The abundance of clustered primordial black holes from quasar microlensing

¹ Argelander Institute for Astronomy, University of Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
² Instituto de Astrofísica de Canarias, 38200 La Laguna, Santa Cruz de Tenerife, Spain
³ Department of Astronomy and Astrophysics, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064 USA
⁴ Departamento de Astrofísica, Universidad de La Laguna, 38200 La Laguna, Santa Cruz de Tenerife, Spain
⁵ Departamento de Física Teórica y del Cosmos, Universidad de Granada, Campus de Fuentenueva, 18071 Granada, Spain
⁶ Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain
⁷ Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, 44001 Teruel, Spain
⁸ Departamento de Astronomía y Astrofísica, Universidad de Valencia, 46100 Burjassot, Valencia, Spain
⁹ Observatorio Astronómico, Universidad de Valencia, 46980 Paterna, Valencia, Spain

^★ Corresponding author; sven@astro.uni-bonn.de

Received: 12 January 2024
Accepted: 8 August 2024

Abstract

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.