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Bondi-Hoyle-Lyttleton accretion onto ultra dense dark matter halos and direct collapse black holes

This paper proposes a formation scenario for intermediate-mass black holes ( $\sim 10^3 M_\odot$ ) at high redshifts, where gas accretes onto ultra-dense dark matter halos formed from rare curvature fluctuations, collapses without fragmenting due to CMB-suppressed molecular cooling, and rapidly forms a massive object that could seed the supermassive black holes observed by the James Webb Space Telescope.

Original authors: Kandaswamy Subramanian, Bikram Phookun

Published 2026-03-31

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CC BY 4.0

Original authors: Kandaswamy Subramanian, Bikram Phookun

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

Imagine the early universe as a vast, quiet ocean just after a storm has passed. In this ocean, there are invisible whirlpools made of dark matter (the invisible stuff that holds galaxies together). Usually, these whirlpools are gentle and spread out. But in this paper, the authors suggest that some of these whirlpools were incredibly dense and tight—like a whirlpool so strong it could grab anything nearby and pull it in.

Here is the story of how these dense whirlpools might have created the "seeds" for the giant black holes we see today, explained in simple terms.

1. The Setup: Invisible Whirlpools (UDMH)

Long ago, just after the Big Bang, the universe was filled with a hot fog of gas and dark matter. The authors propose that in some rare spots, the dark matter clumped together to form Ultra-Dense Dark Matter Halos (UDMH).

The Analogy: Think of these as invisible, super-heavy bowling balls sitting in a swimming pool. They are so heavy and dense that they create a deep pit in the water around them.
The Size: These pits were about the size of our solar system but contained the mass of 100,000 suns.

2. The Rush: The "Wind" of Gas

After the universe cooled down (an event called "recombination"), the gas in the universe started moving. Because the dark matter and the gas didn't move at exactly the same speed, the gas was essentially "streaming" past these invisible bowling balls at supersonic speeds.

The Analogy: Imagine the bowling ball (dark matter) is sitting still in a river, but the water (gas) is rushing past it at 30 km/s. The water can't just flow around it smoothly; it crashes into it.

3. The Crash and The Cool Down (Bondi-Hoyle-Lyttleton Accretion)

When this fast-moving gas hits the invisible pit, it crashes into itself, creating a massive shockwave. This heats the gas up to a scorching 20,000 degrees.

The Cooling Trick: Normally, hot gas wants to expand and escape. But in this specific era, the gas had a special "cooling system" called atomic cooling. It was like a radiator that worked instantly. The gas heated up, then immediately cooled down to about 8,000 degrees.
The Result: Because it cooled so fast, the gas didn't bounce away. Instead, it lost its energy and started falling straight down into the center of the dark matter pit, like water going down a drain.

4. The "No-Break" Rule (Why it didn't break apart)

Usually, when gas falls into a hole, it breaks into smaller chunks (like water droplets) and forms many small stars. This is called fragmentation.

The Problem: If the gas broke into small stars, we would get a cluster of small stars, not a giant black hole.
The Solution: The authors found that at this specific time in the universe (very high redshift), the "spark" needed to break the gas into small chunks (molecular hydrogen) was extinguished. The background radiation of the universe (the Cosmic Microwave Background) was so bright and hot that it prevented the gas from forming the molecules needed to cool down enough to break apart.
The Analogy: It's like trying to build a house of cards in a hurricane. The wind (radiation) is so strong that the cards (gas molecules) can't stick together to form small structures. So, the whole pile of gas stays as one giant, solid block.

5. The Spin and The Collapse

As all this gas fell in, it had a little bit of spin (angular momentum), like water swirling down a drain.

The Disk: Instead of falling straight in, the gas formed a flat, spinning disk around the center.
The Instability: Because there was so much gas (about 1,000 times the mass of our Sun) packed into such a small space, the disk became unstable. It was like a spinning pizza dough that got too heavy and started to wobble violently.
The Final Act: This wobbling caused the gas to lose its spin and crash inward all at once. It didn't have time to become a normal star. Instead, it collapsed directly into a Supermassive Star and then immediately into a Black Hole weighing about 1,000 suns.

Why Does This Matter?

We have a mystery in astronomy: The James Webb Space Telescope (JWST) has found giant black holes in the very early universe. These black holes are too big to have grown from tiny "baby" black holes in the time available. They needed a head start.

This paper suggests that these Ultra-Dense Dark Matter Halos provided that head start. They acted as a "nursery" that gathered gas, kept it from breaking apart, and forced it to collapse directly into a massive seed black hole. These seeds then grew up to become the supermassive black holes we see at the centers of galaxies today.

In a nutshell:
The universe had some invisible, super-dense traps. Gas rushed into them, got hot, cooled down instantly, and was prevented from breaking into small stars by the "sunlight" of the early universe. This forced the gas to collapse directly into a giant black hole seed, solving the mystery of how the universe's biggest monsters got their start so quickly.

1. Problem Statement

The paper addresses two major cosmological puzzles:

The Origin of High-Redshift Supermassive Black Holes (SMBHs): The James Webb Space Telescope (JWST) has detected active galactic nuclei (AGNs) with black hole masses $\sim 10^8 M_\odot$ at redshifts $z \sim 10$ . Standard stellar evolution models struggle to explain how such massive seeds could form and grow to these sizes so early in the universe's history.
Primordial Black Hole (PBH) Constraints: While Primordial Black Holes are a candidate for dark matter and seeds, strict constraints from Cosmic Microwave Background (CMB) spectral distortions and gravitational wave observations limit the abundance of PBHs in certain mass ranges.

The authors propose an alternative formation channel: Direct Collapse Black Holes (DCBHs) formed via baryonic accretion onto Ultra-Dense Dark Matter Halos (UDMHs) that form before recombination, but where the actual black hole seed forms after recombination via efficient gas accretion.

2. Methodology

The authors employ a semi-analytic approach combining linear perturbation theory, hydrodynamic accretion models, and thermodynamic cooling physics.

UDMH Formation: They model the formation of $\sim 10^5 M_\odot$ dark matter halos arising from rare curvature fluctuations ( $\zeta$ ) on small scales. They ensure these fluctuations remain below current CMB spectral distortion limits (specifically $\mu$ -type distortions from COBE).
Pre-Recombination Suppression: Using linear theory (Appendix A), they demonstrate that baryonic accretion onto these halos is strongly suppressed before recombination due to radiative viscosity (Silk damping) and Compton drag from the CMB photons.
Post-Recombination Accretion: They apply the Bondi-Hoyle-Lyttleton (BHL) accretion formalism. Crucially, they account for the relative streaming velocity ( $v_\infty \approx 30$ km/s) between baryons and dark matter, which is supersonic relative to the post-recombination sound speed ( $c_s \approx 6$ km/s).
Thermodynamics & Cooling: They analyze the gas thermal evolution, specifically:
- Shock Heating: Gas is heated to virial temperatures ( $\sim 2 \times 10^4$ K) upon entering the halo.
- Atomic Cooling: Rapid cooling to $\sim 8000$ K via atomic transitions.
- Suppression of Molecular Cooling: They argue that at $z > 400$ , the formation of $H_2$ molecules is suppressed by CMB photons (photo-detachment of $H^-$ and $H_2^+$ ), preventing the gas from cooling to lower temperatures where fragmentation into stars would occur.
Angular Momentum & Instability: They estimate the angular momentum of the infalling gas and apply the Toomre stability criterion ( $Q$ ) to determine if the resulting gas disk becomes gravitationally unstable, facilitating rapid mass transfer to the center.

3. Key Contributions

Identification of a "Sweet Spot" for Accretion: The paper identifies a specific redshift window ( $z \approx 1100$ to $z \approx 400$ ) and halo mass scale ( $M_{DM} \sim 10^5 M_\odot$ ) where BHL accretion is maximally efficient. In this regime, the accretion radius is large enough that Hubble expansion damping is negligible, and the gas remains largely neutral, minimizing Compton drag.
Mechanism for Fragmentation Suppression: The authors provide a robust physical argument for why the gas does not fragment into Population III stars. The suppression of $H_2$ formation by the CMB at high redshifts ( $z > 400$ ) prevents the gas from cooling below $\sim 8000$ K. This maintains a high Jeans mass, allowing the gas to collapse monolithically rather than fragmenting.
Direct Collapse Pathway: They demonstrate that even with small residual angular momentum, the gas forms a compact, self-gravitating, Toomre-unstable disk ( $Q < 1$ ). Viscous forces and gravitational torques in this disk drive rapid inward mass transfer, leading to the formation of a supermassive star or a direct-collapse black hole.

4. Key Results

Accretion Efficiency: For a $10^5 M_\odot$ $1 0^{5} M_{⊙}$ UDMH, the BHL process can accumulate a gas mass of $M_{gas} \sim 10^3 M_\odot$ between recombination and $z=400$ $z = 400$ .
- If the halo mass is fixed: $M_{acc} \approx 1200 \lambda M_\odot$ .
- If the halo grows as $(1+z)^{-1}$ : $M_{acc} \approx 5200 \lambda M_\odot$ .
Thermal Evolution: The gas cools rapidly from shock-heated temperatures ( $\sim 2 \times 10^4$ K) to a stable $\sim 8000$ K. This temperature is below the virial temperature, ensuring continued collapse, but high enough to prevent $H_2$ cooling and fragmentation.
Disk Stability: For typical parameters (initial spin parameter $\lambda_L \sim 0.01$ ), the resulting gas disk has a Toomre parameter $Q \approx 0.63$ . Since $Q < 1$ , the disk is unstable, leading to efficient angular momentum transport and rapid accretion on a timescale of $\sim 10^5$ years (comparable to the free-fall time).
Abundance: The number density of such rare ( $5\sigma - 6\sigma$ ) UDMHs is estimated to be $N \sim 10^{-3} - 10^{-5} \text{ Mpc}^{-3}$ . This abundance is comparable to high-redshift "Little Red Dots" (LRDs) observed by JWST and is sufficient to seed the observed population of high-redshift AGNs without violating CMB constraints on primordial black holes.
Final Mass: The process leads to the formation of intermediate-mass black holes (IMBHs) of $\sim 10^3 M_\odot$ at redshifts $z \sim 400-600$ , which can subsequently grow into the $10^8-10^9 M_\odot$ SMBHs observed at $z \sim 10$ .

5. Significance

This paper offers a compelling solution to the "early SMBH" problem that avoids the need for super-Eddington accretion or extremely massive primordial black hole seeds.

Observational Consistency: The proposed mechanism naturally explains the high mass-to-stellar mass ratios seen in JWST AGNs and aligns with the abundance of high-redshift compact objects.
Theoretical Robustness: It relies on standard physics (BHL accretion, atomic cooling, CMB interaction) without invoking exotic new physics, provided that small-scale power in the primordial power spectrum is slightly enhanced (but still within CMB distortion limits).
Future Implications: The formation of these IMBHs could influence the formation of the first stars and galaxies through feedback. The paper suggests that future simulations of BHL accretion onto UDMHs and observations of high-redshift "Little Red Dots" could further test this scenario.

In summary, the authors propose that ultra-dense dark matter halos act as gravitational wells that capture baryons via Bondi-Hoyle-Lyttleton accretion in a specific high-redshift window. The unique thermodynamic conditions (suppressed molecular cooling) force this gas to collapse directly into $\sim 10^3 M_\odot$ black holes, providing the necessary heavy seeds for the supermassive black holes observed in the early universe.