Internal resonance in non-linear disk oscillations and the amplitude evolution of neutron star kilohertz QPOs

Understand

We explore some properties of twin kilohertz quasiperiodic oscillations (QPOs) in a simple toy-model consisting of two oscillation modes coupled by a general nonlinear force.

• We examine resonant effects by slowly varying the values of the tunable, and nearly commensurable, eigenfrequencies.
• The behavior of the actual oscillation frequencies and amplitudes during a slow transition through the 3:2 resonance is examined in detail and it is shown that both are significantly affected by the nonlinearities in the governing equations.
• In particular, the amplitudes of oscillations reflect a resonant exchange of energy between the modes, as a result the initially weaker mode may become dominant after the transition.