Observations of Kappa Distributions in Solar Energetic Protons and Derived Thermodynamic Properties

Abstract In this paper, we model the high-energy tail of observed solar energetic proton energy distributions with a kappa distribution function. We employ a technique for deriving the thermodynamic parameters of solar energetic proton populations measured by the Parker Solar Probe Integrated Science Investigation of the Sun EPI-Hi high-energy telescope, over energies from 10 to 60 MeV. With this technique, we explore, for the first time, the characteristic thermodynamic properties of the solar energetic protons associated with an interplanetary coronal mass ejection (ICME) and its driven shock. We find that: (1) the spectral index or, equivalently, the thermodynamic parameter kappa of solar energetic protons ( κ EP ) gradually increases, starting from the pre-ICME region (upstream of the CME-driven shock), reaching a maximum in the CME ejecta ( κ EP ≈ 3.5), followed by a gradual decrease throughout the trailing portion of the CME; (2) the solar energetic proton temperature and density ( T EP and n EP ) appear anticorrelated, a behavior consistent with subisothermal polytropic processes; and (3) values of T EP and κ EP appear to be positively correlated, indicating an increasing entropy with time. Therefore, these proton populations are characterized by a complex and evolving thermodynamic behavior, consisting of multiple subisothermal polytropic processes, and a large-scale trend of increasing temperature, kappa, and entropy. This study and its companion study by Livadiotis et al. open up a new set of procedures for investigating the thermodynamic behavior of energetic particles and their shared thermal properties.