Equilibrium spectra of secondary cosmic-ray positrons in the galaxy and the spectrum of cosmic gamma-rays resulting from their annihilation

Abstract

A general formula is derived for calculating the γ-ray spectrum resulting from the annihilation of cosmic-ray positrons. This formula is used to calculate annihilation-γ-ray spectra from various equilibrium spectra of secondary galactic positrons. These spectra are then compared with the γ-ray spectra produced by other astrophysical processes.

Particular attention is paid to the form of the γ-ray spectrum resulting from the annihilation of positrons having kinetic energies below 5 keV. It is found that for mean leakage times out of the galaxy of less than 400 million years, most of the positrons annihilating near rest come from the β-decay of unstable nuclei produced in cosmic-ray p-C¹², p-N¹⁴, and p-O¹⁶ interactions, rather than from pi-meson decay. It is further found that the large majority of these positrons will annihilate from an S state of positronium and that 3/4 of these will produce a three-photon annihilation continuum rather than the two-photon line spectrum at 0.51 MeV. The results of numerical calculations of the γ-ray fluxes from these processes are given. It is concluded that annihilation γ-rays from the galactic halo may remain forever masked by a metagalactic continuum. However, an 0.51 MeV line from the disk may well be detectable. It is most reasonable to assume that this line is formed predominantly by the annihilation of the CNO β-decay positrons. Under this assumption, the intensity of the line becomes a sensitive measure of the galactic cosmic-ray flux below 1000 MeV/nucleon.