In-depth analysis of the clustering of dark matter particles around primordial black holes. Part III: CMB constraints

In a mixed dark matter scenario in which primordial black holes (PBHs) would co-exist with thermally produced self-annihilating particles, one expects the former to be surrounded by extremely dense halos made of the latter, built up during radiation domination. Here, as a continuation of previous work, we derive observational limits on such a scenario from a full statistical analysis of cosmic microwave background (CMB) data. We quantify how a tiny fraction $\fbh$ of PBHs could restrict the parameter space available to thermal particle dark matter, limiting the $s$-wave annihilation cross section to values $\lesssim 10^{-30}\,{\rm cm^3/s}\,(\mchi/100\,{\rm GeV})\,(\fbh/10^{-6})^{-3}$ if PBHs are typically heavier than $\sim 10^{-10}\,\Msun$, which can also be turned into constraints on PBHs in this mass range. In contrast, asteroid mass or lighter PBHs could live in perfect peace with these particles. Finally, we shortly discuss the implications of the recent tentative interpretation of Subaru-HSC microlensing events as PBHs.