⚛️ general relativity

Small-Scale Clustering of Primordial Black Holes: The Little Red Dot Mass Function and the High-Redshift Galaxy Tension

This paper proposes that supermassive black holes in JWST-discovered "little red dots" originate from runaway mergers of primordial black holes within small-scale clusters, a mechanism that simultaneously explains their observed mass and compactness while alleviating tensions with high-redshift galaxy formation in $\Lambda$ CDM cosmology.

Original authors: Borui Zhang, Wei-Xiang Feng, Haipeng An

Published 2026-09-09

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CC BY 4.0

Original authors: Borui Zhang, Wei-Xiang Feng, Haipeng An

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep in the early history of our universe, a cosmic mystery has recently come to light, one that challenges our standard understanding of how galaxies and their central giants are born. For decades, astronomers have relied on a model called the Lambda Cold Dark Matter theory, which suggests that structures in the universe grew slowly, like a tree adding rings over centuries. In this view, massive black holes at the centers of galaxies should have taken billions of years to grow large enough to be seen. However, the James Webb Space Telescope has begun to peer back to a time when the universe was only a few hundred million years old and found something impossible under the old rules: galaxies that are already packed with enormous black holes. These objects, nicknamed "little red dots," are compact, glowing centers of activity that seem to have formed far too quickly and contain black holes that are far too heavy for the amount of starlight surrounding them. They appear to be overgrown seeds, where the central monster is disproportionately large compared to its host, a situation that standard physics struggles to explain.

To solve this puzzle, a team of researchers at Tsinghua University has proposed a new origin story for these cosmic anomalies. They suggest that the seeds of these massive black holes were not formed by the collapse of a single massive star, as is commonly thought, but rather by the clustering of primordial black holes. Primordial black holes are hypothetical objects that could have formed in the very first moments after the Big Bang, created from dense fluctuations in the early universe. The researchers propose that on very small scales, these primordial black holes did not spread out evenly but instead gathered into dense, tight clusters. Within these crowded groups, the black holes would have been forced into a chaotic dance of gravity, colliding and merging with one another at a runaway pace. This rapid merging would have allowed them to grow into the supermassive giants we see today in a fraction of the time it would normally take.

The team built a detailed model to test this idea, calculating how these clusters would form and evolve. They found that if these primordial black holes clumped together, they could create a dense environment where mergers happen almost instantly on a cosmic scale. This process would naturally produce a population of black holes with the specific masses observed in the little red dots. The model also accounts for the strange "overmassive" nature of these objects. Because the black hole seeds form from a dense cluster, they pull in a massive amount of surrounding gas and stars very early on. This creates a situation where the central black hole is huge, but the surrounding galaxy is still in its infancy, explaining why the black hole appears so large compared to the stars around it.

Furthermore, the researchers investigated why these objects look so compact. In their model, the clusters form in regions of the universe with very low spin, meaning the swirling motion of the gas is minimal. Without the centrifugal force of a fast spin to spread the gas out into a wide disk, the material collapses into a tight, dense ball. This explains why the little red dots are so small, with effective sizes of only about 100 parsecs, which is tiny compared to the vast disks of normal galaxies. The model also predicts that the gas surrounding these black holes would be incredibly dense, with densities reaching up to 100 billion particles per cubic centimeter. This extreme density matches the observations of the little red dots, which show strong signs of being shrouded in thick, opaque gas that absorbs light and creates their distinctive red appearance.

Beyond explaining the little red dots, this theory offers a solution to a broader tension in cosmology. The James Webb Space Telescope has also discovered massive, mature galaxies at high redshifts that seem to have formed too quickly for the standard model to allow. The researchers found that their model of primordial black hole clusters produces not just the seeds for the little red dots, but also a population of even heavier black holes at the high-mass end. These massive seeds would act as gravitational anchors, pulling in gas and stars much more efficiently than standard models predict. This accelerated growth could explain how entire galaxies built up their stellar mass so rapidly in the early universe, bringing the observations back into alignment with cosmological theory.

The researchers also addressed the question of how many of these objects should exist. While their model predicts a vast number of primordial black hole clusters, they calculated that only a small fraction would end up as the little red dots we see. This is because the specific conditions required—such as the low spin of the host galaxy and the timing of the black hole's activity—act as a filter. Most of these clusters would either merge into larger galaxies, lose their compact shape, or remain dormant and invisible. When these factors are taken into account, the predicted number of visible little red dots matches the actual count observed by the telescope.

In conclusion, this study presents a coherent picture where the strange properties of the little red dots and the rapid formation of early galaxies are two sides of the same coin. By suggesting that supermassive black holes began as clusters of primordial black holes that merged rapidly, the researchers provide a mechanism that fits the observed masses, sizes, and densities of these distant objects. While the existence of primordial black holes remains a hypothesis, this work demonstrates that if they do exist, their small-scale clustering could be the key to unlocking the secrets of the universe's earliest and most enigmatic structures. The model does not claim to be the final word, but it offers a plausible and mathematically consistent path that resolves several long-standing contradictions between observation and theory.

Technical Summary: Small-Scale Clustering of Primordial Black Holes: The Little Red Dot Mass Function and the High-Redshift Galaxy Tension

Problem Statement
Recent observations by the James Webb Space Telescope (JWST) have revealed a population of compact, red, low-to-intermediate-luminosity active galactic nuclei (AGN) at high redshifts ( $z \sim 4–11$ ), termed "little red dots" (LRDs). These objects host supermassive black holes (SMBHs) with masses $M_\bullet \sim 10^{5–8} M_\odot$ that are significantly more abundant than quasars at similar redshifts. A critical feature of LRDs is that their central SMBHs are often "overmassive" relative to their stellar components ( $M_\bullet/M_\star \sim 0.01–1$ ), deviating by 1–2 orders of magnitude from local scaling relations. Additionally, JWST has detected unexpectedly massive galaxies at $z \gtrsim 7$ , creating a tension with the standard $\Lambda$ CDM cosmology regarding the efficiency of early star formation and the availability of massive dark matter halos. The paper seeks to explain the origin of these SMBHs, the specific properties of LRDs (mass function, compactness, overmassive nature, and dense gas), and the high-redshift galaxy tension within a unified framework.

Methodology
The authors extend a previously proposed scenario where SMBHs form through the runaway mergers of dense clusters of Primordial Black Holes (PBHs). The core mechanism relies on long-short mode coupling in the early Universe, where long-wavelength density perturbations modulate the formation scale of PBHs, leading to localized overdensities.

PBH Cluster Formation: The authors derive the threshold for PBH cluster formation based on the decoupling of local PBH energy density from the Hubble flow. They calculate the cluster mass ( $M_{cl}$ ), number density ( $n_{cl}$ ), and the runaway merger timescale ( $t_{ra}$ ) as functions of the long-mode field amplitude and coupling strength.
SMBH Mass Function: By establishing the probability distribution function (PDF) of the cluster mass and applying a cutoff based on the cosmic time available for runaway mergers (before the observed redshift), the authors derive the initial SMBH mass function. They subsequently incorporate baryonic accretion effects, assuming a duty cycle of $f_{duty} \sim 0.01–0.1$ and high Eddington ratios, to obtain the final predicted mass function.
The "Seed Effect": To explain LRD properties, the authors apply a "seed effect" model. In this framework, the dense PBH cluster acts as a heavy central seed that gravitationally binds a halo of baryons and dark matter. This allows for the calculation of the host halo mass ( $M_h$ ) and the stellar-to-BH mass ratio ( $M_\star/M_\bullet$ ) based on the cluster mass and redshift.
Halo Spin and Compactness: The authors link the observed compactness of LRDs ( $r_{eff} \sim 100$ pc) to the spin parameter ( $\lambda$ ) of the host halo. They assume that LRDs correspond to the low-spin tail of the halo distribution ( $\lambda \lesssim 0.01$ ), which results in smaller effective disk radii.
Gas Density Estimation: The paper estimates the gas density within the seed-induced halos, arguing that the deep potential wells of PBH clusters and low angular momentum lead to significantly enhanced central gas densities. The authors note that atomic hydrogen number densities of $\gtrsim 10^9–10^{11} \text{ cm}^{-3}$ are required to reproduce LRD spectral features, and their model yields a specific consistent estimate of $\sim 10^{11} \text{ cm}^{-3}$ for fiducial parameters.
Galaxy Formation Acceleration: The model is applied to the high-mass tail of the SMBH population ( $M_\bullet \gtrsim 10^8 M_\odot$ ) to demonstrate how these massive seeds can accelerate baryon infall and stellar assembly, thereby addressing the cumulative stellar mass density tension at $z \sim 10$ .

Key Contributions and Results

SMBH Mass Function: The derived SMBH mass function, incorporating accretion, successfully reproduces the observed mass distribution of LRDs and broad-line AGNs (BLAGNs) at $z \sim 4–6$ . The model shows that varying the long-mode coupling strength ( $|\eta|$ ) and scale ( $r_{cl}$ ) can simultaneously fit both LRD and BLAGN populations.
Overmassive Nature: The "seed effect" naturally explains the high $M_\bullet/M_\star$ ratios. Because the halo mass is bound to the heavy seed at high redshift, the stellar mass formed is limited by the star formation efficiency and the redshift evolution of the bound mass, resulting in ratios of $M_\bullet/M_\star \sim 0.01–1$ without requiring extreme stellar suppression.
Compactness: By associating LRDs with low-spin halos ( $\lambda \sim 0.01–0.03$ ), the model predicts effective radii of $46–215$ pc for SMBHs in the range $10^6–10^8 M_\odot$ at $z=5$ . This aligns with observed LRD sizes and the trend of increasing radius with decreasing redshift.
Dense Gas Environment: The model estimates central gas number densities in seed-induced halos that are consistent with the dense gas environment required for LRDs. While the paper notes that densities of $\gtrsim 10^9–10^{11} \text{ cm}^{-3}$ are needed to reproduce observed spectral features, the model yields a specific estimate of $\sim 10^{11} \text{ cm}^{-3}$ for fiducial parameters, providing a plausible explanation for the strong absorption features and weak X-ray/radio emission observed in LRDs.
Alleviating the High-Redshift Tension: The high-mass tail of the PBH-cluster-induced SMBH population ( $M_\bullet \gtrsim 10^8 M_\odot$ ) acts as a catalyst for early galaxy formation. The authors demonstrate that these massive seeds can drive the cumulative stellar mass density at $z \sim 10$ to levels consistent with JWST observations, which are otherwise difficult to reconcile with standard hierarchical assembly in $\Lambda$ CDM.
Abundance Consistency: The authors estimate that while the total comoving number density of PBH clusters is high ( $n \sim 10^{-2}–10^{-1} \text{ cMpc}^{-3}$ ), the observable LRD population is reduced to $n_{LRD} \sim 10^{-5}–10^{-4} \text{ cMpc}^{-3}$ . This reduction is attributed to the selection of low-spin halos (compactness), the survival fraction against major mergers, and the duty cycle of AGN activity.

Significance
The paper claims to provide a unified framework that addresses multiple anomalies in early Universe astrophysics. By positing that SMBHs in LRDs originate from the runaway mergers of small-scale PBH clusters, the model:

Explains the origin of massive black holes within the first billion years without violating CMB constraints.
Naturally accounts for the "overmassive" and "compact" nature of LRDs through the seed effect and low-spin halo selection.
Resolves the tension between JWST's high-redshift galaxy observations and $\Lambda$ CDM predictions by utilizing massive PBH seeds to accelerate early structure formation.
Predicts distinctive gravitational wave signatures from the PBH merger process, offering a potential observational test to distinguish this channel from direct collapse scenarios.

The authors conclude that their modeling is consistent with current JWST data regarding mass functions, morphological properties, and gas densities, offering a viable alternative to standard black hole formation scenarios for the early Universe.

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