On the Power-Law Distributions of X-ray Fluxes from Solar Flares Observed with GOES

TL;DR

This study investigates the power-law distributions of solar flare X-ray fluxes observed by GOES, revealing differences between energy channels and implications for self-organized criticality models.

Contribution

It demonstrates that flux histograms follow power-laws independent of peak flux shape and shows differing spectral indexes between energy channels, challenging existing SOC models.

Findings

Higher energy channel has a harder flux distribution.

Flux histograms follow power-law with the same index as peak flux.

Temperature distribution approaches a power-law with index 2.

Abstract

Power-law frequency distributions of the peak flux of solar flare X-ray emission have been studied extensively and attributed to a system of self-organized criticality (SOC). In this paper, we first show that, so long as the shape of the normalized light curve is not correlated with the peak flux, the flux histogram of solar flares also follows a power-law distribution with the same spectral index as the power-law frequency distribution of the peak flux, which may partially explain why power-law distributions are ubiquitous in the Universe. We then show that the spectral indexes of the histograms of soft X-ray fluxes observed by GOES satellites in two different energy channels are different: the higher energy channel has a harder distribution than the lower energy channel, which challenges the universal power-law distribution predicted by SOC models and implies a very soft distribution of thermal energy content of plasmas probed by the GOES. The temperature ($T$) distribution, on the other hand, approaches a power-law distribution with an index of 2 for high values of $T$. Application of SOC models to statistical properties of solar flares needs to be revisited.