Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars

Ou, Shangli; Tohline, J. E.; Motl, Patrick M.

doi:10.1086/519785

Cited by 7 publications

(9 citation statements)

References 20 publications

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“…A similar mode coupling can be seen in numerical simulations for the one-armed spiral instability [17] and the elliptical instability [19] of rotating stars in Newtonian gravity. The initial models and the growth mechanism are different, but the turbulent-like behavior appears in diagnostics of the azimuthal Fourier components at late times of nonlinear growth [18,19]. The behavior is also important for the nonlinear saturation of the unstable mode.…”

Section: Discussionsupporting

confidence: 76%

“…The initial models and the growth mechanism are different, but the turbulent-like behavior appears in diagnostics of the azimuthal Fourier components at late times of nonlinear growth [18,19]. The behavior is also important for the nonlinear saturation of the unstable mode.…”

Section: Discussionmentioning

confidence: 99%

“…There are many three-dimensional simulations that have been carried out for dynamically unstable modes in rotating stars for decades [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. The calculations describe the onset of the instability for almost axially symmetric states and its evolution in the nonlinear regime.…”

Section: Introductionmentioning

confidence: 99%

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Amplification of azimuthal modes with odd wave numbers during dynamical bar-mode growth in rotating stars

Kojima

Saijo

2008

Phys. Rev. D

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Nonlinear growth of the bar-mode deformation is studied for a differentially rotating star with supercritical rotational energy. In particular, the growth mechanism of some azimuthal modes with odd wave numbers is examined by comparing a simplified mathematical model with a realistic simulation. Mode coupling to even modes, i.e., the bar mode and higher harmonics, significantly enhances the amplitudes of odd modes, unless they are exactly zero initially. Therefore, other modes which are not axially symmetric cannot be neglected at late times in the growth of the unstable bar-mode even when starting from an almost axially symmetric state.

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Section: Discussionsupporting

confidence: 76%

Section: Discussionmentioning

confidence: 99%

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Amplification of azimuthal modes with odd wave numbers during dynamical bar-mode growth in rotating stars

Kojima

Saijo

2008

Phys. Rev. D

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“…2). The presence of the elliptical instability in these purely rotating isolated flows (absence of any tidal forces) is finally confirmed by Ou et al (2004Ou et al ( , 2007 with 3D numerical simulations of an inviscid compressible fluid. These simple self-gravitating stellar models are thus subject to the elliptical instability which can then grow on fully compressible fluid flows.…”

Section: The Elliptical Instabilitymentioning

confidence: 64%

Elliptical instability in hot Jupiter systems

Cébron¹,

Bars²,

Gal³

et al. 2013

Icarus

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Several studies have already considered the influence of tides on the evolution of systems composed of a star and a close-in companion to tentatively explain different observations such as the spin-up of some stars with hot Jupiters, the radius anomaly of short orbital period planets and the synchronization or quasi-synchronization of the stellar spin in some extreme cases. However, the nature of the mechanism responsible for the tidal dissipation in such systems remains uncertain. In this paper, we claim that the so-called elliptical instability may play a major role in these systems, explaining some systematic features present in the observations. This hydrodynamic instability, arising in rotating flows with elliptical streamlines, is suspected to be present in both planet and star of such systems, which are elliptically deformed by tides. The presence and the influence of the elliptical instability in gaseous bodies, such as stars or hot Jupiters, are most of the time neglected. In this paper, using numerical simulations and theoretical arguments, we consider several features associated to the elliptical instability in hot-Jupiter systems. In particular, the use of ad hoc boundary conditions makes it possible to estimate the amplitude of the elliptical instability in gaseous bodies. We also consider the influence of compressibility on the elliptical instability, and compare the results to the incompressible case. We demonstrate the ability for the elliptical instability to grow in the presence of differential rotation, with a possible synchronized latitude, provided that the tidal deformation and/or the rotation rate of the fluid are large enough. Moreover, the amplitude of the instability for a centrally-condensed mass of fluid is of the same order of magnitude as for an incompressible fluid for a given distance to the threshold of the instability. Finally, we show that the assumption of the elliptical instability being the main tidal dissipation process in eccentric inflated hot Jupiters and misaligned stars is consistent with current data.

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“…The ultimate outcome of I and J mode instabilities appears to be quasi-stable, damping nonaxisymmetric figures. The further evolution of the figures will be driven by cooling and may lead to the onset of elliptical instabilities and eventually to fission in the scenario described in Lebovitz 1987 (see also, Lebovitz andLifschitz 1996;Cazes and Tohline 2000;Ou et al 2007). …”

Section: Discussionmentioning

confidence: 99%

Nonaxisymmetric instabilities of self-gravitating disks. I toroids

Hadley

Imamura

2011

Astrophys Space Sci

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We perform an extensive linear investigation of the nonaxisymmetric disk modes referred to in the literature as P , I , and J modes in self-gravitating polytropic toroids with power law angular velocity distributions. For selected models, we also follow the development of instability from the linear regime through the quasi-linear regime to deep into the nonlinear regime. We consider modes with azimuthal dependence e imφ , where m is an integer and φ is the azimuthal angle. We find that instability sets in through m = 2 barlike I modes at T /|W | ∼ 0.16-0.18 depending upon the chosen angular velocity law where T is the rotational kinetic energy and W is the gravitational energy of the toroid. Instability in the barlike I mode peaks in strength around T /|W | = 0.22-0.23 after which it weakens, eventually stabilizing around T /|W | ∼ 0.25-0.26. Onearmed modes (m = 1 modes) become unstable just after instability in the m = 2I modes sets in; instability in m = 1 modes sets in at T /|W | ∼ 0.19. They dominate the barlike I modes in toroids with T /|W | 0.25. However, almost immediately after the m = 1 mode overtakes the barlike I mode, higher-m J modes appear. J modes with m = 2, 3, and 4 become unstable for T /|W | 0.25-0.26, 0.23-0.25, and 0.25-0.26, respectively. m ≥ 3J modes dominate the m = 1 mode in toroids with T /|W | 0.27. As T /|W | increases further, nonaxisymmetric instability sets in through higher and higher m modes. We find quantitative agreement between the early nonlinear behavior of the tested unstable toroids and our linear results. Quasi-linear modeling suggests that a gravitational self-interaction torque which arises early in the nonlinear regime saturates growth of the mode and leads to significant transport of mass and angular momentum. Neither I mode nor J mode instabilities produce prompt fission in toroids.

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Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars

Cited by 7 publications

References 20 publications

Amplification of azimuthal modes with odd wave numbers during dynamical bar-mode growth in rotating stars

Amplification of azimuthal modes with odd wave numbers during dynamical bar-mode growth in rotating stars

Elliptical instability in hot Jupiter systems

Nonaxisymmetric instabilities of self-gravitating disks. I toroids

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