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

Abstract

The intensity and polarization of two-photon annihilation in a magnetic fuieldB≪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 temperatureT the total annihilation rate and energy losses decrease, being higher than for the isotropic thermal distributions at the sameT. The shapes of intensity spectra at sin ϱ=0 (ϱ is the angle betweenB and wave-vector) are close to those in the isotropic case. The widths and blue-shifts of the spectra decrease with increasing sin ϱ and increase with increasingT. Logarthmic singularities arise in the spectra atE»mc ²/sin ϱ. Power-like parts are formed in the wings of the spectra forkT≫mc ² and not too small sin ϱ. The direction-integrated spectra reach their (finite) maxima, atE=mc ² for anyT. The radiation concentrates near the plane, perpendicular to the magnetic field forE close tomc ² and is beamed along the magnetic field forE far frommc ². Energy-integrated angular distributions are stretched alongB, the stronger the higherT. 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/mc ²) sin ϱ and [ln (kT/mc ²)]⁻¹ forkT≪mc ² andkT sin ϱ≫mc ², respectively. Annihilation radiation dominates over Bremsstrahlung in thee ^∓ plasma atkT≲7mc ². 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.