Fast Spectral Fitting of Hard X-Ray Bremsstrahlung from Truncated Power-Law Electron Spectra

Abstract

Hard X-Ray bremsstrahlung continuum spectra, such as from solar flares, are commonly described in terms of power-law fits, either to the photon spectra themselves or to the electron spectra responsible for them. In applications various approximate relations between electron and photon spectral indices are often used for energies both above and below electron low-energy cutoffs. We examine the form of the exact relationships in various situations, and for various cross-sections, showing that empirical relations sometimes used can be highly misleading and consider how to improve fitting procedures. We obtain expressions for photon spectra from single, double and truncated power-law electron spectra for a variety of cross-sections and for the thin and thick target models and simple analytic expressions for the Bethe-Heitler cases. We show that above a low-energy cutoff the Kramers and Bethe-Heitler results match reasonably well with results for exact cross-sections up to energies around 100 keV; that below the low-energy cutoff, Kramers and other constant spectral index forms commonly used are very poor approximations to accurate results; but that our analytical forms are a very good match. Analytical forms of the Bethe-Heitler photon spectra from general power-law electron spectra are an excellent match to exact results for both thin and thick targets and they enable much faster spectral fitting than evaluation of the full spectral integrations.

arXiv comment7 pages, 4 figures, submitted to Astronomy and Astrophysics

References in corpus (4)

• RHESSI Microflare Statistics II. X-ray Imaging, Spectroscopy & Energy Distributions
• Compton backscattered and primary X-rays from solar flares: angle dependent Green's function correction for photospheric albedo
• Determination Of Electron Flux Spectra In A Solar Flare With An Augmented Regularization Method: Application To Rhessi Data
• Electron-Electron Bremsstrahlung Emission and the Inference of Electron Flux Spectra in Solar Flares

Cited by in corpus (6)

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• Diagnostics of non-thermal distributions in solar flare spectra observed by RESIK and RHESSI
• Modifications of thick-target model: re-acceleration of electron beams by static and stochastic electric fields
• The Role of Inverse Compton Scattering in Solar Coronal Hard X-ray and Gamma-ray Sources
• Return currents and energy transport in the solar flaring atmosphere