EDP Sciences
Free access
Volume 486, Number 1, July IV 2008
Page(s) 1 - 8
Section Astrophysical processes
DOI http://dx.doi.org/10.1051/0004-6361:20078305
Published online 22 May 2008

A&A 486, 1-8 (2008)
DOI: 10.1051/0004-6361:20078305

Weak nonlinear coupling between epicyclic modes in slender tori

J. Horák

Astronomical Institute v.v.i., Academy of Sciences, Bocní II, 141 31 Prague, Czech Republic
    e-mail: horak@astro.cas.cz

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