Annihilation radiation from a power-law distributed electron-positron plasma on the ground Landau level: the case of low magnetic fields

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 fieldB∼1010–1012 G. Simple analytical expressions for limiting cases are obtained and results of numerical calculations of radiation characteristics are presented. Power-lawe ± distributionsη ± ∝ e ± are shown to generate power-law spectra of the annihilation radiation atE≫mc 2 andE≪mc 2, with indices depending on the direction of radiation. The annihilation spectra at ϑ=0 show the largest blue-shifts of their maxima and the hardest high-energy tailsI(E≫mc 2, ϑ=0)∝E −(k−1). The blue-shifts reduce, and the hard tials steepen, with increasing ϑ. At ϑ>(2mc 2/E)1/2 the slopes of the high-energy tails rapidly transform to that at ϑ=π2,I(E≫mc 2, ϑ=π/2)∝E −(2k+3). The direction-integrated spectraS(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 decreasingk, being higher than for the isotropice ± power-law distributions at the samek. The radiation is linearly polarized in the plane formed by the magnetic field and wave-vector. The polarization degreeP is maximum atE≫mc 2:P max≃0.6 for ϑ=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 thee − e +-distribution and the gravitational redshift factor in the radiating region.