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.
