Self‐gravitating Gaseous Bars. I. Compressible Analogs of Riemann Ellipsoids with Supersonic Internal Flows

Cazes, John; Tohline, J. E.

doi:10.1086/308609

Cited by 21 publications

(44 citation statements)

References 23 publications

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“…However, according to Hawley et al (1999) Coriolis forces are able to stabilize differentially rotating astrophysical flows against shearing instabilities even in accretion disks in which the shear is much stronger than in our Dedekind-like bar (see, however, Longaretti 2002 for an opposing argument). Furthermore, other models of differentially rotating astrophysical bars (Cazes & Tohline 2000;New et al 2000) do not appear to be susceptible to the dynamical instability that destroyed the bar in our ROT181 model evolution. We suspect, instead, that the latetime behavior of model ROT181 results either from nonlinear coupling of various oscillatory modes within the star or from an ''elliptic flow'' instability similar to the one identified in laboratory fluids that are forced to flow along elliptical streamlines.…”

Section: Discussionmentioning

confidence: 73%

Nonlinear Development of the Secular Bar‐Mode Instability in Rotating Neutron Stars

Tohline

Lindblom

2004

ApJ

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We have modeled the nonlinear development of the secular bar-mode instability that is driven by gravitational radiation reaction (GRR) forces in rotating neutron stars. In the absence of any competing viscous effects, an initially uniformly rotating axisymmetric n ¼ 1=2 polytropic star with a ratio of rotational to gravitational potential energy T = W j j ¼ 0:181 is driven by GRR forces to a barlike structure, as predicted by linear theory. The pattern frequency of the bar slows to nearly zero, that is, the bar becomes almost stationary as viewed from an inertial frame of reference as GRR removes energy and angular momentum from the star. In this ''Dedekind-like'' state, rotational energy is stored as motion of the fluid in highly noncircular orbits inside the bar. However, in less than 10 dynamical times after its formation the bar loses its initially coherent structure as the ordered flow inside the bar is disrupted by what appears to be a purely hydrodynamic short-wavelength ''shearing''-type instability. The gravitational waveforms generated by such an event are determined, and an estimate of the detectability of these waves is presented.

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Section: Discussionmentioning

confidence: 73%

Nonlinear Development of the Secular Bar‐Mode Instability in Rotating Neutron Stars

Tohline

Lindblom

2004

ApJ

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“…If a star rotates sufficiently fast, to a point where the ratio of its rotational to gravitational potential energy T /jW j k 0:27, it will encounter a dynamical bar-mode instability that will result in the deformation of the star into a rapidly spinning, barlike structure. This instability has been verified by a number of numerical hydrodynamics investigations ( Tohline et al 1985;Durisen et al 1986;Williams & Tohline 1988;Cazes & Tohline 2000;New et al 2000;Brown 2000;Liu 2002). At a slower rotation rate, T /jW j k 0:14, a star may also encounter a secular bar-mode instability that can promote deformation into a barlike shape, but only if the star is subjected to a dissipative process capable of redistributing angular momentum within its structure, such as viscosity or gravitational radiation reaction (GRR) forces (Chandrasekhar 1970;Friedman & Schutz 1978;Ipser & Lindblom 1990, 1991Lai & Shapiro 1995).…”

Section: Introductionmentioning

confidence: 70%

Unexpected Dynamical Instabilities in Differentially Rotating Neutron Stars

Tohline

2006

ApJ

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107

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A one-armed spiral instability has been found to develop in differentially rotating stellar models that have a relatively stiff, n ¼ 1 polytropic equation of state and a wide range of rotational energies. This suggests that such instabilities can arise in neutron stars that are differentially, although not necessarily rapidly, rotating. The instability seems to be directly triggered by the presence of a corotation resonance inside the star. Our analysis also suggests that a resonant cavity resulting from a local minimum in the radial vortensity profile of the star plays an important role in amplifying the unstable mode. Hence, it appears as though this instability is closely related to the so-called Rossby wave instability (see work of Lovelace et al.) that has been found to arise in accretion disks. In addition to the onearmed (m ¼ 1) spiral mode, we have found that higher order (m ¼ 2 and 3) nonaxisymmetric modes also can become unstable if corotation points that resonate with the eigenfrequencies of these higher order modes also appear inside the star. The growth rate of each mode seems to depend on the location of its corotation radius with respect to the vortensity profile (or on the depth of its corotation radius inside the vortensity well ). The existence of such instabilities makes the stability criterion for differentially rotating neutron stars nonunique. Also, the gravitational waves emitted from such unstable systems generally will not have a monochromatic frequency spectrum.

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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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Self‐gravitating Gaseous Bars. I. Compressible Analogs of Riemann Ellipsoids with Supersonic Internal Flows

Cited by 21 publications

References 23 publications

Nonlinear Development of the Secular Bar‐Mode Instability in Rotating Neutron Stars

Nonlinear Development of the Secular Bar‐Mode Instability in Rotating Neutron Stars

Unexpected Dynamical Instabilities in Differentially Rotating Neutron Stars

Nonaxisymmetric instabilities of self-gravitating disks. I toroids

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