New mechanism for primordial black hole formation from the QCD axion

We present a new mechanism for the primordial black hole (PBH) production within the QCD axion framework. We take the case where the Peccei-Quinn symmetry breaks during inflation, resulting in a $N_{\rm DW}=1$ string-wall network that re-enters horizon sufficiently late. Therefore, closed axion domain walls naturally arising in the network are sufficiently large to collapse into PBHs. Our numerical simulation shows that $\sim 0.3\%$ of the total wall area is in the form of closed walls. In addition, the relic abundance of dark matter is dominantly accounted for by free axions from the collapse of open walls bounded by strings. In this framework, the abundance of PBH within dark matter is calculated to be $\sim 0.9\%$. This fraction remains unaffected by axion parameters or the re-entering horizon temperature, as it is determined by the fixed proportion of closed walls in the network, governed by the principles of percolation theory. The resultant PBHs uniformly share the same mass, which spans from about $10^{-9}$ to $1$ solar mass, corresponding to the classical QCD axion mass window $10^{-5}-10^{-2}$~eV and the re-entering horizon temperature $300-1$~MeV. Intriguingly, PBHs in this mechanism can naturally account for the ultrashort-timescale gravitational microlensing events observed by the OGLE collaboration.