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The formation of supermassive black holes from Population III.1 seeds. IV. Self-regulated seeding from supermassive star ionizing feedback

This paper presents a self-regulated feedback model demonstrating how ionizing radiation from Population III.1 stars creates isolated HII regions that limit supermassive star formation to specific intervals, ultimately predicting a supermassive black hole number density of approximately 0.2 cMpc⁻³ and low binary merger rates detectable by LISA.

Original authors: Maya A. Petkova, Jonathan C. Tan, Jasbir Singh, Vieri Cammelli, Mahsa Sanati, Benjamin Keller, Pierluigi Monaco, Devesh Nandal

Published 2026-05-28

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CC BY 4.0

Original authors: Maya A. Petkova, Jonathan C. Tan, Jasbir Singh, Vieri Cammelli, Mahsa Sanati, Benjamin Keller, Pierluigi Monaco, Devesh Nandal

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 Big Picture: How Did Giant Black Holes Get So Big So Fast?

Imagine the early universe as a vast, dark construction site. Astronomers have found massive "supermassive black holes" (SMBHs) sitting in the centers of galaxies very early in the universe's history (when the universe was only a baby, about 700 million years old).

The problem is: How did they get so big so quickly?
If they started as tiny "seeds" (like small black holes from normal stars), they would need to eat gas at an impossible speed to grow into giants in time. It's like trying to fill a swimming pool with a teaspoon; you just can't do it fast enough.

This paper proposes a different idea: The seeds started out huge.

The "Supermassive Star" Seed

The authors suggest that the first seeds weren't tiny. Instead, they were born from special, giant stars called Population III.1 stars.

The Recipe: These stars formed in tiny, isolated pockets of pristine gas (gas that had never been touched by other stars).
The Secret Ingredient: Inside these stars, dark matter particles were crashing into each other and heating up the star from the inside (like a hidden furnace). This extra heat prevented the star from shrinking too fast, allowing it to keep eating gas and growing to a massive size (10,000 to 100,000 times the mass of our Sun) before it collapsed into a giant black hole.

The "Social Distancing" Rule

Here is the tricky part. These giant stars can only form if they are completely alone. If they are too close to other stars, the radiation (light and heat) from those neighbors will mess up the gas, causing it to break apart into many small stars instead of one giant one.

Think of it like planting a giant oak tree.

If you plant it in a crowded forest, the other trees block the sun and water, and your oak tree stays small or dies.
But if you plant it in a wide-open field with no neighbors, it can grow into a massive giant.

The paper's main job was to figure out how much empty space is needed between these giant stars so they can grow.

The New "Fence" Model

In previous studies, the scientists just guessed a fixed distance (like saying, "They must be 100 miles apart"). In this new paper, they built a smarter, self-regulating model.

They realized that once a giant star is born, it blasts out a massive bubble of ionized gas (a region where atoms are stripped of their electrons). This bubble acts like a force field or a fence.

The Fence Grows: As the star shines, this bubble expands.
The Rule: No new giant star can form inside someone else's bubble. They have to wait until they are far enough away to be outside the bubble.

The authors calculated the size of these bubbles based on how bright the stars are and how long they live. They found that these bubbles are huge—about 1.3 million light-years across (in the expanding universe's coordinates). This creates a natural "social distancing" rule that limits how many giant black holes can be born in a given area.

What Did They Find?

The "Flash" Phase: Most of these giant black hole seeds were born very early, between redshifts 20 and 16 (when the universe was very young). The process happened quickly, like a flash of lightning, and then stopped because the "fences" (bubbles) had filled up the available space.
The Number of Black Holes: Their model predicts there are about 0.2 giant black holes per cubic megaparsec (a huge volume of space). This is a lot! It suggests there are many more of these seeds out there than we can currently see.
Why We Don't See Them All: The paper explains that while there are many of these seeds, most are "sleeping" (not actively eating gas). We only see the ones that are currently active (shining as bright quasars). This is why our current telescopes might only see a fraction of the total population.
The "Double" Black Holes: When galaxies merge, their central black holes might pair up. The paper predicts that at very high redshifts (early universe), it is very rare to see two active black holes dancing together (less than 0.3% of the time). They mostly pair up later, as the universe gets older.
Future Detection: The paper predicts that the upcoming LISA mission (a space-based gravitational wave detector) should be able to hear the "chirp" of these giant black holes merging a few times per year.

Summary

The paper uses a "social distancing" model based on the giant bubbles of light created by supermassive stars to explain how the universe's first giant black holes formed. Instead of guessing how far apart they needed to be, the authors let the stars' own light create the boundaries. This model successfully explains how we could have so many giant black holes early in the universe without needing them to eat gas impossibly fast. It suggests the universe is full of these "sleeping giants," waiting to be discovered.

Technical Summary: The Formation of Supermassive Black Holes from Population III.1 Seeds. IV. Self-regulated seeding from supermassive star ionizing feedback

Problem Statement
The origin of supermassive black holes (SMBHs), particularly those observed at high redshifts ( $z \sim 7-10$ ), remains a significant open question in astrophysics. While "light" seeds ( $\sim 100 M_\odot$ ) require sustained super-Eddington accretion to reach observed masses, current observations and simulations do not robustly support this feasibility. Conversely, "heavy" seed models, such as direct collapse, often predict number densities too low to explain the observed abundance of SMBHs. A promising alternative involves Population III.1 stars—supermassive stars ( $10^4 - 10^5 M_\odot$ ) formed from pristine, metal-free gas in dark matter minihalos, potentially powered by Weakly Interacting Massive Particle (WIMP) dark matter annihilation. These stars are theorized to form only in isolated, non-irradiated environments to avoid fragmentation. Previous works in this series (Banik et al. 2019; Singh et al. 2023) utilized a constant, free-parameter isolation distance ( $d_{iso}$ ) to seed these stars in cosmological simulations. This paper addresses the need for a physically motivated, self-consistent isolation criterion based on the ionizing feedback of the stars themselves.

Methodology
The authors employ the Pinocchio Lagrangian Perturbation Theory code to simulate the formation and evolution of dark matter halos in a $\Lambda$ CDM universe (box size 59.7 cMpc, $N=4096^3$ particles). The study introduces a new seeding algorithm that replaces the constant isolation distance with a dynamic, feedback-regulated model.

Key methodological components include:

Feedback Distance Calculation: The isolation criterion is defined by the size of the HII region surrounding a Pop III.1 star. The model considers two regimes:
- Strömgren Radius ( $R_S$ ): The equilibrium size where ionization balances recombination, which varies with redshift and gas density.
- R-type Expansion ( $R_R$ ): The expansion of the HII region during the star's lifetime if the lifetime is shorter than the recombination time. The authors derive that for typical Pop III.1 parameters, $R_R$ remains approximately constant in comoving units ( $\sim 1.3$ cMpc for a fiducial model).
Seeding Algorithm: The algorithm processes halos in order of appearance. A new halo is seeded as a Pop III.1 star (and subsequent SMBH) only if it lies outside the feedback distance of all previously formed ionizing sources (both seeded Pop III.1 stars and non-seeded Pop III.2 stars).
Physical Parameters: The study varies stellar ionizing luminosity ( $S$ ), stellar lifetime ( $t$ ), and the time delay between halo formation and star formation ( $t_{del}$ ). The fiducial model assumes $S = 10^{53} \text{ s}^{-1}$ , $t = 10$ Myr, and $t_{del} = 50$ Myr.
Merger Tracking: The simulation tracks halo mergers down to $z=0$ (using a low-resolution run for computational efficiency) to determine the evolution of SMBH number density and the formation of binary SMBHs.

Key Contributions and Results

Self-Regulated Seeding: The paper demonstrates that using the R-type expansion of HII regions as the isolation criterion results in a separation distance that is approximately constant in comoving coordinates ( $\sim 1.3$ cMpc for the fiducial model), unlike previous models that assumed constant proper distances.
Seeding Timeline: The seeding process is rapid, occurring primarily at high redshifts. The median formation redshift is $\sim 20$ , with the process essentially complete by $z \sim 16$ .
SMBH Number Density: The fiducial model yields a final comoving number density of SMBH seeds of $n_{SMBH} \simeq 0.16 \text{ cMpc}^{-3}$ (or $\sim 0.2 \text{ cMpc}^{-3}$ before merger reductions). This is approximately 30 times higher than the observed local SMBH density ( $z=0$ ), suggesting a large population of inactive or undetected SMBHs.
Dual AGN and Mergers:
- The model predicts a low fraction of dual Active Galactic Nuclei (AGN) at high redshifts, specifically $\lesssim 0.3\%$ for $z > 6$ .
- Approximately 25–30% of seeded halos undergo mergers by $z=0$ .
- The predicted merger rate for heavy seeds ( $\sim 10^5 M_\odot$ ) detectable by the future LISA mission is estimated at a few events per year for the fiducial model (up to $\sim 19 \text{ yr}^{-1}$ for other parameter choices).
Comparison to Observations: The predicted number densities are consistent with the existence of high-redshift AGN ( $z \gtrsim 7$ ) and fall within the range of isolation distances ($30-50$ kpc in proper units at seeding) favored by previous semi-analytic studies (Cammelli et al. 2025a).

Significance and Claims
The authors claim that this work provides a more physically grounded framework for Pop III.1 seeding by linking the isolation distance directly to the ionizing feedback of the stars. The primary significance lies in the prediction of an early "flash" ionization phase characterized by a characteristic scale of ionized bubbles ( $\sim 1.3$ cMpc), which has implications for Cosmic Microwave Background (CMB) observations and high-redshift atomic hydrogen studies.

The paper modestly concludes that while the model predicts a high abundance of SMBH seeds (potentially overproducing relative to current $z=0$ observations), this is consistent with the idea that many seeds remain dormant or undetected. The model successfully accommodates high-redshift AGN observations without requiring super-Eddington accretion. The authors emphasize that uncertainties in Pop III.1 star formation conditions (luminosity, lifetime) can alter the final number density by an order of magnitude, motivating further detailed studies of dark matter-powered supermassive stars. The work does not propose new experimental setups but offers testable predictions for LISA merger rates and dual AGN fractions.