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The properties of primordially-seeded black holes and their hosts in the first billion years: implications for JWST

This paper introduces the PHANES analytic framework to demonstrate that primordial black hole (PBH) seeding models naturally explain the unexpectedly massive black holes and high black hole-to-stellar mass ratios observed by JWST at high redshifts, while remaining consistent with all current cosmological and astrophysical constraints.

Original authors: Pratika Dayal, Roberto maiolino

Published 2026-02-04

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Pratika Dayal, Roberto maiolino

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 Mystery: "Little Red Dots" and Giant Monsters

Imagine the early Universe as a construction site that is only a few hundred million years old. According to standard rules of physics (the "standard model" of cosmology), the buildings (galaxies) should be small, and the heavy machinery inside them (black holes) should be tiny seeds waiting to grow.

However, the James Webb Space Telescope (JWST) has started taking photos of this construction site and found something strange. It sees "Little Red Dots"—tiny, faint galaxies that somehow contain giant black holes. These black holes are so massive that they are already as heavy as millions of suns, even though the galaxies they live in are still very young and small.

It's like walking into a house that was built yesterday and finding a massive, fully grown oak tree growing out of the living room floor. It shouldn't be possible. The tree (black hole) is too big for the house (galaxy), and the house is too young for the tree to have grown there naturally.

The Old Theory vs. The New Idea

The Old Theory (Astrophysical Seeds):
Scientists used to think these black holes started as small "seeds" (like a baby black hole the size of a mountain) and grew by eating gas and merging with others. But the paper argues that even if these seeds ate as much as physically possible, they couldn't grow big enough, fast enough, to explain what JWST is seeing.

The New Idea (Primordial Black Holes):
The authors, Pratika Dayal and Roberto Maiolino, propose a different origin story. They suggest these black holes didn't start as seeds that grew; they started as Primordial Black Holes (PBHs).

The Analogy: Imagine the Big Bang didn't just create a smooth soup of matter. Instead, imagine it sprinkled a few "heavy stones" (PBHs) into the soup right at the very beginning.
These heavy stones are much heavier than normal black hole seeds. Because they are so heavy, they act like powerful magnets, pulling in surrounding gas and dark matter much faster than a normal seed could. They essentially "cheat" the growth timeline, allowing the black hole to become a giant while the galaxy around it is still a toddler.

How They Tested This: The "Phanes" Model

To see if this idea works, the authors built a computer simulation called "Phanes" (which stands for Primordial black holes accelerating the assembly of nascent early structures).

Think of Phanes as a video game engine that simulates the first billion years of the Universe. They ran the game with three different settings for how these "heavy stones" spin:

Non-spinning: The black hole is just sitting there.
Spinning backward (Retrograde): The black hole spins against the flow of gas.
Spinning forward (Prograde): The black hole spins with the flow of gas.

They watched how these black holes grew and how the galaxies around them formed.

What They Found: The "Smoking Gun"

The results of their simulation matched the JWST observations in a way that standard theories cannot. Here are the key findings:

1. The "Obese" Black Holes
In their simulation, the black holes grew to be incredibly massive compared to the stars in their host galaxy.

The Metaphor: In our normal universe, a black hole is usually about 0.1% the weight of its galaxy (like a small pebble in a backpack). In the JWST observations, the black holes are 10% to 100% the weight of the galaxy (like a bowling ball inside a backpack).
The Result: The "Phanes" model naturally produces these "obese" black holes. Specifically, if the black holes are spinning backward (retrograde) or not spinning at all, they grow huge very quickly, matching the "Little Red Dots" we see.

2. The "Empty" Galaxies
The JWST also found that some of these galaxies have very low levels of "heavy elements" (metals like carbon and oxygen). Usually, heavy elements are created by stars dying and exploding.

The Metaphor: Imagine a kitchen that has been cooking for a long time; you'd expect the air to smell like food (metals). But these early galaxies are like a kitchen that just started cooking; the air is still fresh.
The Result: The model shows that because the black holes grew so fast and ate so much gas, they prevented the stars from forming enough to create heavy elements. This explains why we see giant black holes in "clean," metal-poor galaxies.

3. The Safety Check
The authors were careful to make sure their theory didn't break the rest of physics. They calculated how many of these "heavy stones" (PBHs) would need to exist to make this work.

The Result: They found that these black holes would make up less than one-billionth of the total "dark matter" in the Universe. This is a tiny amount, meaning their theory fits safely within all current rules of cosmology and doesn't contradict other observations.

The Conclusion

The paper argues that the strange, giant black holes seen by JWST are too big and too young to have grown from normal seeds. Instead, they likely started as Primordial Black Holes—heavy seeds formed in the very first moments of the Universe.

These ancient seeds acted like turbo-chargers, allowing black holes to grow to monstrous sizes while their host galaxies were still in their infancy. If this is true, it changes our understanding of how the first structures in the Universe came to be. The "Little Red Dots" aren't just weird anomalies; they are the smoking gun evidence that the Universe started with a few heavy stones that grew into giants.

Technical Summary: The Properties of Primordially-Seeded Black Holes and Their Hosts in the First Billion Years

Problem Statement
Recent observations by the James Webb Space Telescope (JWST) have revealed a population of active galactic nuclei (AGN) and "Little Red Dots" (LRDs) at redshifts $z \sim 4 - 10.4$ that challenge standard astrophysical models of black hole (BH) formation and growth. These systems exhibit three primary anomalies: (1) Extremely massive black holes ( $M_{\rm BH} > 10^7 - 10^8 M_\odot$ ) existing as early as $z \sim 10$ ; (2) Unusually high black hole-to-stellar mass ratios ( $M_{\rm BH}/M_* \gtrsim 0.1 - 1$ ), significantly exceeding local relations; and (3) Extremely low metallicities ( $Z \lesssim 10^{-2} Z_\odot$ ) in some hosts. While various astrophysical seeding mechanisms (e.g., Population III remnants, direct collapse black holes) combined with super-Eddington accretion have been proposed, they struggle to simultaneously reproduce these extreme properties. This work investigates whether Primordial Black Holes (PBHs), generated shortly after the Big Bang, can serve as seeds that naturally explain these observations.

Methodology: The phanes Framework
The authors present phanes (Primordial black holes accelerating the assembly of nascent early structures), an analytic framework designed to track the evolution of dark matter (DM) halos and their baryons in the first billion years, seeded by a population of PBHs.

PBH Mass Spectrum: The model assumes a power-law mass spectrum for PBHs, $dn/dm = \kappa m^{-\alpha}$ , with slopes $\alpha = 2$ and $3$, covering seed masses from $10^{0.5}$ to $10^6 M_\odot$ . The normalization $\kappa$ is constrained using the observed number density of high-redshift candidates GHZ9 and UHZ1 at $z \sim 10 - 10.4$ .
Halo Assembly: The framework models the "seed effect," where individual PBHs linearly accrete DM halos from the epoch of matter-radiation equality ( $z \sim 3400$ ) down to $z \sim 34$ . Below this redshift, halos grow via smooth accretion from the intergalactic medium (IGM). Gas accretion is permitted once the halo mass exceeds a threshold defined by a baryonic over-density of $\delta_b = 200$ .
Star Formation and Feedback: Once gas is available, the model calculates star formation and black hole accretion. It incorporates feedback from both Type II supernovae (SNII) and black hole accretion, which can eject gas and metals. The model tracks metal enrichment, assuming yields from stars between $8 - 50 M_\odot$ .
Spin Scenarios: The study explores three distinct black hole spin scenarios to test their impact on growth efficiency:
1. Non-spinning ( $s=0$ ): Radiative efficiency $\epsilon = 0.057$ .
2. Maximally retrograde ( $s=-1$ ): $\epsilon = 0.037$ (lowest efficiency, fastest growth).
3. Maximally prograde ( $s=+1$ ): $\epsilon = 0.42$ (highest efficiency, slowest growth).
Cosmology: The model adopts a standard $\Lambda$ CDM cosmology with Planck 2020 parameters and a Salpeter initial mass function (IMF) for stars.

Key Results

Black Hole and Stellar Mass Functions (BHMF/SMF):
- The PBH-seeded models produce a BHMF extending from $10^{1.25} - 10^{11.25} M_\odot$ at $z \sim 5$ and $10^{0.75} - 10^{7.25} M_\odot$ at $z \sim 15$ .
- The fiducial model ( $s=0$ ) with $\alpha=2$ matches the observed BHMF amplitude at $z \sim 5$ for masses $10^7 - 10^{8.5} M_\odot$ .
- Crucially, the resulting Stellar Mass Function (SMF) lies at least four orders of magnitude below observational constraints at $z \sim 5 - 10$ . This implies that PBH-seeded systems do not dominate the star-forming galaxy population; standard DM halos dominate the SMF, while PBHs primarily influence the high-mass end of the BHMF.
Black Hole-to-Stellar Mass Ratios ( $M_{\rm BH}/M_*$ ):
- PBH-seeded models naturally yield extremely high $M_{\rm BH}/M_*$ ratios. For a typical stellar mass of $M_* = 10^9 M_\odot$ at $z=5$ , the fiducial model ( $s=0$ ) predicts an average ratio of $\sim 0.4$ , while the retrograde model ( $s=-1$ ) predicts $\sim 1.6$ .
- The $s=0$ model encompasses the observed data points at $z \sim 5 - 10$ with $M_{\rm BH}/M_* \gtrsim 0.25$ , a regime that is difficult to reach with standard astrophysical seeds without invoking extreme, often unsustainable, accretion scenarios.
- The $s=-1$ case produces the highest ratios ( $M_{\rm BH}/M_* > 1$ ) due to rapid growth and low radiative efficiency, while $s=+1$ models generally fail to reach the observed high masses.
Eddington Accretion Fractions ( $f_{\rm Edd}$ ):
- The models produce a wide range of Eddington fractions ( $f_{\rm Edd} \sim 0.01 - 1$ ).
- The $s=0$ model successfully reproduces the combination of high black hole masses and low Eddington rates ( $f_{\rm Edd} < 0.03$ ) observed in some systems, though it tends to predict lower stellar masses than observed for a given black hole mass.
- The $s=-1$ model predicts very low $f_{\rm Edd}$ values ( $< 0.1$ ) at $z < 7$ because the rapid growth consumes available gas, leading to over-massive black holes relative to their gas reservoirs.
Metallicity:
- The models predict a correlation between metallicity, black hole mass, and stellar mass.
- A significant finding is the ability of the $s=0$ model to produce systems with extremely low metallicities ( $Z < 10^{-2} Z_\odot$ ) co-existing with high $M_{\rm BH}/M_*$ ratios. This specific combination is rare in standard astrophysical models but aligns with recent JWST detections of metal-poor, massive black hole hosts.

Significance and Claims
The paper claims that the "phanes" framework provides a viable cosmological solution to the JWST-era puzzles of early black hole demographics. The authors argue that PBH seeding offers a "smoking gun" signature: the simultaneous presence of extremely high black hole-to-stellar mass ratios ( $M_{\rm BH}/M_* \gtrsim 0.25$ ) and extremely low metallicities ( $Z \lesssim 10^{-2} Z_\odot$ ).

The study emphasizes that these results are achieved without violating current cosmological bounds; the fraction of dark matter in the form of PBHs is constrained to $f \lesssim 10^{-9}$ , which is at least five orders of magnitude below limits set by gravitational waves and dynamical effects. The authors conclude that while observational uncertainties regarding mass inference and stellar population modeling remain, the specific demographic of "obese" black holes in metal-poor, low-stellar-mass hosts is uniquely explained by PBH seeding, distinguishing it from standard astrophysical growth scenarios.

The Big Mystery: "Little Red Dots" and Giant Monsters

The Old Theory vs. The New Idea

How They Tested This: The "Phanes" Model

What They Found: The "Smoking Gun"

The Conclusion

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