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

TL;DR

This paper investigates how nonlinear resonances between coupled oscillation modes can explain the amplitude evolution of neutron star kilohertz QPOs, highlighting energy exchange effects during the 3:2 resonance transition.

Contribution

It introduces a simple nonlinear toy-model to analyze resonant effects and amplitude changes in twin QPOs, providing insights into observed neutron star phenomena.

Findings

Amplitudes exchange energy during resonance, altering dominance of modes.

Nonlinearities significantly influence oscillation frequencies and amplitudes.

Behavior matches observed amplitude sign changes in neutron star QPOs.

Abstract

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. We note that a qualitatively similar behavior has been recently reported in several neutron star sources by Torok (2008, arXiv:0812.4751), who found that the difference of amplitudes in neutron star twin peak QPOs changes sign as the observed frequency ratio of the QPOs passes through the value 3:2.