  The electron-positron annihilation source in the Galactic center region has
recently been observed with INTEGRAL/SPI, which shows that this 511 keV source
is strong and its extension is consistent with the Galactic bulge geometry. The
positron production rate, estimated to more than 10$^{43}$ per second, is very
high and raises a challenging question about the nature of the Galactic
positron source. Commonly considered astrophysical positron injectors, namely
type Ia supernovae are rare events and fall short to explain the observed
positron production rate. In this paper, we study the possibility of Galactic
positron production by hypernovae events, exemplified by the recently observed
SN2003dh/GRB030329, an asymmetric explosion of a Wolf-Rayet star associated
with a gamma-ray burst. In these kinds of events, the ejected material becomes
quickly transparent to positrons, which spread out in the interstellar medium.
Non radioactive processes, such as decays of heavy dark matter particles
(neutralinos) predicted by most extensions of the standard model of particle
physics, could also produce positrons as byproducts. However they are expected
to be accompanied by a large flux of high-energy gamma-rays, which were not
observed by EGRET and ground based Tcherenkov experiments. In this context we
explore the possibility of direct positron production by annihilation of light
dark matter particles.
