Improved Constraints on Dark Matter Annihilations Around Primordial Black Holes

It is quite conceivable that 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 $\Omega_{DM}\approx 0.26$. However, previous studies have highlighted that scenarios with both particle dark matter and PBH are strongly excluded $\gamma$-ray limits assuming particle dark matter with a velocity independent thermal cross section  $<\sigma v>~ 3\times10^{-26}{cm}^3/{s}$, 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 $<\sigma v > ~ v^2$ or d-wave  with $<\sigma v>~ v^4$. 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.