Two-photon annihilation radiation in strong magnetic field: the case of small longitudinal velocities of electrons and positrons

Spectra, angular distributions, and polarization of two-photon annihilation radiation in a magnetic field are studied in detail in the case of small longitudinal velocities of annihilating electrons and positrons which occupy the ground Landau level. Magnetic field essentially affects the annihilation if its magnitude B is not very low in comparison with B_cr=4.4×10¹³G, which may take place near the surface of a neutron star. The magnetic field broadens the spectra (the width depends on an angle θ{symbol} between B and a wave vector) and leads to their asymmetry. The angular distribution may be highly anisotropic, being fan-like or pencillike for different photon energies ω. The total annihilation rate is suppressed by the magnetic field (∝B^-3 for B≫B_cr).The radiation is linearly polarized; the degree and orientation of the polarization depend on B, θ{symbol} and ω. The polarization may reach several tens percent even for comparatively small fields B ∼ 0.1 B_crtypical for neutron stars. This means that the polarization may be detected, e.g., in the annihilation radiation from the gamma-ray bursts.