A Wavelet Exploration of the Q0957+561A,B Brightness Record

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Abstract
We analyze the Q0957+561 A, B brightness record with three types of wavelets in order to define properties that are independent of the nature of the analyzing wavelet. The wavelet analysis picks out features having arbitrary shape, localizes them in time, and fits amplitudes. We find that independently of the analyzing wavelet, the mean wavelet amplitude is zero, meaning that there are as many positive as negative brightness spikes. For all wavelet durations, the fitted amplitudes are equal in the A and B images, except that image B may have larger amplitude brightness fluctuations for the longest duration (64 day) features. Independently of the wavelet family fitted or the kind of statistical measure of the wavelet amplitude, the fitted amplitudes seem to increase as a linear function of the wavelet duration, with the mean absolute deviation being about a factor of 10 greater for 64 day wavelets than for 2 day wavelets. The underlying physical process producing the brightness fluctuations is found to have more power in long-duration wavelets than in short-duration wavelets as compared to a process dominated by white noise. Thus, it is established that the rapid brightness fluctuations observed in the Q0957 images A and B are not the result of observational noise.
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