GRBs and the 511 keV emission of the Galactic bulge

We consider the phenomenology of the 511 keV emission in the Galactic bulge, as recently observed by INTEGRAL, and propose a model in which the positrons are produced by gamma-ray bursts (GRB) associated with mini-starbursts in the central molecular zone (CMZ). We show that the positrons can easily diffuse across the bulge on timescales of similar to 10(7) yr, and that their injection rate by GRBs is compatible with the observed fluxes if the mean time between two GRBs in the bulge is similar to8 x 10(4) yr x(EGRB/10(51) erg). We also explain the low disk-to-bulge emission ratio by noting that positrons from GRBs in the Galactic disk should be annihilated on timescales of less than or similar to10(4) yr in the dense shell of the underlying supernova remnant, after the radiative transition, while the remnants of GRBs occurring in the hot, low-density medium produced by recurrent starbursts in the CMZ become subsonic before they can form a radiative shell, allowing the positrons to escape and fill the whole Galactic bulge. If the mean time between GRBs is smaller than similar to10(4) E-51 yr, INTEGRAL should be able to detect the ( localized) 511 keV emission associated with one or a few GRB explosions in the disk.