Quasi-periodic oscillations under wavelet microscope: the application of Matching Pursuit algorithm

Abstract

We zoom in on the internal structure of the low-frequency quasi-periodic oscillation (LF QPO) often observed in black hole binary systems to investigate the physical nature of the lack of coherence in this feature. We show the limitations of standard Fourier power spectral analysis for following the evolution of the QPO with time and instead use wavelet analysis and a new time-frequency technique -Matching Pursuit algorithm- to maximise the resolution with which we can follow the QPO behaviour. We use the LF QPO seen in a very high state of XTE J1550-564 to illustrate these techniques and show that the best description of the QPO is that it is composed of multiple independent oscillations with a distribution of lifetimes but with constant frequency over this duration. This rules out models where there is continual frequency modulation, such as multiple blobs spiralling inwards. Instead it favours models where the QPO is excited by random turbulence in the flow.

11 pages, 11 figures (9 in color), accepted for publication in Astronomy and Astrophysics

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• Tracking the Evolution of QPO in RE J1034+396 Using the Hilbert-Huang Transform
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• The model constraints from the observed trends for the quasi-periodic oscillation in RE J1034+396
• Pitfalls of periodograms: The non-stationarity bias in the analysis of quasi-periodic oscillations
• Characterizing Intermittency of 4-Hz Quasi-periodic Oscillation in XTE J1550-564 using Hilbert-Huang Transform
• Machine learning application to detect light echoes around black holes
• A Temporal Scale to Track the Spectral Transitions in Low-Mass X-ray Binaries
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