The abundance of clustered primordial black holes from quasar microlensing

While elementary particles are the favored candidate for the elusive dark matter, primordial black holes (PBHs) have also been considered to fill that role. Gravitational microlensing is a very well-suited tool to detect and measure the abundance of compact objects in galaxies. Previous studies based on quasar microlensing exclude a significant presence of substellar to intermediate-mass black holes (BHs; ≲100 M⊙). However, these studies were based on a spatially uniform distribution of BHs while, according to current theories of PBH formation, they are expected to appear in clusters. We study the impact of clustering in microlensing flux magnification, finding that at large scales clusters act like giant pseudo-particles, strongly affecting the emission coming from the broad-line region, which can no longer be used to define the zero microlensing baseline. As an alternative, we set this baseline from the intrinsic magnification ratios of quasar images predicted by macro lens models and compared them with the observed flux ratios in emission lines, infrared, and radio. The (magnitude) differences are the flux-ratio anomalies attributable to microlensing, which we estimate for 35 image pairs corresponding to 12 lens systems. A Bayesian analysis indicates that the observed anomalies are incompatible with the existence of a significant population of clustered PBHs. Furthermore, we find that more compact clusters exhibit a stronger microlensing impact. Consequently, we conclude that clustering makes the existence of a significant population of BHs in the substellar to intermediate mass range even more unlikely.