A&A 486, 1-8 (2008)
Weak nonlinear coupling between epicyclic modes in slender toriJ. Horák
Astronomical Institute v.v.i., Academy of Sciences, Bocní II, 141 31 Prague, Czech Republic
Received 18 July 2007 / Accepted 17 April 2008
We examine nonlinear oscillations of slender tori in the vicinity of black holes and compact stars. These tori represent useful probes of the complicated, nonlinear dynamics of real accretion disks and provide at least qualitative understanding of their oscillations. We demonstrate that epicyclic modes of such tori are weakly coupled due to the pressure and gravitational forces. We explore all possible resonances between two epicyclic modes up to the fourth order. We show that the strongest resonance between axisymmetric modes is 3:2. In addition, any resonance between an axisymmetric and a non-axisymmetric mode is excluded due to axial and equatorial-plane symmetries of the equilibrium torus. We examine a parametric excitation of vertical axisymmetric oscillations by radial oscillations in the 3:2 resonance. We show that the resonance may be significant only for high-amplitude radial oscillations.
Key words: accretion, accretion-disks -- black hole physics -- solar system: formation
© ESO 2008