Muon neutrinos and the cosmological abundance of primordial black holes

In the mixed dark matter scenarios consisting of primordial black holes (PBHs) and particle dark matter (DM), PBHs can accrete surrounding DM particles to form ultracompact minihalos (UCMHs or clothed PBHs) even at an early epoch of the Universe. The distribution of DM particles in a UCMH follows a steeper density profile (${\rho }_{\mathrm{DM}}\propto r^{-9/4}$) compared with a classical DM halo. It is expected that the DM annihilation rate is very large in UCMHs, resulting in a contribution to, e.g., the extragalactic neutrino flux. In this work, we investigate the extragalactic neutrino flux from clothed PBHs due to DM annihilation, and then the muon flux for neutrino detection. Compared with the atmospheric neutrino flux, we derive the upper limits on the cosmological abundance of PBHs for 10 years of exposure time of, e.g., the IceCube experiment. For the DM mass $m_{\chi }=100\left(1000\right)\mathrm{GeV}$, the upper limits ($2\sigma$) on the fraction of DM in PBHs are $f_{\mathrm{PBH}}=1.2\times {10}^{-3}(8.9\times {10}^{-5})$ for contained events and $f_{\mathrm{PBH}}=2.5\times {10}^{-3}(1.3\times {10}^{-5})$ for upward events. Compared with other constraints, although the upper limits obtained by us are not the strongest, it is a different way to study the cosmological abundance of PBHs.