Twin-peak quasiperiodic oscillations as an internal resonance

Abstract

Two inter-related 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 quasi-periodic oscillations (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 evolutionary tracks of the twin peaks. This suggests that the original (Abramowicz and Kluzniak) parametric-resonance scheme can be viewed as an ingenuous 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 we describe a general technique that permits to treat other cases 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 in the circulation region the observed frequencies remain off resonance. Our scheme predicts the power should cyclically be exchanged between the two oscillations. Likewise the high-frequency QPOs in neutron-star binaries, also in black-hole sources one expects, as a general property of the non-linear model, that slight detuning pushes the twin-peak frequencies out of sharp resonance.

Accepted for publication in A&A; 11 pages, 6 figures

Cited by in corpus (20)

• Quasinormal modes, quasiperiodic oscillations and shadow of rotating regular black holes in non-minimally coupled Einstein-Yang-Mills theory
• Shadow, quasinormal modes and quasiperiodic oscillations of rotating Kaluza-Klein black holes
• Orbital mechanics and quasiperiodic oscillation resonances of black holes in Einstein-Æther theory
• Corotational Instability of Inertial-Acoustic Modes in Black Hole Accretion Discs and Quasi-Periodic Oscillations
• Constraints on the magnetized Ernst black hole spacetime through quasiperiodic oscillations
• Weak nonlinear coupling between epicyclic modes in slender tori
• Models of high-frequency quasi-periodic oscillations and black hole spin estimates in Galactic microquasars
• Reversal of the amplitude difference of kHz QPOs in six atoll sources
• Internal resonance in non-linear disk oscillations and the amplitude evolution of neutron star kilohertz QPOs
• Constraining the Generalized Uncertainty Principle Through Black Hole Shadow and Quasiperiodic Oscillations
• Corotational Instability of Inertial-Acoustic Modes in Black-Hole Accretion Discs: Non-Barotropic Flows
• On the parameters of the spherically symmetric parametrized Rezzolla-Zhidenko spacetime through solar system tests, orbit of S2 star about Sgr A${}^{\star }$, and quasiperiodic oscillations
• Upper-twin-peak quasiperiodic oscillation in x-ray binaries and the energy from tidal circularization of relativistic orbits
• Black hole spin inferred from 3:2 epicyclic resonance model of high-frequency quasi-periodic oscillations
• Disc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model
• Equatorial and polar quasinormal modes and quasiperiodic oscillations of quantum deformed Kerr black hole
• Super-spinning compact objects and models of high-frequency quasi-periodic oscillations observed in Galactic microquasars. II. Forced resonances
• Simple analytic formula relating the mass and spin of accreting compact objects to their rapid X-ray variability
• Evidences of an innermost stable bound orbit predicted by general relativity from the amplitude of the twin-peak quasi-periodic oscillations
• Epicyclic oscillations and accretion disk around a special Buchdahl-inspired spacetime