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

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∼10¹⁰-10¹² 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≫mc² and E≪mc², 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≫mc², θ{symbol}=0)∝E^-(k-1). The blue-shifts reduce, and the hard tials steepen, with increasing θ{symbol}. At θ{symbol}>(2 mc²/E)^1/2 the slopes of the high-energy tails rapidly transform to that at θ{symbol}=π2, I(E≫mc², 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≫mc²)∝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≫mc²: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.