Nonaxisymmetric instabilities of self-gravitating disks. I toroids

Details Nonaxisymmetric instabilities of self-gravitating disks. I toroids Nonaxisymmetric instabilities of self-gravitating disks. I toroids

Jul 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011ap%26ss.334....1h&link_type=abstract

Astrophysics and Space Science, Volume 334, Issue 1, pp.1-26

Astronomy and Astrophysics

Astrophysics

Hydrodynamics: Stability, Stars: Rotation

Scientific paper

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. One-armed modes ( m=1 modes) become unstable just after instability in the m=2 I 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≥3 J 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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