WAVELETS WITH RIDGES: A HIGH-RESOLUTION REPRESENTATION OF CATACLYSMIC VARIABLE TIME SERIES

Quasi-periodic oscillations (QPO) and dwarf nova oscillations (DNOs) occur in dwarf novae and nova-like variables during outburst and occasionally during quiescence, and have analogs in high-mass X-ray binaries and black-hole candidates. The frequent low coherence of quasi-period oscillations and DNOs can make detection with standard time-series tools such as periodograms problematic. This paper develops tools to analyze quasi-periodic brightness oscillations. We review the use of time-frequency representations (TFRs) in the astronomical literature, and show that representations such as the Choi-Williams distribution and Zhao-Atlas-Marks representation, which are best suited to high signal-to-noise data, cannot be assumed a priori to be the best techniques for our data, which have a much higher noise level and lower coherence. This leads us to a detailed analysis of the time-frequency resolution and statistical properties of six TFRs. We conclude that the wavelet scalogram, with the addition of wavelet ridges and maxima points, is the most effective TFR for analyzing quasi-periodicities in low signal-to-noise data, as it has high time-frequency resolution, and is a minimum variance estimator. We use the wavelet ridges method to re-analyze archival data from VW Hyi, and find 62 new QPOs and 7 new long-period DNOs. Relative to previous analyses, our method substantially improves the detection rate for QPOs.