The State of Self-Organized Criticality of the Sun During the Last 3 Solar Cycles. I. Observations

TL;DR

This study analyzes solar flare data over three solar cycles, revealing power-law distributions in flare properties and a cyclic variation in their slopes linked to solar magnetic complexity.

Contribution

It provides the first comprehensive analysis of solar flare distributions over multiple cycles, identifying a sinusoidal variation in power-law slopes correlated with solar activity.

Findings

Power-law slopes for flare properties with mean values: 1.72, 1.60, 1.98.

A sinusoidal variation of the peak flux slope with a 12.6-year cycle.

Flattest slopes during solar maximum indicating higher magnetic complexity.

Abstract

We analyze the occurrence frequency distributions of peak fluxes $P$, total fluxes $E$, and durations $T$ of solar flares over the last three solar cycles (during 1980--2010) from hard X-ray data of HXRBS/SMM, BATSE/CGRO, and RHESSI. From the synthesized data we find powerlaw slopes with mean values of $\alpha_P=1.72\pm0.08$ for the peak flux, $\alpha_E=1.60\pm0.14$ for the total flux, and $\alpha_T=1.98\pm0.35$ for flare durations. We find a systematic anti-correlation of the powerlaw slope of peak fluxes as a function of the solar cycle, varying with an approximate sinusoidal variation $\alpha_P(t)=\alpha_0+\Delta \alpha \cos{[2\pi (t-t_0)/T_{cycle}]}$, with a mean of $\alpha_0=1.73$, a variation of $\Delta \alpha =0.14$, a solar cycle period $T_{cycle}=12.6$ yrs, and a cycle minimum time $t_0=1984.1$. The powerlaw slope is flattest during the maximum of a solar cycle, which indicates a higher magnetic complexity of the solar corona that leads to an overproportional rate of powerful flares.