Constraints on a mixed model of dark matter particles and primordial black holes from the Galactic 511 keV line

The galactic 511 keV gamma-ray line has been observed since 1970's, and was identified as the result of electron-positron annihilation, but the origin of such positrons is still not clear. Apart from the astrophysical explanations, the possibilities that such positrons come from dark matter (DM) annihilation are also widely studied. Primordial black hole (PBH) is also an extensively studied candidate of DM. If PBHs exist, the DM particles may be gravitationally bound to the PBHs and form halo around PBHs with density spikes. DM annihilation in these density spikes can enhance the production rate of positrons from DM particles, but the signal morphology is similar to the decaying DM. We consider such a mixed model consisting of DM particles and PBHs and obtain the upper limit from the data of 511 keV gamma-ray line from INTEGRAL/SPI on the decaying component of DM particles and the constraint on the PBH abundance. These constraints are general and independent of particle DM models. For the mixed model consisting of excited DM and PBHs, the constraints on the PBH abundance can be down to $O(10^{-17})$ for DM particle with mass around $1~\mathrm{TeV}$, which is more stringent than that obtained from the extragalactic gamma-ray background.