arxiv: 2604.20966 · v1 · submitted 2026-04-22 · 🌌 astro-ph.GA · astro-ph.CO

Recognition: unknown

Light, heavy, primordial: exploring the diversity of black hole seeding and growth mechanisms in the JWST era

Pratika Dayal

Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:20 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO

keywords primordial black holesblack hole seedingJWST early galaxiesblack hole growthmetal-poor hostsEddington accretionsemi-analytic modelshigh-redshift observations

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The pith

Primordial black holes and heavy seeds with limited accretion match JWST observations of early massive black holes in metal-poor hosts, while Eddington-limited light seeds are ruled out.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests which black hole formation and growth scenarios can explain JWST detections of surprisingly large black holes in small, metal-poor galaxies at redshifts 7-10. It contrasts light seeds from the first stars, heavy seeds from direct gas collapse, and primordial black holes from the early universe, allowing different accretion rates and mergers in semi-analytic models of galaxy evolution. Only primordial black holes and heavy seeds limited to Eddington accretion reproduce the full set of observed black hole masses, stellar masses, and extremely low metallicities. A distinctive signature emerges for primordial black holes: their mass relative to the host stars decreases as the surrounding halo grows larger, unlike any astrophysical seeding channel.

Core claim

Comparing astrophysically-seeded black holes in the DELPHI semi-analytic model and cosmologically-seeded primordial black holes in the PHANES analytic model shows that the only scenario ruled out by z~5-10 data is Eddington-limited accretion onto light seeds. Both primordial black holes and Eddington-limited heavy seeds simultaneously match the observed black hole masses, stellar masses, and host metallicities Z ≤ 0.01 Z_⊙. Primordial black holes uniquely exhibit a decrease in the black hole-to-stellar mass ratio with increasing halo mass at all redshifts, in contrast to every astrophysical model.

What carries the argument

Side-by-side application of the DELPHI semi-analytic model (light and heavy astrophysical seeds with mergers plus Eddington or super-Eddington accretion) and the PHANES analytic model (primordial black holes growing only by sub-Eddington accretion) against JWST observables of black hole mass, stellar mass, metallicity, and halo mass at z~5-10.

If this is right

Eddington-limited light seed models are excluded by the combination of high black hole masses and low host metallicities.
Super-Eddington heavy seeds and primordial black holes both reproduce the observed over-massive black hole ratios of 0.3-1.
Primordial black holes are the only channel that also matches the low metallicities while displaying a falling black hole-to-stellar mass ratio with halo mass.
Systems at z~7 with black hole to stellar mass ratio above 0.1, bolometric luminosities 10^44-46 erg/s, and residing in 10^9-11 solar mass halos can serve as a clustering test for primordial black hole models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Confirmation of the decreasing mass ratio trend would require galaxy formation models to treat primordial black holes as an additional, halo-mass-dependent growth channel separate from stellar or direct-collapse seeds.
The same selection criteria could be applied to larger JWST or future X-ray surveys to map how the black hole occupation fraction changes with halo mass at fixed redshift.
If primordial black holes dominate the early population, the merger rate of intermediate-mass black holes detectable by future gravitational-wave observatories would carry a distinct mass and redshift distribution.

Load-bearing premise

The semi-analytic DELPHI and analytic PHANES models accurately capture black hole growth, merger rates, and host galaxy metallicity evolution at z>5 without full hydrodynamic simulations or extra physics such as feedback or metal mixing.

What would settle it

A survey of z~7 systems showing that the black hole-to-stellar mass ratio does not decrease with increasing halo mass in the 10^9-11 solar mass range would rule out the primordial black hole seeding channel.

Figures

Figures reproduced from arXiv: 2604.20966 by Pratika Dayal.

**Figure 1.** Figure 1: — The redshift evolution of the black hole mass function at 𝑧 ∼ 5 − 15, as marked in panels (a)-(d). Points show observational data from: Wil+10 (Willott et al. 2010), Mat+24 (Matthee et al. 2024), Kok+24 (Kokorev et al. 2024), Tay+25 (Taylor et al. 2025a), Ger+26 (Geris et al. 2026) and Fei+26 (Fei et al. 2026). In each panel, lines show theoretical results for the models noted in panel (a) and detailed i… view at source ↗

**Figure 2.** Figure 2: — The redshift evolution of the bolometric luminosity function for black holes at 𝑧 ∼ 5 − 15, as marked. In each panel, the lines show results for the theoretical models marked in panel (a). Points show observational data: at 𝑧 ∼ 10, the point shows the lower limit to the bolometric luminosity function based on UHZ1 and GHZ9 from Kov+24 (Kovacs ´ et al. 2024). At 𝑧 ∼ 7 the data is from from She+20 (Shen et… view at source ↗

**Figure 3.** Figure 3: — The redshift evolution of the black hole mass-stellar mass relation. Rows show results at 𝑧 ∼ 5 − 10, with each column referring to the theoretical model marked above. In each panel, the colours refer to the host halo mass associated with the object, as marked above the figure. At each redshift, we show observational results from a number of groups: at 𝑧 ∼ 5 from Harikane et al. (2023), Maiolino et al. (… view at source ↗

**Figure 4.** Figure 4: — The redshift evolution of the gas-phase metallicity as a function of the black hole mass. The rows shows results at 𝑧 ∼ 5 − 10, with each column referring to the theoretical model marked above. In each panel, the colours refer to the stellar mass associated with the object, as marked above the figure. The filled points at 𝑧 ∼ 7 and 𝑧 ∼ 10 show upper limits on the metallicity estimate for Abell2744-QSO1 f… view at source ↗

**Figure 5.** Figure 5: — The redshift evolution of the black hole-to-stellar mass ratio as a function of the halo mass. The rows shows results at 𝑧 ∼ 5 − 10, with each column referring to the theoretical model marked above. In each panel, the colours refer to the black hole bolometric luminosity associated with the object, as marked above the figure. In each panel, the horizontal dashed line shows a value of MBH/M∗ = 0.1. (2025)… view at source ↗

read the original abstract

The James Webb Space Telescope (JWST) has revealed a puzzling population of massive black holes in the first billion years, many of which are over-massive compared to their hosts (obese black holes), and reside in metal-poor hosts, posing a challenge for theoretical models at these early epochs. In this work, we compare the observational properties of astrophysically-seeded black holes using the DELPHI semi-analytic model and cosmologically-seeded primordial black holes (PBHs) using the PHANES analytic model. We explore the growth of light ($\sim 100 M_\odot$) and heavy ($\sim 10^{3-5}M_\odot$) seeds through mergers and accretion (both Eddington-limited and at super-Eddington rates) in the astrophysical scenario; PBHs (seeded between $10^{0.5-6}M_\odot$) only grow through accretion at sub-Eddington rates. Comparing to observables at $z \sim 5-10$, the only model that can be ruled out is the one where we allow Eddington-limited accretion onto light seeds. The observed high values of the black hole mass-stellar mass relation ($0.3-1$) can be reproduced by both PBHs and heavy seeds accreting at super-Eddington rates. However, only the PBH and Eddington-limited heavy seeding models can simultaneously reproduce the observed black hole masses (${\rm M_{bh}}$), stellar masses ($M_*$), and extremely low host metallicities ($Z \leq 0.01 Z_\odot$) inferred at $z \sim 7-10$. Crucially, we find PBHs show decrease in the black hole mass-stellar mass ratio with increasing halo mass at all redshifts, contrary to any astrophysical black hole model. Selecting systems at $z \sim 7$ with ${\rm M_{bh}}/M_* > 0.1$ and bolometric luminosities $\sim 10^{44-46} {\rm erg~s^{-1}}$ that show a negative black hole to stellar mass ratio and reside in $10^{9-11}M_\odot$ halos offer a promising clustering-based discriminant of PBH seeding models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper's new angle is a halo-mass trend in M_BH/M* that drops only for PBHs, plus the claim that light Eddington seeds are ruled out while PBHs and heavy seeds fit the JWST M_BH, M*, and low-Z data, but both rest on the author's prior semi-analytic models.

read the letter

The main point worth knowing is that this work runs the DELPHI semi-analytic model for astrophysical seeds and the PHANES analytic model for primordial black holes against JWST z~5-10 data on black hole masses, stellar masses, and host metallicities. It finds that only PBHs and Eddington-limited heavy seeds can hit all three observables at once, while light seeds with Eddington accretion fail, and that PBHs alone produce a declining M_BH/M* ratio with rising halo mass that could serve as a clustering test in 10^9-11 solar mass halos at z~7.

Referee Report

3 major / 2 minor

Summary. The manuscript compares astrophysical black hole seeding scenarios (light seeds of ~100 M_⊙ and heavy seeds of 10^{3-5} M_⊙) using the DELPHI semi-analytic model, which includes mergers and both Eddington-limited and super-Eddington accretion, against primordial black hole (PBH) seeding (masses 10^{0.5-6} M_⊙) using the PHANES analytic model with only sub-Eddington accretion. It confronts these with JWST-inferred properties of massive black holes at z~5-10, including high M_bh/M_* ratios (0.3-1), low host metallicities (Z ≤ 0.01 Z_⊙), and bolometric luminosities, concluding that only PBHs and Eddington-limited heavy seeds simultaneously match all three observables while light-seed Eddington accretion is ruled out; PBHs are further distinguished by a decreasing M_bh/M_* trend with halo mass at all redshifts, offering a clustering-based test in 10^9-11 M_⊙ halos at z~7.

Significance. If the underlying model prescriptions hold, the work supplies a concrete, observationally testable discriminant between seeding channels via the sign of the M_bh/M_*–halo mass slope and the joint reproduction of M_bh, M_* and extremely low Z, which directly addresses the 'obese black hole' tension reported by JWST. The explicit enumeration of accretion modes and seed ranges across two independent frameworks is a strength that allows falsifiable predictions for future clustering measurements.

major comments (3)

[Abstract and §3] Abstract and §3 (model descriptions): the claim that 'only the PBH and Eddington-limited heavy seeding models can simultaneously reproduce the observed black hole masses (M_bh), stellar masses (M_*), and extremely low host metallicities (Z ≤ 0.01 Z_⊙)' is load-bearing for the central conclusion, yet the manuscript provides no quantitative validation of DELPHI/PHANES metallicity evolution or BH growth rates against hydrodynamical simulations at z>5; without this, the exclusion of light-seed Eddington accretion and the uniqueness of the PBH signature cannot be assessed.
[Abstract] Abstract: the reported 'decrease in the black hole mass-stellar mass ratio with increasing halo mass at all redshifts' for PBHs is presented as a unique discriminant, but the text does not quantify how sensitive this trend is to the adopted sub-Eddington accretion efficiency or the PBH mass range (10^{0.5-6} M_⊙); a modest change in either parameter could erase the negative slope and undermine the clustering test proposed for 10^9-11 M_⊙ halos.
[Abstract and results section] Abstract and results section: no error bars, posterior distributions, or Monte-Carlo realizations are shown for the model outputs of M_bh, M_* and Z; the statement that certain models 'can be ruled out' therefore lacks a statistical threshold, making it impossible to judge whether the mismatch for light-seed Eddington accretion exceeds the model uncertainty.

minor comments (2)

[Abstract] The abstract uses 'obese black holes' without a precise definition or reference to the specific observational papers that introduced the term.
[Abstract] Notation for metallicities (Z ≤ 0.01 Z_⊙) and mass ratios (M_bh/M_*) is clear but would benefit from an explicit statement of the solar metallicity value adopted in DELPHI/PHANES.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and valuable comments, which have prompted us to strengthen the presentation of our results. We provide point-by-point responses to the major comments below, indicating the revisions we plan to make in the updated manuscript.

read point-by-point responses

Referee: [Abstract and §3] Abstract and §3 (model descriptions): the claim that 'only the PBH and Eddington-limited heavy seeding models can simultaneously reproduce the observed black hole masses (M_bh), stellar masses (M_*), and extremely low host metallicities (Z ≤ 0.01 Z_⊙)' is load-bearing for the central conclusion, yet the manuscript provides no quantitative validation of DELPHI/PHANES metallicity evolution or BH growth rates against hydrodynamical simulations at z>5; without this, the exclusion of light-seed Eddington accretion and the uniqueness of the PBH signature cannot be assessed.

Authors: We agree with the referee that quantitative validation against hydrodynamical simulations at z>5 would bolster confidence in the model predictions. While the current manuscript relies on the established frameworks of DELPHI and PHANES, which incorporate standard prescriptions for metallicity evolution and accretion, we have not performed new direct comparisons in this work. In the revised manuscript, we will include an expanded discussion in Section 3 on the model calibrations, citing relevant hydrodynamical simulation studies that validate similar approaches at high redshifts, and explicitly state the limitations of our semi-analytic approach. revision: yes
Referee: [Abstract] Abstract: the reported 'decrease in the black hole mass-stellar mass ratio with increasing halo mass at all redshifts' for PBHs is presented as a unique discriminant, but the text does not quantify how sensitive this trend is to the adopted sub-Eddington accretion efficiency or the PBH mass range (10^{0.5-6} M_⊙); a modest change in either parameter could erase the negative slope and undermine the clustering test proposed for 10^9-11 M_⊙ halos.

Authors: We concur that the sensitivity of the PBH M_bh/M_* trend to the sub-Eddington accretion efficiency and seed mass range should be quantified to support its use as a discriminant. We have conducted additional tests by varying these parameters within physically motivated ranges. The negative slope remains a robust feature of the PBH models. We will add a dedicated subsection or appendix in the revised version presenting these sensitivity analyses and updated figures to demonstrate the persistence of the trend. revision: yes
Referee: [Abstract and results section] Abstract and results section: no error bars, posterior distributions, or Monte-Carlo realizations are shown for the model outputs of M_bh, M_* and Z; the statement that certain models 'can be ruled out' therefore lacks a statistical threshold, making it impossible to judge whether the mismatch for light-seed Eddington accretion exceeds the model uncertainty.

Authors: The referee correctly points out the lack of uncertainty quantification in our model outputs. As the models are semi-analytic and analytic, we have now implemented Monte Carlo sampling over key uncertain parameters such as seed masses, accretion efficiencies, and halo merger rates to generate distributions for M_bh, M_*, and Z. The revised manuscript will feature error bars on the relevant plots and a statistical evaluation of how well each model matches the JWST observations, allowing a clearer assessment of which scenarios can be ruled out. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model outputs compared to external JWST data

full rationale

The paper applies pre-existing DELPHI and PHANES models (with parameters drawn from prior literature) to generate outputs for different seeding/accretion scenarios and directly compares those outputs against independent JWST-inferred observables (M_BH, M_*, Z at z~7-10). No equation or claim in the provided text redefines model inputs in terms of the target results, renames a fit as a prediction, or reduces the central discriminant (PBH vs. astrophysical signatures) to a self-referential loop. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 1 invented entities

The central claims rest on the validity of the DELPHI and PHANES models, their assumed seeding mass ranges, accretion prescriptions, and the semi-analytic treatment of galaxy assembly and metal enrichment at high redshift.

free parameters (4)

Light seed mass = ~100 M_sun
Fixed at ~100 solar masses for astrophysical light seeds
Heavy seed mass range = 10^{3-5} M_sun
Range 10^3-10^5 solar masses for direct-collapse or heavy seeds
PBH seed mass range = 10^{0.5-6} M_sun
Primordial black hole masses seeded between 10^{0.5-6} solar masses
Accretion efficiency modes = Eddington and super-Eddington
Choice of Eddington-limited versus super-Eddington rates for different channels

axioms (2)

domain assumption Black hole growth occurs solely via mergers and gas accretion at the stated rates
Core assumption stated for both astrophysical and PBH channels
domain assumption Semi-analytic prescriptions for galaxy stellar mass and metallicity evolution remain valid at z>5
Invoked throughout the DELPHI model comparisons

invented entities (1)

Primordial black holes as early seeds no independent evidence
purpose: Alternative cosmologically seeded population to explain over-massive high-z black holes
Postulated as a distinct channel whose growth is limited to sub-Eddington accretion

pith-pipeline@v0.9.0 · 5722 in / 1891 out tokens · 118187 ms · 2026-05-09T23:20:32.747449+00:00 · methodology

discussion (0)

Reference graph

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