Improved Constraints on Dark Matter Annihilations Around Primordial Black Holes

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.