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Abundant Heavy Black Hole Seeds from Moderate Lyman-Werner Radiation

This paper demonstrates through high-resolution simulations that moderate Lyman-Werner radiation ( $1 \lesssim J_{\rm 21} < 10$ ), rather than extreme radiation or specific halo assembly rates, is the dominant factor enabling the formation of massive black hole seeds, thereby suggesting these seeds could form in significantly more common cosmic environments than previously thought.

Original authors: Ryan Hazlett, Eli Visbal, Greg L. Bryan, Mihir Kulkarni

Published 2026-08-17

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Ryan Hazlett, Eli Visbal, Greg L. Bryan, Mihir Kulkarni

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

The Cosmic Nursery: How the First Giants Were Born

Imagine the universe as a giant, dark ocean. For a long time, it was just a soup of hydrogen and helium gas, too cold and too calm to make anything interesting. Then, gravity started pulling this gas together into giant clouds called "halos." Inside these clouds, the gas wanted to cool down to form stars, but there was a catch: to cool efficiently, the gas needed to turn into molecular hydrogen, like a special kind of frost. If it could frost over, it would shrink, spin, and burst into tiny, normal stars.

But there was a cosmic "heater" floating around: intense ultraviolet light from the very first stars that had already formed. This light, called Lyman–Werner radiation, acted like a blowtorch, blasting the molecular hydrogen apart before it could form. Without that frost, the gas stayed hot and puffy, refusing to shrink into tiny stars. Instead, it kept piling up, getting hotter and heavier, until it collapsed all at once into a single, monstrous object. This is the story of how the universe might have built its first "superstars"—giant stars so massive they could collapse directly into the seeds of the supermassive black holes we see today. Scientists are obsessed with this because we have telescopes like the James Webb Space Telescope that are finding black holes that grew too big, too fast, and we need to know how they got their start.

The Paper: Hunting for the Perfect "Blowtorch"

This paper is a massive digital experiment designed to figure out exactly how much of that "blowtorch" radiation is needed to create these monster stars. The authors, a team of astrophysicists, ran 65 high-resolution computer simulations. They took 15 different cosmic gas clouds (halos) and subjected them to different levels of that ultraviolet radiation, ranging from almost none to extremely intense. They wanted to see: Does the radiation level matter more than how fast the cloud is growing? And how many of these clouds are actually out there in the universe?

The Big Discovery: It's All About the Radiation

The team found a very clear "switch" in the behavior of the gas clouds.

Low Radiation (The "Frosty" Zone): When the radiation was weak (a value called $J_{21} \le 1$ ), the gas cooled down too quickly. It fragmented into many small pieces, forming normal-sized stars (maybe a few hundred times the mass of our Sun).
High Radiation (The "Super-Heated" Zone): When the radiation was strong ( $J_{21} \ge 10$ ), the gas stayed hot and puffy. It didn't break apart. Instead, it poured inward in a massive, steady river. This allowed a single central star to grow to a staggering $10^5$ solar masses (100,000 times the mass of our Sun) before collapsing into a black hole.

The most surprising part? The speed at which the halo was assembling (growing) didn't seem to matter much. The authors tested halos growing at rates from 0.01 to 7 solar masses per year. Whether a halo was growing slowly or rapidly, the radiation level was the only thing that decided if it would make a tiny star or a giant one. The radiation acts like a thermostat: if it's set high enough, it keeps the gas from cooling, forcing it to build a giant.

The "Middle Ground" Mystery

Here is where the story gets even more interesting. The simulations showed a clear jump between the "weak" radiation ( $J_{21} \le 1$ ) and the "strong" radiation ( $J_{21} \ge 10$ ). But what happens in between? The authors didn't simulate the middle ground ( $1 < J_{21} < 10$ ) directly, but they used a clever math model to guess.

They found that in the real universe, halos with that "strong" radiation ( $J_{21} \ge 10$ ) are incredibly rare. They make up only 0.01% of all the places where stars could form. However, halos with "moderate" radiation ( $1 \le J_{21} < 10$ ) are everywhere—they make up 91.6% of the population!

This leads to a huge possibility: If the "switch" to making giant stars turns on anywhere in that moderate range (not just at the extreme high end), then the universe is full of places where these giant seeds could form. Instead of being a rare event happening in one in a million clouds, heavy black hole seeds could be forming in nearly every other cloud. This would explain why we see so many giant black holes so early in the universe's history.

How They Did It (Without Waiting 10 Million Years)

Simulating a star forming takes too long for a computer to run all the way to the end. So, the authors invented a new trick. Instead of waiting for the star to grow, they looked at the gas just as it started to collapse. They measured how fast the gas was rushing inward and used that to predict how big the final star would be. They tested this new method against other famous simulations that did wait for the star to grow, and it worked perfectly, predicting the mass within a factor of 2. This allowed them to run 65 simulations instead of just a few.

What They Don't Know Yet

The authors are careful to say these are "upper limits." Their method assumes the gas falls in perfectly and doesn't get blown away by the star's own light or break into smaller pieces. In reality, the gas might fragment, meaning the final black hole seed could be smaller than predicted. Also, they didn't simulate the "middle" radiation levels directly, so we don't know for sure if the switch flips at $J_{21}=2$ or $J_{21}=9$ .

The Bottom Line

The paper suggests that we might have been looking for these giant seeds in the wrong places. We thought they needed the most extreme, rare radiation environments. But if the "thermostat" works at moderate levels, then the universe is actually teeming with the perfect conditions to build the seeds of the supermassive black holes we see today. The heavy black holes aren't rare accidents; they might be the rule, not the exception.

Technical Summary: Abundant Heavy Black Hole Seeds from Moderate Lyman–Werner Radiation

Problem Statement
The existence of supermassive black holes (SMBHs) with masses $\gtrsim 10^6 - 10^9 M_\odot$ within the first billion years of cosmic time presents a significant challenge to standard formation models. If these objects originate solely from the remnants of typical Population III (Pop III) stars ( $\sim 100 M_\odot$ ), the required growth rates are difficult to achieve. A promising alternative is the formation of supermassive stars (SMSs, $\sim 10^4 - 10^5 M_\odot$ ) via direct collapse in atomic-cooling halos. This process requires sustained gas inflow rates exceeding a critical threshold ( $\sim 0.01 - 1 M_\odot \text{yr}^{-1}$ ) to prevent fragmentation and maintain a bloated, cool protostar.

Previous studies have identified environmental mechanisms capable of suppressing molecular hydrogen ( $H_2$ ) cooling and delaying collapse to the atomic-cooling regime, specifically Lyman–Werner (LW) radiation backgrounds and baryon-dark matter streaming velocities. However, the dependence of SMS formation on the specific intensity of the LW background and the halo assembly history remains poorly constrained. Furthermore, high-resolution simulations capable of resolving protostellar accretion are computationally expensive, limiting statistical studies of how these conditions vary across the broader population of early halos.

Methodology
The authors present a suite of 65 high-resolution cosmological zoom-in simulations using the adaptive mesh refinement code Enzo. The study focuses on 15 pristine dark matter halos selected from a parent $25 \text{ cMpc}$ volume, spanning a wide range of halo assembly rates ( $0.01 - 7 M_\odot \text{yr}^{-1}$ ) and assembly timescales ( $1 - 200 \text{ Myr}$ ).

Radiation Backgrounds: Each halo was simulated under varying uniform LW radiation intensities ( $J_{21}$ ), ranging from weak backgrounds ( $J_{21} \le 1$ ) to strong backgrounds ( $J_{21} \ge 10$ , up to $300$).
Resolution: Simulations achieved spatial resolutions of $\sim 2 \times 10^{-4} \text{ pc}$ , with dark matter particle masses as low as $\sim 950 M_\odot$ for low-LW cases to ensure convergence of baryonic collapse.
Inflow Prescription: Instead of explicitly modeling the full protostellar accretion phase using sink particles (which is computationally prohibitive for large ensembles), the authors introduce a novel post-processing method. This method estimates the final Pop III stellar mass by analyzing the spherically averaged gas density and radial velocity profiles at the onset of runaway collapse.
- The method calculates an enclosed-mass inflow rate ( $\dot{M}_{\text{infall}}$ ) and integrates the accretion history until the rate drops below a calibrated critical threshold of $6.7 \times 10^{-3} M_\odot \text{yr}^{-1}$ .
- This threshold was calibrated against high-resolution sink-particle simulations from Suazo et al. (2019) to reproduce final stellar masses within a factor of $\sim 2$ .
Semi-Analytic Model (SAM): To estimate the cosmological abundance of potential heavy seed sites, the authors applied a semi-analytic model to cosmological volumes. This model tracks radiative and chemical feedback to determine the local LW environment experienced by halos at the onset of Pop III star formation.

Key Results

LW Radiation as the Dominant Predictor: The simulations reveal a clear bifurcation in gas inflow rates based on LW intensity. Halos exposed to $J_{21} \gtrsim 10$ sustain systematically higher inflow rates and gas temperatures compared to those with $J_{21} \lesssim 1$ . Consequently, halos in the high- $J_{21}$ regime frequently produce estimated stellar masses up to $10^5 M_\odot$ .
Weak Dependence on Assembly History: Despite spanning a wide range of halo assembly rates, the study finds no statistically significant correlation between the predicted Pop III stellar mass and the halo assembly timescale ( $M_{\text{Halo}}/\dot{M}_{\text{Halo}}$ ). This suggests that once halos reach the atomic-cooling threshold, variations in assembly history have a negligible impact on the resulting protostellar mass compared to the thermodynamic state set by the LW field.
Intermediate Regime Abundance: The semi-analytic model indicates that halos exposed to intermediate LW backgrounds ( $1 \le J_{21} < 10$ ) are orders of magnitude more common ( $\sim 91.6\%$ of Pop III-forming halos) than those in the high- $J_{21}$ tail ( $J_{21} \ge 10$ , $\sim 0.01\%$ ).
Transition Threshold: The data suggests a transition in the ability to sustain high accretion occurs between $J_{21} \sim 1$ and $J_{21} \sim 10$ . While the simulations do not cover the intermediate range ( $1 < J_{21} < 10$ ) explicitly, the trend implies that if sustained high accretion extends into this regime, the abundance of heavy black hole seed formation sites could be vastly higher than predicted by classical direct-collapse models requiring extreme LW fields ( $J_{21} \sim 10^3 - 10^4$ ).

Significance and Claims
The paper claims that the Lyman–Werner radiation field is a stronger predictor of sustained high accretion and massive Pop III star formation than halo assembly history within the explored parameter space.

The authors argue that the classical direct-collapse scenario, which relies on rare, extreme LW environments, may be overly restrictive. If the transition to supermassive star formation occurs at moderate LW intensities ( $J_{21} \gtrsim 1$ or even within the intermediate $1 \le J_{21} < 10$ range), heavy black hole seeds could form in substantially more common environments. This finding offers a potential explanation for the observed abundance of high-redshift quasars and AGN detected by the James Webb Space Telescope (JWST), suggesting that the necessary conditions for massive seed formation are not confined to exceptional, rare events but may be a feature of a broader population of atomic-cooling halos.

The authors explicitly note that their derived stellar masses are upper limits, as the method assumes 100% accretion efficiency and does not explicitly model fragmentation, outflows, or radiative feedback during the protostellar phase. They emphasize that future simulations spanning the intermediate LW regime and explicitly following protostellar evolution are required to precisely locate the critical LW threshold and determine the true abundance of heavy black hole seeds.

The Cosmic Nursery: How the First Giants Were Born

The Paper: Hunting for the Perfect "Blowtorch"

Technical Summary: Abundant Heavy Black Hole Seeds from Moderate Lyman–Werner Radiation

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