Proton Energy Spectra of Energetic Storm Particle Events and Relation with Shock Parameters and Turbulence

The proton energy spectra of 23 energetic storm particle (ESP) events of various types, occurring either in association with (16 events) or in the absence of (7 events) solar energetic particles (SEPs), are investigated by using data from particle instruments aboard STEREO A in the energy range from 84.1 keV to 100 MeV. The obtained spectra were fitted with several known functions. Out of the 12 ESP events occurring in association with SEPs and quasi-perpendicular shocks, the Weibull distribution provides good fits to the spectra over the whole energy range in five cases. For the other seven events it fits the high energy tail, with lower energies explained by the power law predicted by the diffusive shock acceleration (DSA). Conversely, for the four SEP-associated ESPs at quasi-parallel shocks, a double power law better reproduces the observed spectra. Moreover, a significant correlation of the downstream turbulence level is found with the background subtracted Weibull parameters for quasi-perpendicular shocks, and with the proton peak value in the intermediate energy range of 4–6 MeV for all 16 considered shocks. Our results suggest that the downstream turbulence is a relevant factor in particle acceleration and that stochastic acceleration (SA) can be a plausible mechanism for reacceleration at interplanetary shocks. In the seven cases not associated with SEPs, an Ellison–Ramaty form fits the observed spectra, consistently with a DSA process, suggesting that a strong shock and/or a high energy particle background should be present for the SA to be at work.