Solar flares versus solar energetic particle events: Probabilistic projections to extreme events

¹ Sodankylä Geophysical Observatory, 99600, University of Oulu, Sodankylä, Finland
² Space Physics and Astronomy Research Unit, P.O.Box 8000 90014 University of Oulu, Oulu, Finland
³ Max-Planck-Institut für Sonnensystemforschung, 37077 Göttingen, Germany
⁴ University of Graz, Institute of Physics, 8010 Graz, Austria

^⋆ Corresponding author: sergey.koldobskiy@oulu.fi

Received: 24 June 2025
Accepted: 16 August 2025

Abstract

Aims. Terrestrial cosmogenic isotope records yield that extreme solar particle events (ESPEs) are relatively rare, occurring approximately once every 1500 years. In contrast, stellar observations show that superflares on solar-like stars might be significantly more frequent. This discrepancy raises the question of whether superflares and ESPEs are different manifestations of the same underlying phenomenon or whether they represent fundamentally distinct phenomena.

Methods. We analysed the conditional probability of a solar particle event occurring in relation to a solar flare with a given peak flux in soft X-rays, based on the observed statistics for the last 45 years. The probability was parametrised and extrapolated to extreme events to evaluate the probabilistic relationship between ESPEs and superflares.

Results. We found that the ESPEs may not be directly related to superflares but are likely produced by moderately strong flares if other coronal and interplanetary factors accidentally become favourable. ESPEs tend to occur during periods of weak-to-moderate solar activity. Thus, the difference in the occurrence rates of ESPEs and superflares can be naturally explained by the lack of a direct relation between these types of phenomena.