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

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Abstract
We analyze the Q0957+561 A,B brightness record with 3 types of wavelets to define properties that are independent of the nature of the analyzing wavelet. The wavelet analysis picks out features having arbitrary shape, and 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 of the kind of statistical measure of wavelet amplitude, the fitted amplitudes seem to increase as a linear function of the wavelet duration, with the mean absolute deviation 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 than 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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