Bivariate Number Distribution of Solar Soft X-Ray Flares

Conventionally, researchers investigated the number distribution of solar flares by univariate analysis using all available data. For the first time, we investigate the bivariate number distribution of peak flux (f) and duration (T) of soft X-ray flares observed by the Geostationary Operational Environmental Satellite during the past 10 years. First, the univariate number distribution of f is found to obey a power law either for each class of flares or for the B or >= C flares in a certain range of T. But the power-law index of B-class flares is much smaller than those of other higher-class ones. For the >= C flares, the longer the duration, the smaller the power-law index. The univariate number distribution of T deviates from the power law at shorter durations and is better fitted by a skewed Gaussian function in logarithmic coordinates for almost any given range of f, reflecting the random phenomena in solar flares. Then, based on the univariate analysis, a linear Gaussian function is proposed to describe the bivariate logarithmic number distribution of f and T, from which the local power-law index with respect to either f or T can also be analyzed. The real number distribution of B flares should be in between the observed one and the power-law distribution of stronger flares (>= C). We suggest that nanoflare activity may not be the dominant source of coronal heating.