Isotropic X-ray bound on Primordial Black Hole Dark Matter

We revisit the constraints on evaporating primordial black holes (PBHs) from the isotropic X-ray and soft gamma-ray background in the mass range $10^{16}-10^{18}$ g. We find that they are stronger than usually inferred due to two neglected effects: i) The contribution of the annihilation radiation due to positrons emitted in the evaporation process. ii) The high-latitude, Galactic contribution to the measured isotropic flux. We study the dependence of the bounds from the datasets used, the positron annihilation conditions, and the inclusion of the astrophysical background. We push the exclusion limit for non-spinning PBH with monochromatic mass function as the totality of dark matter to 1.5$\times 10^{17}\,$g, which represents a $\sim$15$\%$ improvement with respect to earlier bounds and translates into almost an order of magnitude improvement in the PBH fraction in the already probed region. We also show that the inclusion of spin and/or an extended, log-normal mass function lead to tighter bounds. Our study suggests that the isotropic flux is an extremely promising target for future missions in improving the sensitivity to PBHs as candidates for dark matter.