Astron. Astrophys. 325, 866-870 (1997)

1. Introduction

The discovery of high-energy -radiation from extragalactic compact objects has motivated many authors to consider the effects of -ray absorption by - pair production, eventually inducing pair cascades. The relevance of - pair production to astrophysical systems has first been pointed out by Nikishov (1962). The first investigation of the - absorption probability of high-energy photons by different soft photon fields, along with some useful approximations, can be found in Gould & Schréder (1967).

The energy spectrum of injected electrons and positrons due to this process has been studied by several authors (e. g., Bonometto & Rees 1971, Aharonian et al. 1983, Zdziarski & Lightman 1985, Coppi & Blandford 1990). In most astrophysically relevant cases, simple approximations can be used for this purpose, without much loss of accuracy. These usually rely on the high-energy photon having much higher energy than the soft photons and thus dominating the energy input and determining the direction of motion of the center-of-momentum frame of the produced pairs. Bonometto & Rees (1971) used basically the same technique as we do, but restricted their analysis to the case , and did not solve the problem analytically. Two recipes to calculate the full energy-dependence of the injected pairs have been published (Aharonian et al. 1983 and Coppi & Blandford 1990), but here the reader is still left with integrations to be carried out numerically.

It is the purpose of this paper to derive the full energy-spectrum of pairs, injected by - pair production, exact to second order QED for the case of isotropic radiation fields. In Sect. 2, we give a short overview of the kinematics which are used in Sect. 3 to calculate the pair injection spectrum. In Sect. 4, we compare our results to well-known approximations and specify the limitations of the various approximations. Our analysis is easily generalized to non-isotropic radiation fields. The derivation presented here is widely analogous to the derivation of the pair annihilation spectrum, given by Svensson (1982).

© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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