MMR, it should be e C < 0.024, while in order to transport Hydra to the 6/1 MMR, it should be e C > 0.04.…”

Section: Introductionmentioning

confidence: 99%

Past and present dynamics of the circumbinary moons in the Pluto-Charon system

Giuppone

¹

,

Rodríguez

²

,

Michtchenko

³

et al. 2022

A&A

Self Cite

View full text Add to dashboard Cite

Context. The Pluto-Charon (PC) pair is usually thought of as a binary in a dual synchronous state, which is the endpoint of its tidal evolution. The discovery of the small circumbinary moons, Styx, Nix, Kerberos, and Hydra, placed close to the mean motion resonances (MMRs) 3/1, 4/1, 5/1, and 6/1 with Charon, respectively, reveals a complex dynamical system architecture. Several formation mechanisms for the PC system have been proposed. Aims. Assuming the hypothesis of an in situ formation of the moons, our goal is to analyse the past and current orbital dynamics of the satellite system. We plan to elucidate on in which scenario the small moons can survive a rapid tidal expansion of the PC binary. Methods. We study the past and current dynamics of the PC system through a large set of numerical integrations of the exact equations of motion, accounting for the gravitational interactions of the PC binary with the small moons and the tidal evolution, modelled by the constant time lag approach. We construct stability maps in a pseudo-Jacobian coordinate system. In addition, considering a more realistic model that accounts for the zonal harmonic, J2, of Pluto’s oblateness and the ad hoc accreting mass of Charon, we investigate the tidal evolution of the whole system. Results. Our results show that, in the chosen reference frame, the current orbits of all satellites are nearly circular, nearly planar, and nearly resonant with Charon, which can be seen as an indicator of the convergent dissipative migration experienced by the system in the past. We verify that, under the assumption that Charon completes its formation during the tidal expansion, the moons can safely cross the main MMRs without their motions being strongly excited and consequently ejected. Conclusions. In the more realistic scenario proposed here, the small moons survive the tidal expansion of the PC binary without the hypothesis of resonant transport having to be invoked. Our results indicate that the possibility of finding additional small moons in the PC system cannot be ruled out.

show abstract

“…There is some evidence that the N/1 mean motion resonances (MMRs) are related to the planetary parking location and their evolution in the disc, as they lead to strong regions of chaos around the binaries (Gallardo et al 2021). For example, Zoppetti et al (2018) applied a simplified model to Kepler-38 and suggested a capture in 5/1 MMR with subsequent tidal evolution of the planet outside MMRs.…”

Section: Introductionmentioning

confidence: 99%

Circumbinary planets: migration, trapping in mean-motion resonances, and ejection

Gianuzzi¹,

Giuppone²,

Cuello³

2022

Preprint

0

View full text Add to dashboard Cite

Context. Most of the planetary systems discovered around binary stars are located at approximately three semi-major axes from the barycentre of their system, curiously close to low-order mean-motion resonances (MMRs). The formation mechanism of these circumbinary planets is not yet fully understood. In situ formation is extremely challenging because of the strong interaction with the binary. One possible explanation is that, after their formation, the interactions between these planets and the surrounding protoplanetary disc cause them to migrate at velocities dependent on the nature of the disc and the mass of the exoplanet. Although extensive data can be obtained with direct hydrodynamical simulations, their computational cost remains too high. On the other hand, the direct n-body simulations approach allows us to model a large variety of parameters at much lower cost. Aims. We analyse the planetary migration around a wide variety of binary stars using Stokes-like forces that mimic planetary migration at a constant rate. Our goal is to identify the main parameters responsible for the ejection of planets at different resonances with the inner binary. Methods. We performed 4200 n-body simulations with Stokes-like forces and analysed their evolution and outcome as a function of the properties of each system. For each simulated exoplanet, we applied an ensemble learning method for classification in order to clarify the relationship between the inspected parameters and the process of MMR capture. Results. We identify the capture probability for different N/1 MMRs, 4/1 being the most prone to capture exoplanets, with 37% probability, followed by MMR 5/1 with ∼ 23% of probability. The eccentricity of the binary is found to be the most important parameter in determining the MMR capture of each circumbinary exoplanet, followed by the mass ratio of the binary and the initial eccentricity of the planet.

show abstract

Semianalytical model for planetary resonances

Cited by 13 publications

References 59 publications

Circumbinary planets: migration, trapping in mean-motion resonances, and ejection

Circumbinary planets: migration, trapping in mean-motion resonances, and ejection

Past and present dynamics of the circumbinary moons in the Pluto-Charon system

Circumbinary planets: migration, trapping in mean-motion resonances, and ejection

Contact Info

Product

Resources

About