Analytical theories for near coplanar and polar circumbinary orbits

Li, Daohai; Zhou, Jingjing; Zhang, Hui

doi:10.1093/mnras/stt2181

Cited by 18 publications

(19 citation statements)

References 34 publications

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“…This allowed for the inclusion of the various non-Keplerian orbital effect found in circumbinary systems (e.g. Leung 2013; Li et al 2013). The planets were put in orbits coplanar with the binaries on periods of 10.2 P bin and 300 d. These were made slightly eccentric (e=0.05, with a uniform distribution of argument of periapsis between 0 and 2π) so that the additional TTVs which eccentricity may bring were not excluded.…”

Section: Transit Injectionsmentioning

confidence: 99%

On the abundance of circumbinary planets

Armstrong

Osborn

Brown

et al. 2014

Monthly Notices of the Royal Astronomical Society

150

162

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We present here the first observationally based determination of the rate of occurrence of circumbinary planets. This is derived from the publicly available Kepler data, using an automated search algorithm and debiasing process to produce occurrence rates implied by the seven systems already known. These rates depend critically on the planetary inclination distribution: if circumbinary planets are preferentially coplanar with their host binaries, as has been suggested, then the rate of occurrence of planets with R p > 6R ⊕ orbiting with P p < 300 d is 10.0 +18 −6.5 % (95% confidence limits), higher than but consistent with single star rates. If on the other hand the underlying planetary inclination distribution is isotropic, then this occurrence rate rises dramatically, to give a lower limit of 47%. This implies that formation and subsequent dynamical evolution in circumbinary disks must either lead to largely coplanar planets, or proceed with significantly greater ease than in circumstellar disks. As a result of this investigation we also show that giant planets (>10R ⊕ ) are significantly less common in circumbinary orbits than their smaller siblings, and confirm that the proposed shortfall of circumbinary planets orbiting the shorter period binaries in the Kepler sample is a real effect.

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Section: Transit Injectionsmentioning

confidence: 99%

On the abundance of circumbinary planets

Armstrong

Osborn

Brown

et al. 2014

Monthly Notices of the Royal Astronomical Society

150

162

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“…7. However, maybe because of the fast precession of induced by the binary (see Farago & Laskar 2010;Li et al 2014), closer resonances are unstable (3/1 and 4/1). In contrast to the planetary case, we identify that regions inside of the stronger N/1 MMRs are chaotic (mainly observed in MMR 3/1 and 4/1).…”

Section: Coplanar Circumbinary Planetsmentioning

confidence: 99%

“…The dynamics of CB inclined planets at these distances leads to circulation of because of the interaction with the binary. Moreover, outside the nodal resonances, the node Ω circulates (Farago & Laskar 2010;Doolin & Blundell 2011;Li et al 2014). Our model calculates the width of the resonance for a fixed value of and Ω, and we analyzed the dependence of widths for different values from 0 • to 180 • .…”

Section: Inclined Circumbinary Planetsmentioning

confidence: 99%

Semianalytical model for planetary resonances

Gallardo

Beaugé

Giuppone

2021

A&A

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Context. Planetary resonances are a common dynamical mechanism acting on planetary systems. However, no general model for describing their properties exists, particularly for commensurabilities of any order and arbitrary eccentricity and inclination values. Aims. We present a semianalytical model that describes the resonance strength, width, location and stability of fixed points, and periods of small-amplitude librations. The model is valid for any two gravitationally interacting massive bodies, and is thus applicable to planets around single or binary stars. Methods. Using a theoretical framework in the Poincaré and Jacobi reference system, we developed a semianalytical method that employs a numerical evaluation of the averaged resonant disturbing function. Validations of the model are presented that compare its predictions with dynamical maps for real and fictitious systems. Results. The model describes many dynamical features of planetary resonances very well. Notwithstanding the good agreement found in all cases, a small deviation is noted in the location of the resonance centers for circumbinary systems. As a consequence of its application to the HD 31527 system, we found that the updated best-fit solution leads to a high-eccentricity stable libration between the middle and outer planets inside the 16/3 mean-motion resonance (MMR). This is the first planetary system whose long-term dynamics appears dominated by such a high-order commensurability. In the case of circumbinary planets, the overlap of N/1 mean-motion resonances coincides very well with the size of the global chaotic region close to the binary, as well as its dependence on the mutual inclination.

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“…7. However, maybe because the fast precession of induced by the binary (see Farago & Laskar 2010;Li et al 2014), closer resonances are unstable (3/1 and 4/1). Contrary to planetary case, we identify that regions inside of the stronger N/1 MMRs are chaotic (mainly observed in MMR 3/1, 4/1).…”

Section: Coplanar Circumbinary Planetsmentioning

confidence: 99%

“…The dynamics of CB inclined planets at these distances leads to circulation of because the interaction with the binary. Also, outside the nodal resonances, the node Ω circulates (Farago & Laskar 2010;Doolin & Blundell 2011;Li et al 2014). Our model calculates the width of the resonance for a fixed value of and Ω and we analyze the dependency of widths for different values from 0 • to 180 • .…”

Section: Inclined Circumbinary Planetsmentioning

confidence: 99%

Semi-analytical model for planetary resonances: application to planets around single and binary stars

Gallardo,

Beaugé,

Giuppone

2020

Preprint

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Context. In spite of planetary resonances being a common dynamical mechanism acting on planetary systems, no general model exists for describing their properties, particularly for commensurabilities of any order and arbitrary values of the eccentricities and inclinations. Aims. The present work presents a semi-analytical model that describes the resonance strength, width, location and stability of fixed points, as well as periods of small-amplitude librations. The model is valid to any two gravitationally interacting massive bodies, and thus applicable to planets around single or binary stars. Methods. Using a theoretical framework in Poincaré and Jacobi reference system we develop a semi-analytical method that employs a numerical evaluation of the averaged resonant disturbing function. Validations of the model are presented comparing its predictions with dynamical maps for real and fictitious systems.Results. The model is shown to describe very well many dynamical features of planetary resonances. Notwithstanding the good agreements found in all cases, a small deviation is noted in the location of the resonance centers for circumbinary systems. As a consequence of its application to the HD31527 system we have found that the updated best-fit solution leads to a high-eccentricity stable libration between the middle and outer planets inside the 16/3 mean-motion resonance. This is the first planetary system whose long-term dynamics appears dominated by such a high-order commensurability. In the case of circumbinary planets, the overlap of N/1 mean-motion resonances coincides very well with the size of the global chaotic region close to the binary, as well as its dependence with the mutual inclination.

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Analytical theories for near coplanar and polar circumbinary orbits

Cited by 18 publications

References 34 publications

On the abundance of circumbinary planets

On the abundance of circumbinary planets

Semianalytical model for planetary resonances

Semi-analytical model for planetary resonances: application to planets around single and binary stars

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