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The morphology and characteristics of the so-called GeV gamma-ray excessdetected in the Milky Way lead us to speculate about a possible common originwith the 511 keV line mapped by the SPI experiment about ten years ago. In theprevious version of our paper, we assumed 30 GeV dark matter particlesannihilating into $b \bar{b}$ and obtained both a morphology and a 511 keV flux(\phi_{511 keV} ~ 10^{-3} ph/cm^2/s) in agreement with SPI observation. Howeverour estimates assumed a negligible number density of electrons in the bulgewhich lead to an artificial increase in the flux (mostly due to negligibleCoulomb losses in this configuration). Assuming a number density greater than$n_e > 10^{-3} cm^{-3}$, we now obtain a flux of 511 keV photons that issmaller than \phi_{511 keV} ~ 10^{-6} ph/cm^2/s and is essentially in agreementwith the 511 keV flux that one can infer from the total number of positronsinjected by dark matter annihilations into $b \bar{b}$. We thus conclude that-- even if 30 GeV dark matter particles were to exist-- it is impossible toestablish a connexion between the two types of signals, even though they arelocated within the same 10 deg region in the galactic centre.

A possible link between the GeV excess and the 511 keV emission line in the Galactic Centre