Pan‐Spectrum Fitting Formula for Suprathermal Particles

• Published in: Journal of geophysical research. Space physics Vol. 125; no. 12
• Main Authors: Liu, Zixuan, Wang, Linghua, Wimmer‐Schweingruber, Robert F., Krucker, Säm, Mason, Glenn M.
• Format: Journal Article
• Language: English
• Published: 01.12.2020
• Subjects: particle acceleration; particle energy spectrum; spectrum fitting
• ISSN: 2169-9380; 2169-9402
• DOI: 10.1029/2020JA028702

We propose a pan‐spectrum fitting formula of suprathermal particles, J=A×E−β11+EE0αβ1−β2α, where J is the particle flux (or intensity), E is the particle energy, A is the amplitude coefficient, E0 represents the spectral transition energy, α (>0) describes the sharpness and width of spectral transition around E0, and the power‐law index β1 (β2) gives the spectral shape before (after) the transition. This formula incorporates many commonly used spectrum functions as special cases. When α goes to infinity (zero), this spectral formulabecomes the classical double‐power‐law (logarithmic‐parabola) function. When both β2 and E0 approach infinity and α is equal to 1, this formula can be simplified to the Ellison‐Ramaty function. Under some other specific parameter conditions, this formula can be transformed to the Kappa or Maxwellian distribution. Considering the uncertainties in both particle intensity and energy, we improve the fitting method and fit this pan‐spectrum formula well to the representative energy spectra of various suprathermal particle phenomena including SEPs (electrons, protons, 3He, and heavier ions), ESPs, bow‐shocked electrons, solar wind suprathermal electrons, anomalous cosmic rays, and hard X‐rays. Therefore, this pan‐spectrum fitting formula would help us comparatively examine the properties of energy spectrum of different suprathermal particle phenomena typically with a single energy break. Key Points We propose a new spectrum formula that is suitable to fit the single‐break energy spectra of various suprathermal particle phenomena We can obtain the shape and width of energy transition in particle spectrum This fitting enables us to quantitatively compare the spectral features of different suprathermal particles