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A non-linear theory of vertical resonances in accretion discs | | G. I. Ogilvie
; | | Date: |
19 Dec 2001 | | Journal: | Mon.Not.Roy.Astron.Soc. 331 (2002) 1053 | | Subject: | astro-ph | | Affiliation: | Institute of Astronomy, Cambridge | | Abstract: | An important and widely neglected aspect of the interaction between an accretion disc and a massive companion with a coplanar orbit is the vertical component of the tidal force. As shown by Lubow, the response of the disc to vertical forcing is resonant at certain radii, at which a localized torque is exerted, and from which a compressive wave (p mode) may be emitted. Although these vertical resonances are weaker than the corresponding Lindblad resonances, the m=2 inner vertical resonance in a binary star is typically located within the tidal truncation radius of a circumstellar disc. In this paper I develop a general theory of vertical resonances, allowing for non-linearity of the response, and dissipation by radiative damping and turbulent viscosity. The problem is reduced to a universal, non-linear ordinary differential equation with two real parameters. Solutions of the complex non-linear Airy equation are presented to illustrate the non-linear saturation of the resonance and the effects of dissipation. It is argued that the m=2 inner vertical resonance is unlikely to truncate the disc in cataclysmic variable stars, but contributes to angular momentum transport and produces a potentially observable non-axisymmetric structure. | | Source: | arXiv, astro-ph/0112443 | | Services: | Forum | Review | PDF | Favorites | |
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