Primordial black hole dark matter in the presence of p-wave WIMP annihilation

We study the allowed primordial black hole (PBH) dark matter abundance in the mixed dark matter scenarios consisting of PBHs and self-annihilating weakly interacting massive particles (WIMPs) with a velocity dependent annihilation cross section. We first briefly illustrate how the WIMP dark matter halo profile changes for the velocity suppressed p-wave annihilation scenarios, compared with the familiar s-wave annihilation scenarios, and then discuss the PBH mass dependent upper bound on the allowed PBH dark matter abundance. The WIMPs can accrete onto a PBH to form an ultracompact minihalo with a spiky density profile. Such a spike is moderated in the central region of a halo because the WIMPs are annihilated away and this moderation is less effective for a smaller annihilation cross section. The WIMP core density becomes larger while the core radius becomes smaller for a velocity suppressed p-wave annihilation cross section than those for the s-wave annihilation scenarios. The annihilation cross section is dependent on the velocity which varies across the halo, and, in addition to the change of the WIMP density profile, another interesting feature is the PBH mass dependent bound on PBH dark matter abundance. This is in stark contrast to the s-wave annihilation scenarios where the PBH abundance bound is independent of the PBH mass. The allowed PBH dark matter fraction (with respect to the total dark matter abundance) is of order $f_{PBH}\lesssim {\cal O}(10^{-7})(M_{\odot}/M_{PBH})^{(-6+2\gamma_{sp})/(3\gamma_{sp}+3)}$ for the thermal relic p-wave dark matter with the mass $100$ GeV where $\gamma_{sp}$ is the slope index of the spike profile, to be compared with $f_{PBH}\lesssim {\cal O}(10^{-9})$ for the corresponding thermal relic s-wave dark matter scenarios.