Exploiting periodic orbits as dynamical clues for Kepler and K2 systems

Kyriaki I. Antoniadou; Anne Sophie Libert

doi:10.1051/0004-6361/202037779

Exploiting periodic orbits as dynamical clues for Kepler and K2 systems

Kyriaki I. Antoniadou, Anne Sophie Libert

University of Namur

Research output: Contribution to journal › Article › peer-review

Abstract

Aims. Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital parameters of the systems, but suffers from observational limitations. When a (near-)resonant planetary system resides in the dynamical neighbourhood of a stable periodic orbit, its long-term stability, and thus survival, can be guaranteed. We use the intrinsic property of the periodic orbits, namely their linear horizontal and vertical stability, to validate or further constrain the orbital elements of detected two-planet systems. Methods. We computed the families of periodic orbits in the general three-body problem for several two-planet Kepler and K2 systems. The dynamical neighbourhood of the systems is unveiled with maps of dynamical stability. Results. Additional validations or constraints on the orbital elements of K2-21, K2-24, Kepler-9, and (non-coplanar) Kepler-108 near-resonant systems were achieved. While a mean-motion resonance locking protects the long-term evolution of the systems K2-21 and K2-24, such a resonant evolution is not possible for the Kepler-9 system, whose stability is maintained through an apsidal anti-alignment. For the Kepler-108 system, we find that the stability of its mutually inclined planets could be justified either solely by a mean-motion resonance, or in tandem with an inclination-type resonance. Going forward, dynamical analyses based on periodic orbits could yield better constrained orbital elements of near-resonant extrasolar systems when performed in parallel to the fitting of the observational data.

Original language	English
Article number	A55
Number of pages	10
Journal	Astronomy and Astrophysics
Volume	640
DOIs	https://doi.org/10.1051/0004-6361/202037779
Publication status	Published - 1 Aug 2020

Funding

Acknowledgements. We thank the anonymous reviewer whose remarks helped us improve our manuscript. The research of KIA is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme \u201CHuman Resources Development, Education and Lifelong Learning\u201D in the context of the project \u201CReinforcement of Postdoctoral Researchers \u2013 2nd Cycle\u201D (MIS-5033021), implemented by the State Scholarships Foundation (IKY). This work was supported by the Fonds de la Recherche Scientifique \u2013 FNRS under Grant No. F.4523.20 (DYNAMITE MIS-project). Computational resources have been provided by the Consortium des \u00C9quipements de Calcul Intensif, supported by the FNRS-FRFC, the Walloon Region, and the University of Namur (Conventions No. 2.5020.11, GEQ U.G006.15, 1610468 et RW/GEQ2016).

Funders	Funder number
FNRS‐FRFC
European Commission
Fonds de la Recherche Scientifique F.R.S.-FNRS
University of Namur	1610468, 2.5020.11, RW/GEQ2016, GEQ U.G006.15
UK Research and Innovation	45364
European Social Fund	MIS-5033021

Keywords

Celestial mechanics
Chaos
Methods: Analytical
Methods: Numerical
Planetary systems
Planets and satellites: dynamical evolution and stability

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10.1051/0004-6361/202037779

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@article{a1c54de1ce9446ea8ddf5b108b2053a7,

title = "Exploiting periodic orbits as dynamical clues for Kepler and K2 systems",

abstract = "Aims. Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital parameters of the systems, but suffers from observational limitations. When a (near-)resonant planetary system resides in the dynamical neighbourhood of a stable periodic orbit, its long-term stability, and thus survival, can be guaranteed. We use the intrinsic property of the periodic orbits, namely their linear horizontal and vertical stability, to validate or further constrain the orbital elements of detected two-planet systems. Methods. We computed the families of periodic orbits in the general three-body problem for several two-planet Kepler and K2 systems. The dynamical neighbourhood of the systems is unveiled with maps of dynamical stability. Results. Additional validations or constraints on the orbital elements of K2-21, K2-24, Kepler-9, and (non-coplanar) Kepler-108 near-resonant systems were achieved. While a mean-motion resonance locking protects the long-term evolution of the systems K2-21 and K2-24, such a resonant evolution is not possible for the Kepler-9 system, whose stability is maintained through an apsidal anti-alignment. For the Kepler-108 system, we find that the stability of its mutually inclined planets could be justified either solely by a mean-motion resonance, or in tandem with an inclination-type resonance. Going forward, dynamical analyses based on periodic orbits could yield better constrained orbital elements of near-resonant extrasolar systems when performed in parallel to the fitting of the observational data. ",

keywords = "Celestial mechanics, Chaos, Methods: Analytical, Methods: Numerical, Planetary systems, Planets and satellites: dynamical evolution and stability",

author = "Antoniadou, {Kyriaki I.} and Libert, {Anne Sophie}",

note = "Funding Information: Acknowledgements. We thank the anonymous reviewer whose remarks helped us improve our manuscript. The research of KIA is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme “Human Resources Development, Education and Lifelong Learning” in the context of the project “Reinforcement of Postdoctoral Researchers – 2nd Cycle” (MIS-5033021), implemented by the State Scholarships Foundation (IKY). This work was supported by the Fonds de la Recherche Scientifique – FNRS under Grant No. F.4523.20 (DYNAMITE MIS-project). Computational resources have been provided by the Consortium des {\'E}quipements de Calcul Intensif, supported by the FNRS-FRFC, the Walloon Region, and the University of Namur (Conventions No. 2.5020.11, GEQ U.G006.15, 1610468 et RW/GEQ2016). Publisher Copyright: {\textcopyright} ESO 2020.",

year = "2020",

month = aug,

day = "1",

doi = "10.1051/0004-6361/202037779",

language = "English",

volume = "640",

journal = "Astronomy and Astrophysics",

issn = "0004-6361",

publisher = "EDP Sciences",

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T1 - Exploiting periodic orbits as dynamical clues for Kepler and K2 systems

AU - Antoniadou, Kyriaki I.

AU - Libert, Anne Sophie

N1 - Funding Information: Acknowledgements. We thank the anonymous reviewer whose remarks helped us improve our manuscript. The research of KIA is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme “Human Resources Development, Education and Lifelong Learning” in the context of the project “Reinforcement of Postdoctoral Researchers – 2nd Cycle” (MIS-5033021), implemented by the State Scholarships Foundation (IKY). This work was supported by the Fonds de la Recherche Scientifique – FNRS under Grant No. F.4523.20 (DYNAMITE MIS-project). Computational resources have been provided by the Consortium des Équipements de Calcul Intensif, supported by the FNRS-FRFC, the Walloon Region, and the University of Namur (Conventions No. 2.5020.11, GEQ U.G006.15, 1610468 et RW/GEQ2016). Publisher Copyright: © ESO 2020.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - Aims. Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital parameters of the systems, but suffers from observational limitations. When a (near-)resonant planetary system resides in the dynamical neighbourhood of a stable periodic orbit, its long-term stability, and thus survival, can be guaranteed. We use the intrinsic property of the periodic orbits, namely their linear horizontal and vertical stability, to validate or further constrain the orbital elements of detected two-planet systems. Methods. We computed the families of periodic orbits in the general three-body problem for several two-planet Kepler and K2 systems. The dynamical neighbourhood of the systems is unveiled with maps of dynamical stability. Results. Additional validations or constraints on the orbital elements of K2-21, K2-24, Kepler-9, and (non-coplanar) Kepler-108 near-resonant systems were achieved. While a mean-motion resonance locking protects the long-term evolution of the systems K2-21 and K2-24, such a resonant evolution is not possible for the Kepler-9 system, whose stability is maintained through an apsidal anti-alignment. For the Kepler-108 system, we find that the stability of its mutually inclined planets could be justified either solely by a mean-motion resonance, or in tandem with an inclination-type resonance. Going forward, dynamical analyses based on periodic orbits could yield better constrained orbital elements of near-resonant extrasolar systems when performed in parallel to the fitting of the observational data.

AB - Aims. Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital parameters of the systems, but suffers from observational limitations. When a (near-)resonant planetary system resides in the dynamical neighbourhood of a stable periodic orbit, its long-term stability, and thus survival, can be guaranteed. We use the intrinsic property of the periodic orbits, namely their linear horizontal and vertical stability, to validate or further constrain the orbital elements of detected two-planet systems. Methods. We computed the families of periodic orbits in the general three-body problem for several two-planet Kepler and K2 systems. The dynamical neighbourhood of the systems is unveiled with maps of dynamical stability. Results. Additional validations or constraints on the orbital elements of K2-21, K2-24, Kepler-9, and (non-coplanar) Kepler-108 near-resonant systems were achieved. While a mean-motion resonance locking protects the long-term evolution of the systems K2-21 and K2-24, such a resonant evolution is not possible for the Kepler-9 system, whose stability is maintained through an apsidal anti-alignment. For the Kepler-108 system, we find that the stability of its mutually inclined planets could be justified either solely by a mean-motion resonance, or in tandem with an inclination-type resonance. Going forward, dynamical analyses based on periodic orbits could yield better constrained orbital elements of near-resonant extrasolar systems when performed in parallel to the fitting of the observational data.

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KW - Chaos

KW - Methods: Analytical

KW - Methods: Numerical

KW - Planetary systems

KW - Planets and satellites: dynamical evolution and stability

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DO - 10.1051/0004-6361/202037779

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VL - 640

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

M1 - A55

ER -

Exploiting periodic orbits as dynamical clues for Kepler and K2 systems

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