2023ApJ...956...24K

Energetic particle environments are an important factor for the viability of life on exoplanets surrounding flare stars. In the heliosphere, large gradual solar energetic (E > 10 MeV) particle (SEP) events are produced by shocks from fast coronal mass ejections (CMEs). Extensive observations of solar X-ray flares, CMEs, and SEP events can provide guidance for flare star models of stellar energetic particle (StEP) events, for which stellar flares, but only rarely the associated CMEs, are observed. Comparing an extensive list of peak fluxes, timescales, and peak temperatures of 585 ≥ M3.0 solar X-ray flares with the occurrence of associated SEP events of peak flux Ip > 1.4 proton flux units, enhanced with proxy decametric-hectometric type II radio bursts, we determine guidelines for StEP event outcomes, given only stellar X-ray flare inputs. Longer timescales and lower peak temperatures of X-ray flares with a given peak X-ray flux Fp are more favorable for occurrence of associated SEP/StEP events, which, however, are only a minority of all solar flare outcomes. Most solar flares do not result in SEP events, invalidating scaling laws between stellar flares, CMEs, and StEP events. We discuss recent observations and models of the flare-CME relationship and suggest that StEP intensities Ip may often be overestimated.