Annihilation radiation from thermal electron-positron plasma on the ground Landau level: The case of low magnetic fields

The intensity and polarization of two-photon annihilation in a magnetic fuield B≪B_cr=4.4×10¹³ G are studied in detail for a, one-dimensional thermal distribution of annihilating electrons and positrons on the ground Landau level. With the increase of temperature T the total annihilation rate and energy losses decrease, being higher than for the isotropic thermal distributions at the same T. The shapes of intensity spectra at sin ρ{variant}=0 (ρ{variant} is the angle between B and wave-vector) are close to those in the isotropic case. The widths and blue-shifts of the spectra decrease with increasing sin ρ{variant} and increase with increasing T. Logarthmic singularities arise in the spectra at E»mc²/sin ρ{variant}. Power-like parts are formed in the wings of the spectra for kT≫mc² and not too small sin ρ{variant}. The direction-integrated spectra reach their (finite) maxima, at E=mc² for any T. The radiation concentrates near the plane, perpendicular to the magnetic field for E close to mc² and is beamed along the magnetic field for E far from mc². Energy-integrated angular distributions are stretched along B, the stronger the higher T. The rediation is linearly polarized in the plane formed by the magnetic field and weve-vector. Typical values of the polarization inside the cores of the annihilation spectra are ∼(kT/mc²) sin ρ{variant} and [ln (kT/mc²)]^-1 for kT≪mc² and kT sin ρ{variant}≫mc², respectively. Annihilation radiation dominates over Bremsstrahlung in the e^∓ plasma at kT≲7 mc². The results are useful for interpretation of the annihilation radiation in the gamma-ray bursts. They permit to estimate temperature, gravitational potential, and emission measure of radiating regions and the beaming of the radiation.