Statistics – Computation
Scientific paper
Jul 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987mnras.227..403s&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 227, July 15, 1987, p. 403-451.
Statistics
Computation
211
Compton Effect, Electron Photon Cascades, Pair Production, Radiation Distribution, Thomson Scattering, X Ray Sources, Computational Astrophysics, Integral Equations, Optical Thickness, Radiation Pressure, Seyfert Galaxies
Scientific paper
Non-thermal pair cascades, where injected relativistic electrons (or pairs) cool by inverse Compton scattering on soft photons in the Thomson limit and where the resulting hard photons pair produce on other up-scattered photons, are described by an integral equation. A general integral equation for all relevant optical depths is obtained by using a simple prescription for the radiative transfer effects due to photon-photon absorption and to Compton scattering by the cooled pairs. The integral equation is solved analytically in the limit of large injection compactness Li/R (Li is the injected particle power and R the size of the injection region), where every γ-ray photon produces a pair (saturated pair production). Each photon generation is described separately and has a well-determined spectral index at small photon energies, being α = 1/2 and 3/4 for the first and second generation, respectively. Analytical and numerical solutions of the general integral are discussed in detail.
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