### Abstract

Intensity, polarization, and cooling rate of the two-photon annihilation radiation are studied in detail in the case of one-dimensional power-law distributions of electrons and positrons, assuming that they occupy the ground Landau level in a strong magnetic field B∼10^{10}-10^{12} G. Simple analytical expressions for limiting cases are obtained and results of numerical calculations of radiation characteristics are presented. Power-law e^{±} distributions η_{±} ∝ ε_{±}^{-k} are shown to generate power-law spectra of the annihilation radiation at E≫mc^{2} and E≪mc^{2}, with indices depending on the direction of radiation. The annihilation spectra at θ{symbol}=0 show the largest blue-shifts of their maxima and the hardest high-energy tails I(E≫mc^{2}, θ{symbol}=0)∝E^{-(k-1)}. The blue-shifts reduce, and the hard tials steepen, with increasing θ{symbol}. At θ{symbol}>(2 mc^{2}/E)^{1/2} the slopes of the high-energy tails rapidly transform to that at θ{symbol}=π2, I(E≫mc^{2}, θ{symbol}=π/2)∝E^{-(2 k+3)}. The direction-integrated spectra S(E) also display the power-law tials at low and high energies, S(E≫mc^{2})∝E^{-(k+1)}. The total annihilation rate and energy losses decrease with decreasing k, being higher than for the isotropic e^{±} power-law distributions at the same k. The radiation is linearly polarized in the plane formed by the magnetic field and wave-vector. The polarization degree P is maximum at E≫mc^{2}:P_{max}≃0.6 for θ{symbol}=π/2. Annihilation features and power-law-like hard tails observed in many gamma-ray burst spectra may be associated with the annihilation radiation of the magnetized power-law distributed plasma near neutron stars. Comparison of the observed and theoretical spectra allows one to estimate the power-law index of the e^{-}e^{+}-distribution and the gravitational redshift factor in the radiating region.

Original language | English (US) |
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Pages (from-to) | 175-200 |

Number of pages | 26 |

Journal | Astrophysics and Space Science |

Volume | 192 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 1 1992 |

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### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysics and Space Science*,

*192*(2), 175-200. https://doi.org/10.1007/BF00684478