Revisiting empirical solar energetic particle scaling relations

II. Coronal mass ejections

¹ Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing (IAASARS), National Observatory of Athens, I. Metaxa & Vas. Pavlou St., 15236 Penteli, Greece
² Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, 24118 Kiel, Germany
³ Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, 24118 Kiel, Germany
⁴ NASA, Goddard Space Flight Center, Heliophysics Science Division, Greenbelt, MD 20771, USA
⁵ Institute of Physics & Kanzelhöhe Observatory for Solar and Environmental Research, University of Graz, A-8010 Graz, Austria

Received: 13 May 2024
Accepted: 3 August 2024

Abstract

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 (I_P) and fluences (F_P) 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 (V_CME) 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 I_P and F_P, 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 V_CME, I_P, and F_P 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 V_CME associated with these events were investigated.

Results. A scaling law relating I_P and F_P to the CME speed as V_CME⁵ for CMEs ranging between ∼3400–5400 km/s is consistent with values of F_P 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 V_CME ≤ 5500 km/s.