The Bursty Nature of Solar Flare X-Ray Emission. II. The Neupert Effect

We carry out a novel statistical test of the Neupert effect based on multifractal spectra. The multifractal spectrum is the number distribution of the strengths (i.e., the Hölder exponents) of bursts in a signal. This is tested on simulations and carried out on RHESSI X-ray data from a well observed GOES X4.8 magnitude flare. The multifractal spectra is ideally suited to quantifying the relative smooth and bursty signals typically found in (thermal) soft X-ray and (non-thermal) hard X-ray data of solar flares. We show that light curves from all energies between 3 keV and 25 keV are statistically similar, suggesting that all these signals are dominated by the same (presumably thermal) emission. Emission lying between 25 keV and 100 keV probably contains some contribution from both thermal and non-thermal sources. The multifractal spectrum of a signal and that of its (cumulative) temporal integration are statistically similar (i.e., low residuals upon subtraction), but shifted by one in the peak Hölder exponent. We find the pairs of 3-6 keV and 100-300 keV emissions, the 6-12 keV and 100-300 keV emissions and the 12-25 keV and 100-300 keV emissions are all consistent with the Neupert effect. The best agreement with the Neupert effect is between the 12-25 keV and 100-300 keV pair, although possibly with some secondary source of thermal emission present.