Simple analytical approximations for treatment of inverse Compton scattering of relativistic electrons in the blackbody radiation field
Abstract
The inverse Compton (IC) scattering of relativistic electrons is one of the major gammaray production mechanisms in different environments. Often, the target photons for IC scattering are dominated by blackbody (or graybody) radiation. In this case, the precise treatment of the characteristics of IC radiation requires numerical integrations over the Planckian distribution. Formally, analytical integrations are also possible but they result in series of several special functions; this limits the efficiency of usage of these expressions. The aim of this work is the derivation of approximate analytical presentations that would provide adequate accuracy for the calculations of the energy spectra of upscattered radiation, the rate of electron energy losses, and the mean energy of emitted photons. Such formulae have been obtained by merging the analytical asymptotic limits. The coefficients in these expressions are calculated via the leastsquares fitting of the results of numerical integrations. The simple analytical presentations, obtained for both the isotropic and anisotropic target radiation fields, provide adequate (as good as 1%) accuracy for broad astrophysical applications.
 Authors:

 Institute of Space and Astronautical Science/JAXA, 311 Yoshinodai, Chuoku, Sagamihara, Kanagawa 2525210 (Japan)
 Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2 (Ireland)
 Publication Date:
 OSTI Identifier:
 22351581
 Resource Type:
 Journal Article
 Journal Name:
 Astrophysical Journal
 Additional Journal Information:
 Journal Volume: 783; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004637X
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; ANISOTROPY; APPROXIMATIONS; ASTROPHYSICS; ASYMPTOTIC SOLUTIONS; BLACKBODY RADIATION; COMPTON EFFECT; DISTRIBUTION; ELECTRONS; EMISSION; ENERGY LOSSES; ENERGY SPECTRA; GAMMA RADIATION; PHOTONS; RELATIVISTIC RANGE; SCATTERING; STARS
Citation Formats
Khangulyan, D., Aharonian, F. A., and Kelner, S. R., Email: khangul@astro.isas.jaxa.jp, Email: Felix.Aharonian@mpihd.mpg.de, Email: Stanislav.Kelner@mpihd.mpg.de. Simple analytical approximations for treatment of inverse Compton scattering of relativistic electrons in the blackbody radiation field. United States: N. p., 2014.
Web. doi:10.1088/0004637X/783/2/100.
Khangulyan, D., Aharonian, F. A., & Kelner, S. R., Email: khangul@astro.isas.jaxa.jp, Email: Felix.Aharonian@mpihd.mpg.de, Email: Stanislav.Kelner@mpihd.mpg.de. Simple analytical approximations for treatment of inverse Compton scattering of relativistic electrons in the blackbody radiation field. United States. doi:10.1088/0004637X/783/2/100.
Khangulyan, D., Aharonian, F. A., and Kelner, S. R., Email: khangul@astro.isas.jaxa.jp, Email: Felix.Aharonian@mpihd.mpg.de, Email: Stanislav.Kelner@mpihd.mpg.de. Mon .
"Simple analytical approximations for treatment of inverse Compton scattering of relativistic electrons in the blackbody radiation field". United States. doi:10.1088/0004637X/783/2/100.
@article{osti_22351581,
title = {Simple analytical approximations for treatment of inverse Compton scattering of relativistic electrons in the blackbody radiation field},
author = {Khangulyan, D. and Aharonian, F. A. and Kelner, S. R., Email: khangul@astro.isas.jaxa.jp, Email: Felix.Aharonian@mpihd.mpg.de, Email: Stanislav.Kelner@mpihd.mpg.de},
abstractNote = {The inverse Compton (IC) scattering of relativistic electrons is one of the major gammaray production mechanisms in different environments. Often, the target photons for IC scattering are dominated by blackbody (or graybody) radiation. In this case, the precise treatment of the characteristics of IC radiation requires numerical integrations over the Planckian distribution. Formally, analytical integrations are also possible but they result in series of several special functions; this limits the efficiency of usage of these expressions. The aim of this work is the derivation of approximate analytical presentations that would provide adequate accuracy for the calculations of the energy spectra of upscattered radiation, the rate of electron energy losses, and the mean energy of emitted photons. Such formulae have been obtained by merging the analytical asymptotic limits. The coefficients in these expressions are calculated via the leastsquares fitting of the results of numerical integrations. The simple analytical presentations, obtained for both the isotropic and anisotropic target radiation fields, provide adequate (as good as 1%) accuracy for broad astrophysical applications.},
doi = {10.1088/0004637X/783/2/100},
journal = {Astrophysical Journal},
issn = {0004637X},
number = 2,
volume = 783,
place = {United States},
year = {2014},
month = {3}
}