Extended pan-spectrum fitting of energetic particle spectra

The energy spectrum of energetic particles in space often shows a non-thermal spectral shape with two spectral transitions/breaks over a wide energy range, carrying crucial information about their acceleration, release and transportation process. To self-consistently characterize the spectral features of energetic particles, here we propose a novel extended pan-spectrum (EPS) formula to fit the particle energy-flux spectrum, which has the merit that can incorporate many commonly used spectrum functions with one spectral transition, including the pan-spectrum, double-power-law, Kappa, Ellison-Ramaty (ER) functions, etc. The formula can also determine the spectral shape with two spectral transitions, including the triple-power-law function, Kappa distribution (at low energy) plus power law (at high energy), power law (at low energy) plus ER function, etc. Considering the uncertainties in both J and E, we can fit this EPS formula well to the representative energy spectra of various particle phenomena in space, including solar energetic particles (electrons, protons, ³He and heavier ions), anomalous cosmic rays, solar wind suprathermal particles (halo and superhalo electrons; pick-up ions and the suprathermal tail), etc. Therefore, the EPS fitting can help us self-consistently determine the spectral features of different particle phenomena, and improve our understanding of the physical nature of the origin, acceleration, and transportation of energetic particles in space.