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Linear and non-linear theory of a parametric instability of hydrodynamic warps in Keplerian discs

Authors

  • Charles F. Gammie,

    1. Isaac Newton Institute, 20 Clarkson Road, Cambridge CB3 0EH
    2. Center for Astrophysics, MS-51, 60 Garden St, Cambridge, MA 02138, USA
    3. Center for Theoretical Astrophysics, University of Illinois, 1002 W. Green St, Urbana, IL 61801, USA
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  • Jeremy Goodman,

    1. Isaac Newton Institute, 20 Clarkson Road, Cambridge CB3 0EH
    2. Peyton Hall, Princeton, NJ 08544, USA
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  • Gordon I. Ogilvie

    Corresponding author
    1. Isaac Newton Institute, 20 Clarkson Road, Cambridge CB3 0EH
    2. Institute of Astronomy, Madingley Road, Cambridge CB3 0HA
    3. Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Straße 1, D-85740 Garching bei München, Germany
      ★ E-mail: gogilvie@ast.cam.ac.uk
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★ E-mail: gogilvie@ast.cam.ac.uk

Abstract

We consider the stability of warping modes in Keplerian discs. We find them to be parametrically unstable using two lines of attack, one based on three-mode couplings and the other on Floquet theory. We confirm the existence of the instability and investigate its non-linear development in three dimensions, via numerical experiment. The most rapidly growing non-axisymmetric disturbances are the most nearly axisymmetric (low-m) ones. Finally, we offer a simple, somewhat speculative model for the interaction of the parametric instability with the warp. We apply this model to the masing disc in NGC 4258 and show that, provided the warp is not forced too strongly, parametric instability can fix the amplitude of the warp.

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