Effect of clustering on primordial black hole microlensing constraints

TL;DR

This paper investigates how clustering of primordial black holes affects stellar microlensing constraints, finding that for typical cluster masses, the impact is minimal except at the highest masses probed.

Contribution

It demonstrates that clustering has negligible effects on microlensing constraints for typical PBH clusters formed from inflationary perturbations.

Findings

Clusters with mass >10^6 M_sun significantly alter event duration distributions.

For typical clusters (~10^3 PBHs), clustering effects are negligible.

Microlensing constraints remain robust for most PBH mass ranges.

Abstract

Stellar microlensing observations tightly constrain compact object dark matter in the mass range $(10^{-11} - 10^{3}) M_{\odot}$. Primordial Black Holes (PBHs) form clusters, and it has been argued that these microlensing constraints are consequently weakened or evaded. For the most commonly studied PBH formation mechanism, the collapse of large gaussian curvature perturbations generated by inflation, the clusters are sufficiently extended that the PBHs within them act as individual lenses. We find that if the typical mass of the clusters is sufficiently large, $ \gtrsim 10^{6} M_{\odot}$, then the event duration distribution can deviate significantly from that produced by a smooth dark matter distribution, in particular at the shortest durations. As a consequence of this, the probability distribution of the number of observed events is non-Poissonian, peaking at a lower value, with an extended tail to large numbers of events. However, for PBHs formed from the collapse of large inflationary perturbations, the typical cluster is expected to contain $\sim 10^{3}$ PBHs. In this case the effect of clustering is negligibly small, apart from for the most massive PBHs probed by decade-long stellar microlensing surveys ($M_{\rm PBH} \sim 10^{3} M_{\odot}$).