Energetic Protons in the Inner Heliosphere Exhibit Consistent ∼1 MeV Temperatures

The solar energetic particle (SEP) proton population follows a kappa distribution distinct from the solar wind. This conclusion has been reached based on a method that tests whether there is a kappa distribution behind observed SEP power-law spectra, also estimating thermodynamic properties (density, temperature, and kappa) of the SEP population. Previously, this method was applied to a single SEP event using only measurements from IS⊙IS/HET on board the Parker Solar Probe. In this study, we applied this method to Parker Solar Probe data from 2018 to 2024. A surprising result is that despite both having small local fluctuations, the temperature is almost always close to ∼1 MeV, whereas the density spans several orders of magnitude. To validate this finding, we use an alternative method by directly fitting kappa distributions to measurements over energies ranging from 3 to 50 MeV using both LET and HET. This allows us to include energies sufficiently close to the typical temperature of ∼1 MeV. We also applied both methods to measurements from STEREO-A from 2006 to 2024. The results from both methods with both spacecraft were in agreement that the temperature of the SEP proton population is almost always close to ∼1 MeV.