Probability Distribution Functions of Solar and Stellar Flares

TL;DR

This study analyzes the energy distribution of solar and stellar flares, revealing that solar flares follow a tapered power law with large flares dominating energy output, while stellar superflares have a flatter distribution, indicating different underlying processes.

Contribution

It provides a comparative analysis of solar and stellar flare energy distributions, highlighting differences in their statistical properties and implications for flare energy contributions.

Findings

Solar flare fluence follows a tapered power law with exponent slightly less than 2.

Largest predicted solar flares could reach X70 class in 1000 years.

Stellar superflares have a flatter distribution with an exponent around 1.05.

Abstract

We studied the soft X-ray data of solar flares and found that the distribution functions of flare fluence are successfully modeled by tapered power law or gamma function distributions whose power exponent is slightly smaller than 2, indicating that the total energy of the flare populations is mostly contributed from a small number of large flares. The largest possible solar flares in 1000 years are predicted to be around X70 in terms of the GOES flare class. We also studied superflares (more energetic than solar flares) from solar-type stars, and found that their power exponent in the fitting of the gamma function distribution is around 1.05, much flatter than solar flares. The distribution function of stellar flare energy extrapolated downward does not connect to the distribution function of solar flare energy.