Constraints on primordial black holes from the Galactic gamma-ray background

The fraction of the Universe going into primordial black holes (PBHs) with initial mass M*510^14 g, such that they are evaporating at the present epoch, is strongly constrained by observations of both the extragalactic and Galactic -ray backgrounds. However, while the dominant contribution to the extragalactic background comes from the time-integrated emission of PBHs with initial mass M*, the Galactic background is dominated by the instantaneous emission of those with initial mass slightly larger than M* and current mass below M*. Also, the instantaneous emission of PBHs smaller than 0. 4M* mostly comprises secondary particles produced by the decay of directly emitted quark and gluon jets. These points were missed in the earlier analysis by Lehoucq et al. using EGRET data. For a monochromatic PBH mass function, with initial mass (1+) M* and 1, the current mass is (3) ^1/3M*, and the Galactic background constrains the fraction of the Universe going into PBHs as a function of. However, the initial mass function cannot be precisely monochromatic, and even a tiny spread of mass around M* would generate a current low-mass tail of PBHs below M*. This tail would be the main contributor to the Galactic background, so we consider its form and the associated constraints for a variety of scenarios with both extended and nearly monochromatic initial mass functions. In particular, we consider a scenario in which the PBHs form from critical collapse and have a mass function which peaks well above M*. In this case, the largest PBHs could provide the dark matter without the M* ones exceeding the -ray background limits.