Improved Constraints on Dark Matter Annihilations Around Primordial Black Holes

Abstract: 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 $\Omega_{\rm DM}\approx0.26$. However, previous studies have highlighted that scenarios with both particle dark matter and PBH are strongly excluded by $\gamma$-ray limits for particle dark matter with a velocity independent thermal cross section $\langle\sigma v\rangle\sim3\times10^{-26}{\rm cm}^3/{\rm s}$, as is the case for classic WIMP dark matter. Here we extend these existing studies on $s$-wave annihilating particle dark matter to ascertain the limits from diffuse $\gamma$-rays on velocity dependent annihilations which are $p$-wave with $\langle\sigma v \rangle\propto v^2$ or $d$-wave with $\langle\sigma v \rangle\propto v^4$, which we find to be considerably less constraining. Furthermore, we highlight that even if the freeze-out process is $p$-wave it is relatively common for (loop/phase-space) suppressed $s$-wave processes to actually provide the leading contributions to the experimentally constrained $\gamma$-ray flux from the PBH halo. This work also utilyses a refined treatment of the PBH dark matter density profile and outlines an improved application of extra-galactic $\gamma$-ray bounds.