Soft gamma-ray background and light dark matter annihilation

The bulk of the extragalactic background between 10 keV and 10 GeV is likely to be explained by the emission of Seyfert galaxies, type Ia supernovae, and blazars. However, as revealed by the INTEGRAL satellite, the bulge of our galaxy is an intense source of a 511 keV gamma-ray line, indicating the production of a large number of positrons that annihilate. The origin of the latter is debated, and they could be produced, in particular, by the ($S$- or $P$-wave) annihilation of light dark matter particles into ${e}^{+}{e}^{\ensuremath{-}}$. In any case, the cumulated effect of similar sources at all redshifts could lead to a new background of hard x-ray and soft gamma-ray photons. On the basis of the hierarchical model of galaxy formation, we compute analytically the SNIa contribution to the background, and add it to Seyfert and blazars emission models. Confronting these expected contributions to observation, we find that any extra contribution to this unresolved background around 511 keV should be lower than about $4\text{ }\text{ }\mathrm{keV}\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\text{ }{\mathrm{sr}}^{\ensuremath{-}1}$. We also estimate analytically the extragalactic background due to dark matter annihilation, increasing the accuracy of the earlier computations. Indeed, we take into account the large positron escape fraction from low mass dark matter halos, unable to confine a dense and magnetized interstellar medium. Our new background estimate turns out to be 1 order of magnitude lower so that the hypothesis of a light dark matter candidate remains compatible with the observed extragalactic background for a wider range of particle masses and cross sections.