期刊
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
卷 331, 期 4, 页码 1053-1064出版社
BLACKWELL PUBLISHING LTD
DOI: 10.1046/j.1365-8711.2002.05270.x
关键词
accretion, accretion discs; hydrodynamics; waves; celestial mechanics; binaries : close
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 in = 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.
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