  The excess of the 511 keV line from the Milky Way galactic bulge, confirmed
by the INTEGRAL detector, is a longstanding mystery. The morphology of the line
appears to be proportional to the square of the dark matter density, hinting
towards a dark matter origin. On the other hand, in 2020, XENON1T has reported
an excess of electrons with a recoil energy of $2-4$ keV. We present a model
based on a dark matter of a few MeV mass that decays into a pair of
pico-charged particles with a lifetime much larger than the age of the
Universe. The magnetic field of the galaxy accumulates these relativistic
pico-charged particles whose scattering on the electrons can explain the signal
reported by XENON1T. The annihilation of the pico-charged particles in the
galactic bulge leads to $e^-e^+$ production and therefore to an excess of the
511 keV line. We review the present observational bounds and the strategies to
test the model.
