Clustering of primordial black holes from QCD axion bubbles

Abstract

We study the clustering of primordial black holes (PBHs) and axion miniclusters produced in the model proposed to explain the LIGO/Virgo events or the seeds of the supermassive black holes (SMBHs) in ref. [1]. It is found that this model predicts large isocurvature perturbations due to the clustering of PBHs and axion miniclusters, from which we obtain stringent constraints on the model parameters. Specifically, for the axion decay constant fa = 1016 GeV, which potentially accounts for the seeds of the SMBHs, the PBH fraction in dark matter should be f PBH ≲ 7 × 10-10. Assuming that the mass of PBHs increases by more than a factor of 𝒪(10) due to accretion, this is consistent with the observed abundance of SMBHs. On the other hand, for fa = 1017 GeV required to produce PBHs of masses detected in the LIGO/Virgo, the PBH fraction should be f PBH ≲ 6 × 10-8, which may be too small to explain the LIGO/Virgo events, although there is a significant uncertainty in calculating the merger rate in the presence of clustering.