"Thermal Dark Matter and Primordial Black Hole"

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 $\Omega_{\rm DM}\approx0.26$. Early studies 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 examine the limits from diffuse $\gamma$-rays on velocity-dependent, including annihilations which are $p$-wave with $\langle\sigma v \rangle\propto v^2$ or $d$-wave  $\langle\sigma v \rangle\propto v^4$, 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 is $p$-wave it is typical 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.