| Abstract
| - Context. The connection between solar energetic proton events and X-ray flares has been the focus of many studies over the past 13 yr. In the course of these investigations several peak size distribution functions based on Geostationary Operational Environmental Satellite (GOES) measurements of both quantities have been developed. In more recent studies one of these functions has been used to estimate the stellar proton fluence around the M-dwarf star AD Leonis. However, a comparison of the existing peak size distribution functions reveals strong discrepancies with respect to each other. Aims. The aim of this paper is to derive a new peak size distribution function that can be utilized to give a more realistic estimate of the stellar proton flux of G-, K-, and M-dwarf stars. Methods. By updating and extending the GOES-based peak size distribution down to B-class X-ray flare intensities with the help of SphinX data from the solar minimum conditions of 2009 and newly derived GOES data between 1975 and 2005, we developed a new power-law peak size distribution function for solar proton fluxes ( E > 10 MeV). However, its resulting slope differs from values reported in the literature. Therefore, we also developed a double-power-law peak size distribution function. An extension to much higher X-ray flare intensities (10 −1) W m −2 and above, for the first time, results in an approximation of best- and worst-case scenarios of the stellar proton flux around G-, K-, and M-dwarf stars. Results. Investigating the impact of the newly developed peak size distribution function for G-, K-, and M-dwarf star flare intensities we show that in the worst-case scenario previous studies may underestimate the stellar proton flux by roughly one to five orders of magnitude.
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