Restrictions on the injection energy of positrons annihilating near the Galactic center

The origin and properties of the source of positrons annihilating in the Galactic Center is still a mystery. One of the criterion, which may discriminate between different mechanisms of positron production there, is the positron energy injection. Beacom and Yueksel (2006) suggested a method to estimate this energy from the ratio of the 511 keV line to the MeV in-flight annihilation fluxes. From the COMPTEL data they derived that the maximum injection energy of positron should be about several MeV that cut down significantly a class of models of positron origin in the GC assuming that positrons lose their energy by Coulomb collisions only. However, observations show that the strength of magnetic field in the GC is much higher than in other parts of the Galaxy, and it may range there from 100 $\mu$G to several mG. In these conditions, synchrotron losses of positrons are significant that extends the range of acceptable values of positron injection energy. We show that if positrons injection in the GC is non-stationary and magnetic field is higher than 0.4 mG both radio and gamma-ray restrictions permit their energy to be higher than several GeV.