Parametric resonance as a model for QPO sources -- I. A general approach to multiple scales
Abstract
In the resonance model, high-frequency quasi-periodic oscillations (QPOs) are supposed to be a consequence of nonlinear resonance between modes of oscillations occurring within the innermost parts of an accretion disk. Several models with a prescribed mode--mode interaction were proposed in order to explain the characteristic properties of the resonance in QPO sources. In this paper, we examine nonlinear oscillations of a system having a quadratic nonlinearity and we show that this case is particularly relevant for QPOs. We present a very convenient way how to study internal resonances of a fully general system using the method of multiple scales. Finally, we concentrate to conservative systems and discuss their behavior near the 3:2 resonance.
Cite
@article{arxiv.astro-ph/0408092,
title = {Parametric resonance as a model for QPO sources -- I. A general approach to multiple scales},
author = {J. Horak},
journal= {arXiv preprint arXiv:astro-ph/0408092},
year = {2007}
}
Comments
To appear in proceedings of the Workshop Processes in the vicinity of black holes and neutron stars, held at Silesian University (Opava, October 2003); 16 pages, 4 figures