Weak nonlinear coupling between epicyclic modes in slender tori

Understand

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.