Capture into resonance: An extension of the use of adiabatic invariants

Henrard, Jacques

doi:10.1007/bf01228946

Cited by 212 publications

(147 citation statements)

References 22 publications

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“…Classical works (e.g. Neishtadt 1975;Henrard 1982;Beaugé & Ferraz-Mello 1993;Nelson & Papaloizou 2002) predict that capture is only possible in cases of convergent migration and, thus, the behavior shown in Fig. 8 should not occur.…”

Section: Simulations Of Individual Particles With Gas Dragmentioning

confidence: 99%

Secular dynamics of planetesimals in tight binary systems: application toγ-Cephei

Giuppone

Leiva

Correa-Otto

et al. 2011

A&A

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Context. The secular dynamics of small planetesimals in tight binary systems play a fundamental role in establishing the possibility of accretional collisions in such extreme cases. The most important secular parameters are the forced eccentricity and secular frequency, which depend on the initial conditions of the particles, as well as on the mass and orbital parameters of the secondary star. Aims. We construct a second-order theory (with respect to the masses) for the planar secular motion of small planetasimals and deduce new expressions for the forced eccentricity and secular frequency. We also reanalyze the radial velocity data available for γ-Cephei and present a series of orbital solutions leading to residuals compatible with the best fits. Finally, we discuss how different orbital configurations for γ-Cephei may affect the dynamics of small bodies in circumstellar motion. Methods. The secular theory is constructed using a Lie series perturbation scheme restricted to second order in the small parameter. The orbital fits were analyzed with a minimization code that employs a genetic algorithm for a preliminary solution plus a simulated annealing for the fine tuning. Results. For γ-Cephei, we find that the classical first-order expressions for the secular frequency and forced eccentricity lead to large inaccuracies ∼50% for semimajor axes larger than one tenth the orbital separation between the stellar components. Low eccentricities and/or masses reduce the importance of the second-order terms. The dynamics of small planetesimals only show a weak dependence with the orbital fits of the stellar components, and the same result is found including the effects of a nonlinear gas drag. Thus, the possibility of planetary formation in this binary system largely appears insensitive to the orbital fits adopted for the stellar components, and any future alterations in the system parameters (due to new observations) should not change this picture. Finally, we show that planetesimals migrating because of gas drag may be trapped in mean-motion resonances with the binary, even though the migration is divergent.

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Section: Simulations Of Individual Particles With Gas Dragmentioning

confidence: 99%

Secular dynamics of planetesimals in tight binary systems: application toγ-Cephei

Giuppone

Leiva

Correa-Otto

et al. 2011

A&A

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“…In general, though, the motion near a separatrix in a nonlinear dynamical system is not regular but chaotic. The calculation of capture probabilities is a well-developed art (see Henrard, 1982;Borderies and Goldreich, 1984), but the effect of the chaotic separatrix has never been mentioned. Of course, when COo is very small the chaotic separatrix is microscopically small, and even a very small tidal torque can sweep the system across the chaotic zone so quickly that it has essentially no effect.…”

Section: Tidal Evolutionmentioning

confidence: 99%

The chaotic rotation of Hyperion

Wisdom

Peale

Mignard³

1984

Icarus

335

248

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A plot of spin rate versus orientation when Hyperion is at the pericenter of its orbit (surface of section) reveals a large chaotic zone surrounding the synchronous spin-orbit state of Hyperion, if the satellite is assumed to be rotating about a principal axis which is normal to its orbit plane. This means that Hyperion's rotation in this zone exhibits large, essentially random variations on a short time scale. The chaotic zone is so large that it surrounds the 1/2 and 2 states, and libration in the 3/2 state is not possible. Stability analysis shows that for libration in the synchronous and 1/2 states, the orientation of the spin axis normal to the orbit plane is unstable, whereas rotation in the 2 state is attitude stable. Rotation in the chaotic zone is also attitude unstable. A small deviation of the principal axis from the orbit normal leads to motion through all angles in both the chaotic zone and the attitude unstable libration regions. Measures of the exponential rate of separation of nearby trajectories in phase space (Lyapunov characteristic exponents) for these three-dimensional motions indicate the the tumbling is chaotic and not just a regular motion through large angles. As tidal dissipation drives Hyperion's spin toward a nearly synchronous value, Hyperion necessarily enters the large chaotic zone. At this point Hyperion becomes attitude unstable and begins to tumble. Capture from the chaotic state into the synchronous or 1/2 state is impossible since they are also attitude unstable. The 3/2 state does not exist. Capture into the stable 2 state is possible, but improbable. It is expected that Hyperion will be found tumbling chaotically.

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“…Intuitively, it can be understood that if accretion of disk material is sufficiently rapid, then the star will continuously realign with the disk and thereby prevent the excitation of significant misalignments (Lai et al 2011). On the other hand, if the star rotates rapidly enough for its gravitational quadrupole to couple adiabatically to the disk (Henrard 1982), its spin pole will trail the angular momentum vector of the disk. This means that the distributions of stellar rotation rates and spin-orbit misalignments may be intimately connected.…”

Section: Introductionmentioning

confidence: 99%

Magnetic and Gravitational Disk-Star Interactions: An Interdependence of PMS Stellar Rotation Rates and Spin-Orbit Misalignments

Batygin

Adams

2013

ApJ

123

126

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The presence of giant gaseous planets that reside in close proximity to their host stars, i.e., hot Jupiters, may be a consequence of large-scale radial migration through the protoplanetary nebulae. Within the framework of this picture, significant orbital obliquities characteristic of a substantial fraction of such planets can be attributed to external torques that perturb the natal disks out of alignment with the spin axes of their host stars. Therefore, the acquisition of orbital obliquity likely exhibits sensitive dependence on the physics of disk-star interactions. Here, we analyze the primordial excitation of spin-orbit misalignment of Sun-like stars in light of disk-star angular momentum transfer. We begin by calculating the stellar pre-main-sequence rotational evolution, accounting for spin-up due to gravitational contraction and accretion as well as spin-down due to magnetic star-disk coupling. We devote particular attention to angular momentum transfer by accretion, and show that while generally subdominant to gravitational contraction, this process is largely controlled by the morphology of the stellar magnetic field (that is, specific angular momentum accreted by stars with octupole-dominated surface fields is smaller than that accreted by dipole-dominated stars by an order of magnitude). Subsequently, we examine the secular spin-axis dynamics of diskbearing stars, accounting for the time-evolution of stellar and disk properties, and demonstrate that misalignments are preferentially excited in systems where stellar rotation is not overwhelmingly rapid. Moreover, we show that the excitation of spin-orbit misalignment occurs impulsively through an encounter with a resonance between the stellar precession frequency and the disk-torquing frequency. Cumulatively, the model developed herein opens up a previously unexplored avenue toward understanding star-disk evolution and its consequences in a unified manner.

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Capture into resonance: An extension of the use of adiabatic invariants

Cited by 212 publications

References 22 publications

Secular dynamics of planetesimals in tight binary systems: application toγ-Cephei

Secular dynamics of planetesimals in tight binary systems: application toγ-Cephei

The chaotic rotation of Hyperion

Magnetic and Gravitational Disk-Star Interactions: An Interdependence of PMS Stellar Rotation Rates and Spin-Orbit Misalignments

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