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

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

2000-01-31

arxiv.org/abs/astro-ph/0001539v2

Mon.Not.Roy.Astron.Soc. 318 (2000) 1005

Astronomy and Astrophysics

Astrophysics

14 pages, 6 figures, revised version with appendix added, to be published in MNRAS

Scientific paper

10.1046/j.1365-8711.2000.03669.x

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 nonlinear 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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