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Astron. Astrophys. 325, 401-413 (1997)

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1. Introduction

Positron production and annihilation are widespread processes in nature. Gamma-ray spectra of many astrophysical sources exhibit an annihilation feature, while their continuum indicates the presence of mid-relativistic thermal plasmas with [FORMULA] keV. Spectra of [FORMULA] -ray bursts and Crab pulsar show emission features in the vicinity of 400-500 keV (Mazets et al. 1982; Parlier et al. 1990), which are generally believed to be red-shifted annihilation lines. Recent observations with SIGMA telescope have exhibited annihilation features in the vicinity of [FORMULA] keV in spectra of two Galactic black hole candidates, 1E 1740.7-2942 (Bouchet et al. 1991; Sunyaev et al. 1991; Churazov et al. 1993; Cordier et al. 1993) and Nova Muscae (Goldwurm et al. 1992; Sunyaev et al. 1992). A narrow annihilation line has been observed from solar flares (Murphy et al. 1990) and from the direction of the Galactic center (Leventhal et al. 1978).

The region of the Galactic center contains several sources which demonstrate their activity at various wavelengths and particularly above several hundred keV (e.g., see Churazov et al. 1994). Escape of positrons from such a source or several sources into the interstellar medium, where they slow down and annihilate, can account for the 511 keV narrow line observed from this direction. The 1E 1740.7-2942 object has been proposed as the most likely candidate to be responsible for this variable source of positrons (Ramaty et al. 1992). This would only require that a small fraction of [FORMULA] -pairs, which is generally believed to be produced in the hot inner region of an accretion disc, escapes into surrounding space (Meirelles & Liang 1993). Nova Muscae shows a spectrum which is consistent with Comptonization by a thermal plasma [FORMULA] keV in its hard X-ray part, while a relatively narrow annihilation line observed by SIGMA during the X-ray flare on 20-21 January, 1991 implies that positrons annihilate in a much colder medium (Gilfanov et al. 1991; Goldwurm et al. 1992).

Numerous studies of positron propagation and annihilation in cold interstellar gas (e.g., see Guessoum et al. 1991 and references therein) have been inspired by observations of a narrow 511 keV line emission from the Galactic center region. Relativistic pair plasmas have been a matter of investigation during a decade (for a review, see Svensson 1990). In all thermal models, however, particles are assumed to be Maxwellian a priori and very often one only pays attention to the relevant relaxation time scales. Herewith, the annihilation line shape, the main feature which can be actually measured, is strongly influenced by the real particle distribution. The latter can differ from a Maxwellian under certain circumstances, such as particle injection, escape, and annihilation. It is thus of astrophysical interest to study particle distributions in various physical conditions.

In this paper we use a Fokker-Planck approach to examine the effects of annihilation, particle escape and injection on the form of a steady-state positron distribution in thermal hydrogen plasmas with [FORMULA]. Pairs are assumed to be produced in the bulk of the plasma due to [FORMULA] -, [FORMULA] -particle, or particle-particle interactions, or to be permanently injected into the plasma volume by an external source. We don't touch here upon the cause of particle escape, it could be of diffusive origin or due to the radiation pressure (e.g., see Kovner 1984). Since the plasma cloud serves as a thermostat, it is therefore reasonable, as the first step into the problem, to consider that the electron distribution approaches Maxwellian. The positron fraction considered is small enough, so it does not affect the electron distribution.

Suggesting that the features observed by SIGMA in [FORMULA] keV region are due to the electron-positron annihilation in thermal plasma, we apply the obtained results to Nova Muscae and the 1E 1740.7-2942 source in order to get the parameters of the emitting regions where the annihilation features have been observed.

In Sect. 2 the Fokker-Planck treatment is considered and we present a method to obtain a steady-state solution. The reaction rate formalism is introduced in Sect. 3. The expressions for energy changes and losses due to Coulomb scattering, bremsstrahlung and Comptonization are given in Sect. 4-6. Electron-positron annihilation is considered in Sect. 7. The results of calculation are discussed in Sect. 8. In the last section (Sect. 9) we discuss the physical parameters of the emitting regions in Nova Muscae and the 1E 1740.7-2942 source. Throughout the paper units [FORMULA] are used.

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© European Southern Observatory (ESO) 1997

Online publication: May 5, 1998