Evolution of planetary systems in resonance

Kley, W.; Peitz, J.; Bryden, G.

doi:10.1051/0004-6361:20031589

Cited by 138 publications

(208 citation statements)

References 34 publications

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“…The inner planet is located at x = −0.11, y = −0.61 and the outer one at x = −0.48, y = −1.37. In contrast to previous models where the two planets orbit in an inner cavity of the disk without any inner disk (Kley et al 2004), here the inner disk has not been cleared and is still present due to the more realistic inner boundary condition given in Eq. (1).…”

Section: A Hydrodynamical Model For Hd 73526mentioning

confidence: 98%

“…According to full hydrodynamical simulations a cavity opens between the giant planets, and the inner planet orbits in a low density gaseous environment. The outer giant planet is still connected to the disk, thus it can accrete more material, which may result in larger mass for it than for the inner planet (Kley et al 2004). …”

Section: New Orbital Data and Their Stabilitymentioning

confidence: 99%

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Stability and formation of the resonant system HD 73526

Sándor

Kley²,

Klagyivik

2007

A&A

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Context. Based on radial velocity measurements, it has been found that the two giant planets detected around the star HD 73526 are in 2:1 resonance. However, as our numerical integration shows, the derived orbital data for this system result in chaotic behavior of the giant planets, which is uncommon among the resonant extrasolar planetary systems. Aims. We present regular (non-chaotic) orbital solutions for the giant planets in the system HD 73526 and offer formation scenarios based on combining planetary migration and sudden perturbative effects such as planet-planet scattering or rapid dispersal of the protoplanetary disk. A comparison with the already-studied resonant system HD 128311, exhibiting similar behavior, is given. Methods. The new sets of orbital solutions were derived using the Systemic Console. The stability of these solutions was investigated using the Relative Lyapunov indicator, while the migration and scattering effects are studied by gravitational N-body simulations applying non-conservative forces. Additionally, hydrodynamic simulations of embedded planets in protoplanetary disks were performed to follow the capture into resonance. Results. For the system HD 73526 we demonstrate that the observational radial velocity data are consistent with a coplanar planetary system in a stable 2:1 resonance exhibiting apsidal corotation. We have shown that, similarly to the system HD 128311, the present dynamical state of HD 73526 could be the result of a mixed evolutionary process combining planetary migration and a perturbative event.

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Section: A Hydrodynamical Model For Hd 73526mentioning

confidence: 98%

Section: New Orbital Data and Their Stabilitymentioning

confidence: 99%

Stability and formation of the resonant system HD 73526

Sándor

Kley²,

Klagyivik

2007

A&A

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“…The observed inner and outer planet masses are such that, if (as is commonly assumed for multiplanetary systems of this kind) the planets are initially separated widely enough that their period ratio exceeds 2, a 2:1 commensurability is expected to form at low migration rates (e.g. Nelson & Papaloizou 2002;Kley et al 2004). Pierens & Nelson (2008) have studied a similar scenario where the goal was to resemble the 3:2 resonance between Jupiter and Saturn in the early solar system.…”

Section: Convergent Migration and Resonance Capturementioning

confidence: 99%

The dynamical origin of the multi-planetary system HD 45364

Rein¹,

Papaloizou²,

Kley

2010

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The recently discovered planetary system HD 45364, which consists of a Jupiter and Saturn-mass planet, is very likely in a 3:2 mean motion resonance. The standard scenario for forming planetary commensurabilities is convergent migration of two planets embedded in a protoplanetary disc. When the planets are initially separated by a period ratio larger than two, convergent migration will most likely lead to a very stable 2:1 resonance. Rapid type III migration of the outer planet crossing the 2:1 resonance is one possible way around this problem. In this paper, we investigate this idea in detail. We present an estimate of the required convergent migration rate and confirm this with N-body and hydrodynamical simulations. If the dynamical history of the planetary system had a phase of rapid inward migration that forms a resonant configuration, we predict that the orbital parameters of the two planets will always be very similar and thus should show evidence of that. We use the orbital parameters from our simulation to calculate a radial velocity curve and compare it to observations. Our model provides a fit that is as good as the previously reported one. The eccentricities of both planets are considerably smaller and the libration pattern is different. Within a few years, it will be possible to observe the planet-planet interaction directly and thus distinguish between these different dynamical states.

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“…Numerous theoretical studies have been carried out since the discovery of the second planet to determine what physical processes gave rise to the system's unique architecture (e.g. Lee & Peale 2002;Ji et al 2002;Kley et al 2004Kley et al , 2005Zhou et al 2005;Crida et al 2008) because such specific consideration has the potential for constraining general theories of planet formation and evolution. Determining what mechanisms could have led to the current system arrangement depends critically on knowing the masses of the planets involved, and what the current arrangement itself even is.…”

Section: Introductionmentioning

confidence: 99%

The architecture of the GJ 876 planetary system

Bean¹,

Seifahrt²

2009

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We present a combined analysis of previously published high-precision radial velocities and astrometry for the GJ 876 planetary system using a self-consistent model that accounts for the planet-planet interactions. Assuming the three planets so far identified in the system are coplanar, we find that including the astrometry in the analysis does not result in a best-fit inclination significantly different than that found by Rivera and collaborators from analyzing the radial velocities alone. In this unique case, the planet-planet interactions are of such significance that the radial velocity data set is more sensitive to the inclination of the system through the dependence of the interactions on the true masses of the two gas giant planets in the system (planets b and c). The astrometry does allow determination of the absolute orbital inclination (i.e. distinguishing between i and 180 − i) and longitude of the ascending node for planet b, which allows us to quantify the mutual inclination angle between its orbit and planet c's orbit when combined with the dynamical considerations. We find that the planets have a mutual inclination Φ bc = 5.0 • +3.9 • −2.3 • . This result constitutes the first determination of the degree of coplanarity in an exoplanetary system around a normal star. That we find the two planets' orbits are nearly coplanar, like the orbits of the Solar System planets, indicates that the planets likely formed in a circumstellar disk, and that their subsequent dynamical evolution into a 2:1 mean motion resonance only led to excitation of a small mutual inclination. This investigation demonstrates how the degree of coplanarity for other exoplanetary systems could also be established using data obtained from existing facilities.

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Evolution of planetary systems in resonance

Cited by 138 publications

References 34 publications

Stability and formation of the resonant system HD 73526

Stability and formation of the resonant system HD 73526

The dynamical origin of the multi-planetary system HD 45364

The architecture of the GJ 876 planetary system

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