Twin-peak quasiperiodic oscillations as an internal resonance

Two peaks occur in high-frequency power spectra of X-ray lightcurves of several black-hole candidates. We further explore the idea that a non-linear resonance mechanism operating in strong-gravity regime is responsible for these inter-related quasi-periodic oscillations (twin QPOs). By extending the multiple-scales analysis of Rebusco, we construct two-dimensional phase-space sections, which enable us to identify different topologies governing the system and to follow the evolutionary tracks of the twin peaks. This approach suggests that the original (Abramowicz & Kluźniak) parametric-resonance scheme can be viewed as a naïve account of the QPOs model with an internal resonance.We show an example of internal resonance in a system with up to two critical points, and describe a general technique that permits other cases to be treated in a systematical manner. A separatrix divides the phase-space sections into regions of different topology. Inside the libration region, the evolutionary tracks bring the observed twin-peak frequencies to an exact rational ratio, whereas the observed frequencies remain off resonance in the circulation region. Our scheme predicts the power should be cyclically exchanged between the two oscillations. Like the high-frequency QPOs in neutron-star binaries, one also expects, as a general property of the non-linear model, that in black-hole sources slight detuning pushes the twin-peak frequencies out of sharp resonance.

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