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A<sc>bstract</sc> Cosmology may give rise to appreciable populations of both particle dark matter and primordial black holes (PBH) with the combined mass density providing the observationally inferred value ΩDM≈ 0.26. Early studies highlighted that scenarios with both particle dark matter and PBH are strongly excluded byγ-ray limits for particle dark matter with a velocity independent thermal cross section 〈σν〉 ~ 3 × 10−26cm3/s, as is the case for classic WIMP dark matter. Here we examine the limits from di useγ-rays on velocity-dependent, including annihilations which arep-wave with 〈σν〉 ∝v2ord-wave 〈σν〉 ∝v4, which we find to be considerably less constraining. This work also utilizes a refined treatment of the PBH dark matter density profile. Importantly, we highlight that even if the freeze-out process isp-wave it is typical for (loop/phase-space) suppresseds-wave processes to actually provide the leading contributions to the experimentally constrainedγ-ray flux from the PBH halo.more » « less
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