Little Red Dots from Small-Scale Primordial Black Hole Clustering

Borui Zhang, Wei-Xiang Feng, Haipeng An

First listed 2025-07-09 | Last updated 2025-07-23

Abstract

The James Webb Space Telescope (JWST) observations have identified a class of compact galaxies at high redshifts ($4 \lesssim z \lesssim 11$), dubbed "little red dots" (LRDs). The supermassive black holes (SMBHs) of $10^{5-8}{\rm\,M}_{\odot}$ in LRDs favor a heavy-seed origin. We propose a mechanism for their formation: Clusters of primordial black holes, formed through long-short mode coupling on small scales in the early Universe, undergo sequential mergers over extended timescales. This mechanism can evade cosmic microwave background distortions and result in heavy-seed SMBHs via runaway mergers. We employ Monte Carlo simulations to solve the Smoluchowski coagulation equation and determine the runaway merging timescale. The resulting stochastic gravitational wave background offers a distinct signature of this process, and the forming SMBHs can be highly spinning at their formation due to the spin residual of the cluster from tidal fields. This mechanism may explain the rapidly spinning SMBHs in LRDs under the assumption of obscured active galactic nuclei.

Short digest

Proposes LRD heavy seeds as runaway-merger products of primordial black holes initially clustered by small-scale long–short mode coupling. Monte Carlo solutions of the Smoluchowski equation yield merger timescales sufficient to assemble 10^5–10^8 Msun SMBHs within the first Gyr while evading CMB distortion limits. The scenario predicts a distinctive stochastic gravitational-wave background and high birth spins inherited from cluster tidal torques. Interpretation assumes LRDs host obscured AGN.

Key figures to inspect

• Figure 1 (parameter plane βLS vs kL/kS): Identify the light-gray region where clusters decouple early and enable high-spin SMBH formation while satisfying μ-distortion constraints; note how changing the mode ratio shifts viable cluster masses.
• Figure 2 (PBH mass population evolution): Track when the mass function runs away and a central ~SMBH emerges; read off the redshift/time when ~50% of PBHs have merged and confirm two-body dominance assumptions.
• GW background prediction plot: Examine ΩGW(f) from sequential mergers for spectral shape and amplitude; note which frequency bands carry most power and the distinctiveness relative to other PBH or astrophysical backgrounds.
• Spin-at-formation figure (if provided): Check the predicted a* distribution inherited from cluster tidal fields and how it correlates with cluster parameters (velocity dispersion, coupling strength).