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

¹ Astronomical Institute of the Academy of Sciences, Boční II 1401/1a, 141-31 Praha 4, Czech Republic e-mail: horak@astro.cas.cz
² Department of Physics, Göteborg University, 41296 Göteborg, Sweden
³ Copernicus Astronomical Centre PAN, Bartycka 18, 00-716 Warsaw, Poland
⁴ Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám. 13, 746-01 Opava, Czech Republic
⁵ Johannes Kepler Institute of Astronomy, Zielona Góra University, ul. Lubuska 2, 65-265 Zielona Góra, Poland
⁶ MIT Kavli Institute for Astrophysics and Space Research, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

Received: 4 August 2008
Accepted: 6 January 2009

Abstract

We study the properties of twin kilohertz quasiperiodic oscillations (QPOs) with a simple toy model consisting of two oscillation modes coupled with a general nonlinear force. We examine resonant effects by slowly varying the values of the tunable, and nearly commensurable, eigenfrequencies. The behavior of the true oscillation frequencies and amplitudes during a slow transition through the 3:2 resonance is examined in detail, and it is shown that both are affected significantly by the nonlinearities in the governing equations. In particular, the amplitudes of oscillations reflect a resonant exchange of energy between the modes, and as a result the initially weaker mode may become dominant after the transition. We note that a qualitatively similar behavior was reported for several neutron-star sources where the difference in the amplitudes of neutron-star twin-peak QPOs changes sign as the observed frequency ratio of the QPOs passes through the value 3:2.