Dynamics of Two Planets in the 3/2 Mean-motion Resonance: Application to the Planetary System of the Pulsar PSR B1257+12

Callegari, Nelson; Ferraz-Mello, S.; Michtchenko, T. A.

doi:10.1007/s10569-006-9002-4

Cited by 41 publications

(18 citation statements)

References 19 publications

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“…This is due to the presence of the separatrix of the secular resonance inside the MMR. Resonances of this type were already studied in the case of the 2:1 and 3:2 MMR by Callegari et al (2004Callegari et al ( , 2006. As described by these studies, the secular frequency (dominating the motion of ∆ ) falls to zero near the separatrix and the angle ∆ librates in the opposite direction from one side to the other of the separatrix.…”

Section: N-body Simulationsmentioning

confidence: 89%

Resonance breaking due to dissipation in planar planetary systems

Delisle

Laskar

Correia

2014

A&A

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We study the evolution of two planets around a star, in mean-motion resonance and undergoing tidal effects. We derive an integrable analytical model of mean-motion resonances of any order which reproduce the main features of the resonant dynamics. Using this simplified model, we obtain a criterion showing that, depending on the balance of the tidal dissipation in both planets, their final period ratio may stay at the resonant value, increase above, or decrease below the resonant value. Applying this criterion to the two inner planets orbiting GJ 163, we deduce that the current period ratio (2.97) could be the outcome of dissipation in the 3:1 MMR provided that the innermost planet is gaseous (slow dissipation) while the second one is rocky (faster dissipation). We perform N-body simulations with tidal dissipation to confirm the results of our analytical model. We also apply our criterion on GJ 581b, c (5:2 MMR) and reproduce the current period ratio (2.4) if the inner planet is gaseous and the outer is rocky (as in the case of GJ 163). Finally, we apply our model to the Kepler mission's statistics. We show that the excess of planets pairs close to first-order MMRs but in external circulation, i.e., with period ratios P out /P in > (p + 1)/p for the resonance (p + 1):p, can be reproduced by tidal dissipation in the inner planet. There is no need for any other dissipative mechanism, provided that these systems left the resonance with non-negligible eccentricities.

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Section: N-body Simulationsmentioning

confidence: 89%

Resonance breaking due to dissipation in planar planetary systems

Delisle

Laskar

Correia

2014

A&A

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“…The Grand Tack model, a scenario proposed to explain the current architecture of the inner solar system, asserts that Jupiter and Saturn were once captured into a 3:2 MMR while embedded in the nascent solar nebula (Walsh et al 2011;Pierens et al 2014). Furthermore, the first extrasolar planetary system ever confirmed, around PSR 1257+12 (Wolszczan & Frail 1992;Wolszczan 1994), includes two planets whose orbits are tightly coupled and are very close to residing within the 3:2 MMR (Malhotra et al 1992;Goździewski et al 2005;Callegari et al 2006).…”

Section: Introductionmentioning

confidence: 99%

One of the closest exoplanet pairs to the 3:2 mean motion resonance: K2-19b and c

Armstrong

Santerne

Veras

et al. 2015

A&A

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Aims. The K2 mission has recently begun to discover new and diverse planetary systems. In December 2014, Campaign 1 data from the mission was released, providing high-precision photometry for ∼22 000 objects over an 80-day timespan. We searched these data with the aim of detecting more important new objects. Methods. Our search through two separate pipelines led to the independent discovery of K2-19b and c, a two-planet system of Neptune-sized objects (4.2 and 7.2 R ⊕ ), orbiting a K dwarf extremely close to the 3:2 mean motion resonance. The two planets each show transits, sometimes simultaneously owing to their proximity to resonance and the alignment of conjunctions. Results. We obtained further ground-based photometry of the larger planet with the NITES telescope, demonstrating the presence of large transit timing variations (TTVs), and used the observed TTVs to place mass constraints on the transiting objects under the hypothesis that the objects are near but not in resonance. We then statistically validated the planets through the PASTIS tool, independently of the TTV analysis.

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“…Beaugé et al 2003Beaugé et al , 2008Ferraz-Mello et al 2006;Marzari et al 2006;Callegari et al 2006;Baluev 2008;Gozdziewski et al 2008;Schwarz et al 2009). In these papers different methods have been applied, as the averaging method, direct numerical integrations of orbits, or various numerical methods which provide indicators for the exponential growth of nearby orbits.…”

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confidence: 99%

On the dynamics of extrasolar planetary systems under dissipation: Migration of planets

Hadjidemetriou

Voyatzis

2010

Celest Mech Dyn Astr

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We study the dynamics of planetary systems with two planets moving in the same plane, when frictional forces act on the two planets, in addition to the gravitational forces. The model of the general three-body problem is used. Different laws of friction are considered. The topology of the phase space is essential in understanding the evolution of the system. The topology is determined by the families of stable and unstable periodic orbits, both symmetric and non symmetric. It is along the stable families, or close to them, that the planets migrate when dissipative forces act. At the critical points where the stability along the family changes, there is a bifurcation of a new family of stable periodic orbits and the migration process changes route and follows the new stable family up to large eccentricities or to a chaotic region. We consider both resonant and non resonant planetary systems. The 2/1, 3/1 and 3/2 resonances are studied. The migration to larger or smaller eccentricities depends on the particular law of friction. Also, in some cases the semimajor axes increase and in other cases they are stabilized. For particular laws of friction and for special values of the parameters of the frictional forces, it is possible to have partially stationary solutions, where the eccentricities and the semimajor axes are fixed.

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Dynamics of Two Planets in the 3/2 Mean-motion Resonance: Application to the Planetary System of the Pulsar PSR B1257+12

Cited by 41 publications

References 19 publications

Resonance breaking due to dissipation in planar planetary systems

Resonance breaking due to dissipation in planar planetary systems

One of the closest exoplanet pairs to the 3:2 mean motion resonance: K2-19b and c

On the dynamics of extrasolar planetary systems under dissipation: Migration of planets

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