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

¹ Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warszawa, Poland e-mail: pawel@ieee.org
² Centre for Wavelets, Approximation and Information Processing, Temasek Laboratories at National University of Singapore, 5A Engineering Drive 1, #09-02 Singapore 117411, Singapore
³ Department of Physics, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE, UK

Received: 19 August 2009
Accepted: 5 March 2010

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.