  We want to estimate whether the positrons produced by the beta plus decay of
26Al, 44Ti and 56Ni synthesised in massive stars and supernovae are sufficient
to explain the 511 keV annihilation emission observed in our Galaxy. Such a
possibility has often been put forward in the past. We developed a Monte Carlo
Galactic propagation code for ~MeV positrons in which the Galactic interstellar
medium, the Galactic magnetic field (GMF) and the propagation are finely
described. This code allows us to simulate the spatial distribution of the 511
keV annihilation emission. We test several GMFs models and several positron
escape fractions from type-Ia supernova for 56Ni positrons. We consider the
collisional ballistic transport mode and then compare the simulated 511 keV
intensity spatial distributions to the INTEGRAL/SPI data. Whatever the GMF
configuration and the escape fraction chosen for 56Ni positrons, the 511 keV
intensity distributions are very similar. The main reason is that ~MeV
positrons do not propagate very far away from their birth sites in our model.
The direct comparison to the data does not allow us to constrain the GMF
configuration and the escape fraction for 56Ni positrons. In any case,
nucleosynthesis positrons produced in steady state cannot explain the full
annihilation emission. The comparison to the data shows that: (a) the
annihilation emission from the Galactic disk can be accounted for; (b) the
strongly peaked annihilation emission from the inner Galactic bulge can be
explained by positrons annihilating in the central molecular zone but this
seems to require more positron sources than the population of massive stars and
type Ia supernovae usually assumed for this region; (c) the more extended
emission from the Galactic bulge cannot be explained. We show that a transient
source at the GC, such as a starburst episode, could explain this extended
component.
