AMD-stability and the classification of planetary systems

Laskar, Jacques; Petit, Antoine C.

doi:10.1051/0004-6361/201630022

Cited by 131 publications

(140 citation statements)

References 36 publications

Supporting

Mentioning

132

Contrasting

Order By: Relevance

“…We plot in Figure 3 the overlap criteria (75) for ε = 10 −6 , the two approximations (77) and (79) from (Deck et al 2013), as well as the collision condition used in (Laskar & Petit 2017) approximated for α → 1,…”

Section: Overlap Criterion For Low-eccentricity Orbitsmentioning

confidence: 99%

“…The AMD-stability is based on the conservation of the angular momentum deficit (AMD, Laskar 1997) in the secular system at all orders of averaging (Laskar 2000;Laskar & Petit 2017). Indeed, the conservation of the AMD fixes an upper bound to the eccentricities.…”

Section: Introductionmentioning

confidence: 99%

“…Since the semi-major axes are constant in the secular approximation, a low enough AMD forbids collisions between planets. The AMD-stability criterion has been used to classify planetary systems based on the stability of their secular dynamics (Laskar & Petit 2017).…”

Section: Introductionmentioning

confidence: 99%

“…However, while the analytical criterion developed in (Laskar & Petit 2017) does not depend on series expansions for small masses or spacing between the orbits, the secular hypothesis does not hold for systems experiencing mean motion resonances (MMR). Although a system with planets in MMR can be dynamically stable, chaotic behavior may result from the overlap of adjacent MMR, leading to a possible increase of the AMD and eventually to close encounters, collisions or ejections.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 4, we then use the defined stability criterion to limit the region where the dynamics can be considered to be secular and adapt the notion of AMDstability thanks to the new limit of the secular dynamics. Finally we study in Section 5 how the modification of the AMD-stability definition affects the classification proposed in (Laskar & Petit 2017). …”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

AMD-stability in the presence of first-order mean motion resonances

Petit

Laskar

Boué

2017

A&A

Self Cite

View full text Add to dashboard Cite

The AMD-stability criterion allows to discriminate between a-priori stable planetary systems and systems for which the stability is not granted and needs further investigations. AMD-stability is based on the conservation of the Angular Momentum Deficit (AMD) in the averaged system at all orders of averaging. While the AMD criterion is rigorous, the conservation of the AMD is only granted in absence of mean-motion resonances (MMR). Here we extend the AMD-stability criterion to take into account mean-motion resonances, and more specifically the overlap of first-order MMR. If the MMR islands overlap, the system will experience generalized chaos leading to instability. The Hamiltonian of two massive planets on coplanar quasi-circular orbits can be reduced to an integrable one degree of freedom problem for period ratios close to a first-order MMR. We use the reduced Hamiltonian to derive a new overlap criterion for first-order MMR. This stability criterion unifies the previous criteria proposed in the literature and admits the criteria obtained for initially circular and eccentric orbits as limit cases. We then improve the definition of AMD-stability to take into account the short term chaos generated by MMR overlap. We analyze the outcome of this improved definition of AMD-stability on selected multi-planet systems from the Extrasolar Planets Encyclopaedia.

show abstract

Section: Overlap Criterion For Low-eccentricity Orbitsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

AMD-stability in the presence of first-order mean motion resonances

Petit

Laskar

Boué

2017

A&A

Self Cite

View full text Add to dashboard Cite

show abstract

The HD 217107 planetary system: Twenty years of radial velocity measurements

et al. 2020

View full text Add to dashboard Cite

The hot Jupiter HD 217107 b was one of the first exoplanets detected using the radial velocity (RV) method, originally reported in the literature in 1999. Today, precise RV measurements of this system span more than 20 years, and there is clear evidence of a longer‐period companion, HD 217107 c. Interestingly, both the short‐period planet (Pb ∼ 7.13 d) and long‐period planet (Pc ∼ 5059 d) have significantly eccentric orbits (eb ∼ 0.13 and ec ∼ 0.40). We present 42 additional RV measurements of this system obtained with the MINERVA telescope array and carry out a joint analysis with previously published RV measurements from four different facilities. We confirm and refine the previously reported orbit of the long‐period companion. HD 217107 b is one of a relatively small number of hot Jupiters with an eccentric orbit, opening up the possibility of detecting the precession of the planetary orbit due to general relativistic effects and perturbations from other planets in the system. In this case, the argument of periastron, ω, is predicted to change at the level of ∼0.8∘ century−1. Despite the long time baseline of our observations and the high quality of the RV measurements, we are only able to constrain the precession to be ω˙<65.9∘ century−1. We discuss the limitations of detecting the subtle effects of precession in exoplanet orbits using RV data.

show abstract