Abstract
We consider constraints on primordial black holes (PBHs) in the mass range $(
10^-18$ - $10^15 )\,M_ødot$ if the dark matter (DM) comprises weakly
interacting massive particles (WIMPs) which form halos around them and generate
$\gamma$-rays by annihilations. The observed extragalactic $\gamma$-ray
background then implies that the PBH DM fraction is $f^_PBH łesssim
10^-10\,( m_\chi / TeV )^1.1$ in the mass range $2 \times
10^-11\,M_ødot\,( m_\chi / TeV )^-3.2 M 3
10^11\,M_ødot\,( m_\chi / TeV )^1.1$, where $m_\chi$
and $M$ are the WIMP and PBH masses, respectively. This limit is independent of
$M$ and therefore applies for any PBH mass function.For $M 2\times
10^-11\,M_ødot\,( m_\chi / TeV )^-3.2$, the constraint on
$f^_PBH$ is a decreasing function of $M$ and PBHs could still make a
significant DM contribution at very low masses. We also consider constraints on
WIMPs if the DM is mostly PBHs. If the merging black holes recently discovered
by LIGO/Virgo are of primordial origin, this would rule out the standard WIMP
DM scenario. More generally, the WIMP DM fraction cannot exceed $10^-4$ for
$M > 10^-9\,M_ødot$ and $m_\chi >10\,$GeV. There is a region of
parameter space, with $M 10^-11\,M_ødot$ and $m_\chi łesssim
100\,$GeV, in which WIMPs and PBHs can both provide some but not all of the DM,
so that one requires a third DM candidate.
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