Resonant periodic orbits in the exoplanetary systems

Antoniadou, Kyriaki I.; Voyatzis, George

doi:10.1007/s10509-013-1679-8

Cited by 40 publications

(36 citation statements)

References 31 publications

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“…This fact is known (e.g. [Beaugé et al(2006)] and [Michtchenko et al(2006)] using the numerical averaging of the Hamiltonian, [Hadjidemetriou(2002)] and [Antoniadou & Voyatzis(2014)] tracking periodic orbits). We further note that while the expansion to order 2 in the eccentricities captures this behaviour, it does not agree quantitatively with the averaged Hamiltonian.…”

Section: Equilibrium Points Of the Averaged Hamiltonianmentioning

confidence: 99%

Capture into first-order resonances and long-term stability of pairs of equal-mass planets

Pichierri

Morbidelli

Crida

2018

Celest Mech Dyn Astr

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Massive planets form within the lifetime of protoplanetary disks and therefore they are subject to orbital migration due to planet-disk interactions. When the first planet reaches the inner edge of the disk its migration stops and consequently the second planet ends up locked in resonance with the first one. We detail how the resonant trapping works comparing semi-analytical formulae and numerical simulations. We restrict to the case of two equal-mass coplanar planets trapped in first order resonances but the method can be easily generalised. We first describe the family of resonant stable equilibrium points (zero-amplitude libration orbits) using series expansions up to different orders in eccentricity as well as a non-expanded Hamiltonian. Then we show that during convergent migration the planets evolve along these families of equilibrium points. Eccentricity damping from the disk leads to a final equilibrium configuration that we predict precisely analytically. The fact that observed multi-exoplanetary systems are rarely seen in resonances suggests that in most cases the resonant configurations achieved by migration become unstable after the removal of the protoplanetary disk. Here we probe the stability of the resonances as a function of planetary mass. For this purpose, we fictitiously increase the masses of resonant planets, adiabatically maintaining the low-amplitude libration regime until instability occurs. We discuss two hypotheses for the instability, that of a low-order secondary resonance of the libration frequency with a fast synodic frequency of the system, and that of minimal approach distance between planets. We show that secondary resonances do not seem to impact resonant systems at low-amplitude of libration. Resonant systems are more stable than non-resonant ones for a given minimal distance at close encounters, but we show that the latter nevertheless play the decisive role in the destabilisation of resonant pairs. We show evidence that, as the planetary mass increases and the minimal distance between planets gets smaller in terms of mutual Hill radius, the region of stability around the resonance center shrinks, until the equilibrium point itself becomes unstable.

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Section: Equilibrium Points Of the Averaged Hamiltonianmentioning

confidence: 99%

Capture into first-order resonances and long-term stability of pairs of equal-mass planets

Pichierri

Morbidelli

Crida

2018

Celest Mech Dyn Astr

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“…Moreover, regarding 5/1 MMR, all of the results are new, since, to our knowledge, 5/1 MMR has only been studied for the general TBP (GTBP) by . Let us note that all of the rest above-mentioned MMRs have also been studied for the planar GTBP by and by Antoniadou and Voyatzis (2014) with respect to their vertical stability (Hénon, 1973), thus, both for the planar and the spatial GTBP.…”

Section: Motivationmentioning

confidence: 99%

“…In this problem, we found new bifurcation points leading to the ERTBP and hence, new families emanating from them for every MMR studied. In this way, the families of each MMR that exist in the GTBP can be generated if we start from the periodic orbits of the ERTBP and through mono-parametric continuation increase the mass of the inner body (see Antoniadou and Voyatzis, 2014). We also computed some isolated families, in particular at high eccentricities, for each MMR.…”

Section: /2 Mmrmentioning

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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“…Thus, we represent them on the eccentricities plane. When q = 2k + 1, k ∈ Z * , we use the pair (θ 1 , θ 2 ) and when q = 2k, k ∈ Z * , we use the pair (θ 3 , θ 1 ), in order to distinguish the different groups of families (see [24]). For small planetary masses, it has been shown by [30,31] that the characteristic curves belonging to the same configuration differ one another in planetary mass ratio ρ = m2 m1 .…”

Section: Periodic Orbits and Mean-motion Resonancesmentioning

confidence: 99%

Regular and chaotic orbits in the dynamics of exoplanets

Antoniadou

2016

Eur. Phys. J. Spec. Top.

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Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a meanmotion resonance (MMR), which offers a phase protection mechanism, so that, even highly eccentric planets can avoid close encounters. However, the present estimation of their initial conditions, which may change significantly after obtaining additional observational data in the future, locate most of the systems in chaotic regions and consequently, they are destabilized. Hence, dynamical analysis is imperative for the derivation of proper planetary orbital elements. We utilize the model of spatial general three body problem, in order to simulate such resonant systems through the computation of families periodic orbits. In this way, we can figure out regions in phase space, where the planets in resonances should be ideally hosted in favour of long-term stability and therefore, survival. In this review, we summarize our methodology and showcase the fact that stable resonant planetary systems evolve being exactly centered at stable periodic orbits.

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Resonant periodic orbits in the exoplanetary systems

Cited by 40 publications

References 31 publications

Capture into first-order resonances and long-term stability of pairs of equal-mass planets

Capture into first-order resonances and long-term stability of pairs of equal-mass planets

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

Regular and chaotic orbits in the dynamics of exoplanets

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