Revisiting empirical solar energetic particle scaling relations

Aims. The space radiation environment conditions and the maximum expected coronal mass ejection (CME) speed are assessed by investigating scaling laws between the peak proton flux and fluence of solar energetic particle (SEP) events with the speed of the CMEs. Methods. We used a complete catalog of SEP events, covering the last ∼25 years of CME observations (i.e., 1997–2017). We calculated the peak proton fluxes and integrated event fluences for events that reached an integral energy of up to E > 100 MeV. For a sample of 38 strong SEP events, we first investigated the statistical relations between the recorded peak proton fluxes (IP) and fluences (FP) at a set of integral energies of E > 10 MeV, E > 30 MeV, E > 60 MeV, and E > 100 MeV versus the projected CME speed near the Sun (VCME) obtained by the Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph (SOHO/LASCO). Based on the inferred relations, we further calculated the integrated energy dependence of both IP and FP, assuming that they follow an inverse power law with respect to energy. By making use of simple physical assumptions, we combined our derived scaling laws to estimate the upper limits for VCME, IP, and FP by focusing on two cases of known extreme SEP events that occurred on 23 February 1956, (GLE05) and in AD774/775, respectively. Based on the physical constraints and assumptions, several options for the upper limit VCME associated with these events were investigated. Results. A scaling law relating IP and FP to the CME speed as VCME5 for CMEs ranging between ∼3400–5400 km/s is consistent with values of FP inferred for the cosmogenic nuclide event of AD774/775. At the same time, the upper CME speed that the current Sun can provide possibly falls within an upper limit of VCME ≤ 5500 km/s.