Could electron-positron annihilation lines in the Galactic center result from pulsar winds?

we study the possibility of pulsar winds in the Galactic center (GC) to produce the 511 keV line. We propose that there may exist three possible scenarios of pulsar winds as the positron sources: normal pulsars; rapidly spinning strongly magnetized neutron stars in GRB progenitors; a population of millisecond pulsars in the Galactic center region. These $e^\pm$pairs could be trapped in the region by the magnetic field in the GC, and cool through the synchrotron radiation and Coulomb interactions with the medium. The cooling timescales are lower than the diffuse timescale of positrons, so low energy positrons could annihilate directly with electrons into 511 keV photons or form positronium before annihilation. We find that normal pulsars cannot be a significant contributor to the positron sources. Although magnetars in the GC could be potential sources of positrons, their birth rate and birth locations may impose some problems for this scenario. We believe that the most likely candidate positron sources in the GC may be a population of millisecond pulsars in the GC. Our preliminary estimations predict the e$^\pm$ annihilation rate in the GC is $> 5\times 10^{42}$ s$^{-1}$. Therefore, the $e^\pm$ pairs from pulsars winds can contribute significantly to the positron sources in the GC. Furthermore, since the diffusion length of positrons is short, we predict that the intensity distribution of the annihilation line should follow the distribution of millisecond pulsars, which should correlate to the mass distribution in the GC.