Sublunar-Mass Primordial Black Holes from Closed Axion Domain Walls

We study the formation of primordial black holes (PBHs) from the collapse of closed domain walls (DWs) which naturally arise in QCD axion models near the QCD scale together with the main string-wall network. The size distribution of the closed DWs is determined by percolation theory, from which we further obtain PBH mass distribution and abundance. Various observational constraints on PBH abundance in turn also constrain axion parameters. Our model prefers axion mass around the meV scale ($f_{a}\sim 10^{9}$ GeV). The corresponding PBHs are in the sublunar-mass window $10^{20}$-$10^{22}$ g (i.e., $10^{-13}$-$10^{-11}M_{\odot}$), one of few mass windows still available for PBHs contributing significantly to dark matter (DM). In our model, PBH abundance could reach $\sim1\%$ or even more of DM, sensitive to the formation efficiency of closed axion DWs.