Regular and chaotic orbits in the dynamics of exoplanets

Antoniadou, Kyriaki I.

doi:10.1140/epjst/e2016-02651-6

Cited by 15 publications

(10 citation statements)

References 41 publications

(71 reference statements)

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“…The resonant angles librate in a similar manner (for details, see e.g. Antoniadou 2016). These angles rotate if the periodic orbits are unstable.…”

Section: Periodic Orbitsmentioning

confidence: 94%

Linking long-term planetaryN-body simulations with periodic orbits: application to white dwarf pollution

Antoniadou¹,

Veras²

2016

Mon. Not. R. Astron. Soc.

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Mounting discoveries of debris discs orbiting newly-formed stars and white dwarfs (WDs) showcase the importance of modeling the long-term evolution of small bodies in exosystems. WD debris discs are in particular thought to form from very long-term (0.1-5.0 Gyr) instability between planets and asteroids. However, the time-consuming nature of N -body integrators which accurately simulate motion over Gyrs necessitates a judicious choice of initial conditions. The analytical tools known as periodic orbits can circumvent the guesswork. Here, we begin a comprehensive analysis directly linking periodic orbits with N -body integration outcomes with an extensive exploration of the planar circular restricted three-body problem (CRTBP) with an outer planet and inner asteroid near or inside of the 2:1 mean motion resonance. We run nearly 1000 focused simulations for the entire age of the Universe (14 Gyr) with initial conditions mapped to the phase space locations surrounding the unstable and stable periodic orbits for that commensurability. In none of our simulations did the planar CRTBP architecture yield a long-timescale ( 0.25% of the age of the Universe) asteroid-star collision. The pericentre distance of asteroids which survived beyond this timescale (≈ 35 Myr) varied by at most about 60%. These results help affirm that collisions occur too quickly to explain WD pollution in the planar CRTBP 2:1 regime, and highlight the need for further periodic orbit studies with the eccentric and inclined TBP architectures and other significant orbital period commensurabilities.

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“…The resonant angles librate in a similar manner (for details, see e.g. Antoniadou 2016). These angles rotate if the periodic orbits are unstable.…”

Section: Periodic Orbitsmentioning

confidence: 94%

Linking long-term planetaryN-body simulations with periodic orbits: application to white dwarf pollution

Antoniadou¹,

Veras²

2016

Mon. Not. R. Astron. Soc.

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“…The stable periodic orbits constitute the backbone of the stability domains in phase space and via dynamical analyses we can provide the regions, where the newly discovered exoplanets locked in MMRs should be ideally hosted in favour of their long-term stability (e.g. Antoniadou, 2016). Therefore, the knowledge of the families in the ERTBP is important for the dynamical vicinities of terrestrial planets trapped in MMR with giant planets.…”

Section: Linear Stability and Ds-mapsmentioning

confidence: 99%

Origin and continuation of 3/2, 5/2, 3/1, 4/1 and 5/1 resonant periodic orbits in the circular and elliptic restricted three-body problem

Antoniadou

Libert

2018

Celest Mech Dyn Astr

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We consider a planetary system consisting of two primaries, namely a star and a giant planet, and a massless secondary, say a terrestrial planet or an asteroid, which moves under their gravitational attraction. We study the dynamics of this system in the framework of the circular and elliptic restricted three-body problem, when the motion of the giant planet describes circular and elliptic orbits, respectively. Originating from the circular family, families of symmetric periodic orbits in the 3/2, 5/2, 3/1, 4/1 and 5/1 mean-motion resonances are continued in the circular and the elliptic problems. New bifurcation points from the circular to the elliptic problem are found for each of the above resonances and thus, new families, continued from these points are herein presented. Stable segments of periodic orbits were found at high eccentricity values of the already known families considered as whole unstable previously. Moreover, new isolated (not continued from bifurcation points) families are computed in the elliptic restricted problem. The majority of the new families mainly consist of stable periodic orbits at high eccentricities. The families of the 5/1 resonance are investigated for the first time in the restricted three-body problems. We highlight the effect of stable periodic orbits on the formation of stable regions in their vicinity and unveil the boundaries of such domains in phase space by computing maps of dynamical stability. The long-term stable evolution of the terrestrial planets or asteroids is dependent on the existence of regular domains in their dynamical neighbourhood in phase space, which could host them for long time spans. This study, besides other celestial architectures that can be efficiently modelled by the circular and elliptic restricted problems, is particularly appropriate for the discovery of terrestrial companions among the single-giant planet systems discovered so far.

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“…For a visual representation of the phase space and the delineation of the boundaries of the domains, maps of dynamical stability are utilized; for coplanar periodic orbits (Antoniadou 2016;Antoniadou & Voyatzis 2016b,a) and mutually inclined orbits (Antoniadou et al 2014a,b;Antoniadou 2016). It is straightforward that the families of stable periodic orbits constitute the backbone of stability domains.…”

Section: The Modelmentioning

confidence: 99%

Circular periodic orbits, resonance capture and inclination excitation during type II migration

Antoniadou¹,

Voyatzis²

2017

Preprint

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We consider planetary systems evolving under the effect of a Stokestype dissipative force mimicking the outcome of a type II migration process. As inward migration proceeds and the planets follow the circular family (they start on circular orbits) and even though they are initially almost coplanar, resonance capture can be realized. Then, at the vertical critical orbits (VCOs), that the circular family possesses, the inclination excitation can abruptly take place. The planets are now guided by the spatial elliptic families, which bifurcate from those critical orbits. We herein, perform a direct link of mutually inclined stable planetary systems on circular orbits trapped in mean-motion resonance (MMR) with the existence of VCOs of high values of multiplicity. It is shown that the more the multiplicity of the periodic orbits of the circular family increases, the more VCOs (corresponding to more MMRs) appear. In this way, we can provide a justification for the existence of resonant planets on circular orbits, which could, even further to that, evolve stably if they were mutually inclined.

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Regular and chaotic orbits in the dynamics of exoplanets

Cited by 15 publications

References 41 publications

Linking long-term planetaryN-body simulations with periodic orbits: application to white dwarf pollution

Linking long-term planetaryN-body simulations with periodic orbits: application to white dwarf pollution

Origin and continuation of 3/2, 5/2, 3/1, 4/1 and 5/1 resonant periodic orbits in the circular and elliptic restricted three-body problem

Circular periodic orbits, resonance capture and inclination excitation during type II migration

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