Extended Pan-Spectrum Fitting of Energetic Particle Spectra

WenYan Li,LingHua Wang,YongFu Wang, XinNian Guo, QianYi Ma

Earth and Planetary Physics（2025）

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Abstract

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.

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Key words

energy spectrum fitting,solar energetic particle,solar wind suprathermal particle,anomalous cosmic ray,pick-up ion

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【要点】：本文提出了一种新型的扩展全谱(EPS)公式，能够一致性地描述空间高能粒子的能量-通量谱特征，并包含了多种常见的单转折点和双转折点谱函数，有助于深入理解高能粒子的起源、加速和传输过程。

【方法】：作者通过综合多种常用的单转折点谱函数，构建了一个EPS公式，该公式可以适用于具有一个或两个能量转折点的粒子能谱，从而实现高能粒子能量-通量谱的自洽拟合。

【实验】：文中利用该EPS公式对多种空间粒子现象的代表性能量谱进行了拟合，包括太阳高能粒子（电子、质子、3He及重离子）、异常宇宙射线、太阳风超热粒子（光环和超光环电子；拾取离子及超热尾）等，并取得了良好的拟合效果。