Statistical study of the peak and fluence spectra of solar energetic particles observed over four solar cycles

Context. Solar energetic particles (SEPs) are an important space radiation source, especially for the space weather environment in the inner heliosphere. The energy spectrum of SEP events is crucial both for evaluating their radiation effects and for understanding their acceleration process at the source region, along with their propagation mechanism. Aims. In this work, we investigate the properties of the SEP peak flux spectra and the fluence spectra and their potential formation mechanisms using statistical methods. We aim to advance our understanding of SEP acceleration and propagation mechanisms. Methods. Employing a dataset from the European Space Agency’s Solar Energetic Particle Environment Modelling (SEPEM) program, we obtained and fit the peak-flux and fluence proton spectra of more than a hundred SEP events from 1974 to 2018. We analyzed the relationship among the solar activity, X-ray peak intensity of solar flares, and the SEP’s spectral parameters. Results. Based on the assumption that the initial spectrum of accelerated SEPs generally displays a power-law distribution and that the diffusion coefficient has a power-law dependence on the particle energy, we can assess both the source and propagation properties using the observed SEP event peak flux and fluence energy spectra. We confirm that the spectral properties of SEPs are influenced by the solar source and the interplanetary conditions, whereas their transportation process can be influenced by different phases of solar cycle. Conclusions. This study provides an observational perspective on the double power-law spectral characteristics of the SEP energy spectra, revealing their correlation with the adiabatic cooling and diffusion processes during the particle propagation from the Sun to the observer. This result contributes to forging a deeper understanding of the acceleration and propagation of SEP events, in particular, the possible origins of the double power law.