Early black-hole seeds in the first billion years

Umberto Maio

REVIEW 3 major objections 4 minor 57 references

Early black-hole seeds in the first billion years

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper argues that ordinary stellar black holes cannot grow into the billion-solar-mass black holes seen by redshift 7.5, so the early Universe needs heavier seeds formed by direct collapse of pristine gas, which requires extreme…

desk verdict A clear and honest proceedings summary of the author's simulation results, whose main new element is the powerful-vs-weak Pop III comparison; the DCBH conclusion rests on a single, untested assumption and should be treated as conditional. read the letter →

arxiv 1908.04823 v4 pith:6QMP5RRO submitted 2019-08-13 astro-ph.GA astro-ph.HE

Umberto Maio This is my paper · ORCID

classification astro-ph.GAastro-ph.HE

keywords blackholeseedsdirectcollapseholespopulationIIIstarsLyman-Wernerradiationcosmologicalsimulationsradiativetransferfirstbillionyearssupermassive

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks how the supermassive black holes observed within the first billion years could have formed. It argues that the usual light-seed route, black holes left behind by ordinary stars, mostly of 1 to 10 solar masses, cannot work because these remnants do not accrete enough mass in under a gigayear. The alternative examined is direct collapse: pristine gas in a small dark-matter halo, kept warm and unable to form stars by ultraviolet radiation from a neighboring star-forming region, collapses straight into a heavy seed of roughly $10^4$--$10^6$ solar masses. Using cosmological simulations with coupled chemistry and multifrequency radiative transfer, the paper finds only three candidate halos at $z\simeq 9$, and only in a model where the first stars are extremely massive and emit $10^5$ K radiation; with cooler, ordinary stellar spectra no candidates appear. The conclusion is that heavy seeds are possible but require a fine balance between radiative feedback and chemical enrichment.

What carries the argument

The machinery is a cosmological hydrodynamic simulation that couples multifrequency radiative transfer over 150 frequency bins to non-equilibrium primordial chemistry, atomic and molecular cooling, star formation, feedback, stellar evolution, and metal spreading from SNII, AGB and SNIa phases for both popIII and popII-I stellar generations. The named object carrying the direct-collapse argument is the DCBH candidate selection: halos with virial temperature around $10^4$ K and dark-matter mass $\gtrsim 2\times 10^6\,M_\odot$, exposed to Lyman-Werner fluxes in the $J_{\rm LW}=1$--$1000\,J_{21}$ range, hosting pristine gas whose H$_2$ has been dissociated so it cannot cool and fragment into stars. Comparing a powerful popIII SED ($10^5$ K) with a weak one ($10^4$ K) is what isolates the role of the first stellar populations: the radiation field must be hot enough to destroy molecular cooling, yet not so strong or so close that metal enrichment or photo-evaporation ruins the halo.

What would settle it

Rerun the same simulation with the first stars' spectrum at $10^4$ K while keeping the top-heavy initial mass function: the paper reports zero direct-collapse candidates in that case, so finding candidates there would falsify the claimed environmental selectivity. Observationally, a supermassive black hole at redshift above 7 located far from any massive star-forming region, in gas without strong Lyman-Werner radiation, would show that heavy seeds can form without the powerful-radiation condition.

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Extended reading notes

Core claim

The central claim is that stellar-origin black holes cannot serve as the seeds of the highest-redshift supermassive black holes, because the simulated population of light seeds is dominated by $1$--$10\,M_\odot$ remnants after $z\simeq 16$, and even the most favorable accretion studied in the literature does not let $\sim 10^2\,M_\odot$ seeds grow within a few hundred million years. The paper instead identifies direct-collapse black holes as a plausible heavy-seed channel. In a simulation box evolved from $z=100$ to $z=6$ with non-equilibrium atomic and molecular chemistry, metal enrichment from SNII, AGB and SNIa phases, and 150-frequency radiative transfer, only the powerful population III case, a top-heavy IMF over $100$--$500\,M_\odot$ and a $10^5$ K black-body spectrum, produces halos meeting the direct-collapse criteria. Three candidates, labelled A, B and C, lie at $z=9$ with gas masses of $1$--$3\times 10^5\,M_\odot$, Lyman-Werner fluxes $J_{\rm LW}\approx 1$--$50$ in units of $10^{-21}$ erg s${}^{-1}$ cm${}^{-2}$ Hz${}^{-1}$ sr${}^{-1}$, pristine composition, fully dissociated H$_2$, and distances larger than 5 physical kpc from the irradiating star-forming source; the weaker $10^4$ K SED case yields no candidates at all. The paper concludes that direct collapse can explain at least part of the supermassive black hole population, but only under peculiar environmental conditions.

Load-bearing premise

The argument depends on assuming that the first stars were extremely massive, 100 to 500 solar masses, with a very hot $10^5$ K spectrum; if the first stellar population instead resembled ordinary cooler $10^4$ K stars, the simulated direct-collapse candidates disappear and the heavy-seed channel as described would not operate.

Editorial extensions

If this is right

If the central claim is right, the $1$--$10\,M_\odot$ remnants that dominate stellar black-hole production after $z\simeq 16$ cannot by themselves account for $z\simeq 7.5$ supermassive black holes, so some heavier seed or faster growth channel is required.
Direct-collapse seeds should be rare and located in pristine mini-haloes a few kiloparsecs away from intensely star-forming regions, so searches for the first supermassive black holes should target metal-free, H$_2$-free gas pockets near strong ultraviolet sources at $z\gtrsim 10$.
The transition redshift $z\simeq 16$ separates a popIII-dominated light-seed epoch from a popII-I-dominated one, meaning the usefulness of light seeds depends sensitively on when and how the first stellar populations gave way to ordinary star formation.
Because only the powerful popIII SED case yields candidates, the cosmic abundance of direct-collapse black holes depends directly on the IMF and spectra of the first stars; measuring those would turn this scenario into a quantitative prediction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An implicit threshold sits between the two SED cases: if the true first-star spectrum lies between $10^4$ and $10^5$ K, the number of direct-collapse seeds could be highly sensitive to the exact spectral shape, so a wider grid of SEDs would map where the channel switches on.
A natural extension is to follow the three identified candidates with zoom-in simulations that actually resolve the final collapse; this paper checks literature-based criteria but does not simulate the collapse itself, leaving open what fraction of such candidates become black holes.
If heavy seeds are as environmentally selective as this paper argues, supermassive black holes at $z\gtrsim 7$ should be spatially clustered near the most massive early star-forming regions rather than uniformly distributed, a signature future surveys could test.
The light-seed argument also implies that a $z\simeq 7$ supermassive black hole found in a halo with no nearby massive star-forming region would require an alternative channel, such as super-Eddington accretion onto light seeds or primordial black holes, because the simulated environment would not produce a heavy seed there.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Umberto Maio's arXiv:1908.04823 is a proceedings-style summary of his simulation work on early black-hole seeds. The most useful thing here is the side-by-side comparison of a 'powerful' Population III model (top-heavy IMF, 10^5 K black-body SED) with a 'weak' model (Salpeter IMF, 10^4 K): DCBH host candidates appear only in the powerful run, and the paper is honest about that. That gives the reader a sharp, quantitative sense of how much the direct-collapse outcome depends on the assumed primordial stellar population. The rest is largely a recap of earlier results, especially Maio & Tescari 2015 and Maio et al. 2019, and the light-seed growth argument is imported from Hirano et al. 2014 rather than derived here.

What the paper does well: the simulation setup is broad (non-equilibrium chemistry, metal spreading, 150-bin multifrequency RT) and the text clearly states the caveats. The BH formation rate densities in Fig. 3 are simple time-delay convolutions of published SFRs, but they are correctly computed and shown for both populations. The DCBH candidates are checked against literature criteria and the paper itself notes that two of the three haloes have substructure that may prevent collapse. So the text is more careful than many proceedings contributions.

The soft spots are real but not hidden. The entire heavy-seed claim hangs on one assumption: that the first stars had a top-heavy IMF and a 10^5 K SED. The paper has no run in between and no external constraint on that SED, and one of the three candidate haloes is the only plausible one. No simulation actually follows gas to collapse; the candidates only satisfy JLW and temperature criteria. There are no convergence tests or error bars, and the box is only 0.5 Mpc/h, so the candidate statistics are tiny. The citation pattern is self-heavy but legitimate: the referenced prior papers do contain the methods and the earlier candidate identification.

Net: if you work on high-z seeding, this is a clear summary worth reading alongside the original papers, but it does not stand alone as a new result. A serious referee would ask for a wider parameter exploration and direct collapse tests for the candidates. I would send it to peer review if submitted as a journal article, because the load-bearing assumption needs to be challenged in the literature; as a proceedings note, its main value is the candid caveats.

Referee Report

3 major / 4 minor

Summary. The paper argues that standard stellar-origin (light) black holes are unlikely to serve as seeds for the supermassive black holes observed at z ≳ 7, because their masses (∼1–10 M⊙, or ∼100 M⊙ for Pop III remnants) are too small to grow substantially within the first billion years. It then argues that direct-collapse black holes (DCBHs) forming in pristine mini-haloes exposed to Lyman–Werner radiation from nearby star-forming regions provide a plausible alternative. The evidence comes from N-body hydrodynamic simulations with non-equilibrium atomic/molecular chemistry, cooling, star formation, feedback, stellar evolution, metal spreading, and multifrequency radiative transfer. In the simulation with a 'powerful' Pop III model (top-heavy IMF, 100–500 M⊙, and a 10^5 K black-body SED), three haloes satisfy literature-based DCBH criteria (JLW ∼ 1–50 J21, H2 dissociated, gas near 10^4 K, at distances ≳5 physical kpc from the irradiating source); in the 'weak' Pop III case, no candidates are found. The paper concludes that DCBHs could explain at least part of the high-redshift SMBH population, while acknowledging that local substructure may inhibit formation in two of the three candidates.

Significance. If the central claim holds, the paper would strengthen the case that the formation of early SMBH seeds is extremely sensitive to the assumed spectral energy distribution and initial mass function of the first stellar populations, and that direct collapse requires a fine balance between radiative and chemical feedback. The simulations are genuinely comprehensive in their treatment of chemistry, feedback, stellar evolution, and radiative transfer, and the comparison of the powerful and weak Pop III cases is a real parameter study rather than a fit to a desired conclusion. The paper also honestly reports the fragility of its candidate sample: only one of the three haloes is a structurally clean DCBH candidate, and no simulation follows the gas to actual collapse. The main limitation is that the positive DCBH signal rests entirely on the 'powerful' Pop III assumption, which is plausible but not independently tested or quantified in this manuscript.

major comments (3)

[§3, Fig. 4] The entire DCBH candidate signal is conditional on the 'powerful' Pop III model: a top-heavy IMF over 100–500 M⊙ and a 10^5 K black-body SED. The paper states that in the weak case (Salpeter IMF, 10^4 K black-body) there are no candidates, so the powerful-Pop III assumption is the decisive input that produces all three haloes. No independent evidence or uncertainty quantification is given for this extreme SED/IMF being representative of the first stellar populations. This is load-bearing because §2 argues that the Pop III-to-Pop II-I transition is fast at z > 15 and that Pop II-I remnants dominate at most times, so the prevalence of nearby powerful Pop III sources at the epochs of interest is not established. Please either provide a quantitative estimate of the fraction of the cosmic volume or of candidate haloes that are exposed to such powerful radiation, or explicitly reframe the result as an existence proof under a stated assumption.
[§3, candidates A, B, C] The candidates are identified only by checking literature-based criteria (JLW ∼ 1–50 J21, H2 dissociated, gas temperature near 10^4 K, halo mass constraints); the simulation does not follow the collapse of the gas in these haloes into a black hole. The paper itself notes that candidate B has an irregular interacting shape and candidate C consists of two distinct sub-clumps that may inhibit DCBH formation, leaving candidate A as the only potentially viable object. Thus the conclusion that DCBHs 'could explain at least part of the SMBH population' rests on a single candidate whose actual collapse is not simulated. Please clarify whether this is intended as an existence proof, and if so, state that explicitly; or, if a statistical claim is intended, provide an estimate of the number density or probability of such configurations.
[§2, Fig. 3] The conclusion that light seeds cannot grow significantly in less than a billion years is not derived in this paper; the growth argument is cited from Hirano et al. (2014) and other external studies. Within this manuscript, Fig. 3 only shows that Pop II-I remnants dominate the BH formation rate density after z ≃ 16 and that their masses are ∼1–10 M⊙. This is a reasonable and clearly attributed use of the literature, but the strength of the light-seed claim depends on assumptions about accretion efficiency and radiative feedback that are not tested here. Please state more precisely which parts of the light-seed argument are new simulation results and which parts rest on external calculations, so the reader can weigh the evidence.

minor comments (4)

[Throughout] There are several typographical and formatting issues: 'in pl ace' in the abstract, 'z /greaterorsimilar10' and similar broken glyphs in the main text, and 'We acknowledge detailed comments by the the referee' in the Acknowledgments. These should be cleaned up.
[Fig. 4] The right panel of Fig. 4 uses yellow bullets to denote 'the same objects' as the DCBH candidates in the left panel, but in the weak case there are no candidates. Please clarify whether these are the same physical haloes now hosting cold gas, and distinguish more clearly between 'candidate haloes' and 'the same positions in a different run'.
[§3, resolution and numerical convergence] The paper reports Reynolds numbers around 10^4–10^8 in the candidate haloes, which seems extraordinarily high for a simulation with 256^3 particles per species in a 0.5 Mpc/h box. Please either justify this estimate or soften the claim, and add a comment on numerical resolution and convergence for the identification of DCBH candidates.
[§4, generality] The discussion of alternative cosmological models, non-Gaussianities, warm dark matter, and streaming motions is appropriately brief, but the statement that these are 'unlikely to change substantially our conclusions' is asserted without quantitative support. A single sentence citing the relevant sensitivity tests would be sufficient.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: simulation outputs are conditional on stated inputs, not equivalent to them.

full rationale

The paper's derivation chain is self-contained with respect to circularity. The light-seed BH formation rates (Fig. 3) are computed from simulated star-formation-rate densities using fixed stellar lifetimes and IMF prescriptions; these are input quantities, and the BH rates are a straightforward convolution, not a fit to the conclusion that light seeds cannot grow. The claim that popII-I BHs dominate at z <~ 16 follows from the simulated SFR densities and the assumed IMF, and it is not used to define the SFR. The heavy-seed DCBH analysis is explicitly a parameter comparison: the simulation is run with a powerful popIII SED (top-heavy IMF, 10^5 K black body) and a weak popIII SED (Salpeter IMF, 10^4 K black body), and haloes are checked against literature-based criteria (JLW ~ 1-1000 J21, H2 dissociation, virial temperature ~10^4 K, pristine gas, no star formation). The appearance of three candidates only in the powerful case and zero in the weak case is a genuine conditional result of the radiative-transfer calculation, not a quantity fitted to the paper's own conclusions. The paper explicitly hedges the final claim as 'could explain at least part of the SMBH population' and notes limitations, including the lack of a simulated collapse and the possible disruption of candidates B and C by substructure. The heavy reliance on self-citations is for numerical methods and earlier published implementations (e.g., Maio et al. 2007, 2010, 2019); none of these citations is invoked as a uniqueness theorem or as a substitute for the simulation results presented here. The powerful-popIII assumption is real and load-bearing for the DCBH candidate signal, but an untested or uncertain assumption is a correctness risk, not a circular step: the paper does not define the assumption in terms of the DCBH conclusion, nor does it fit the SED to the candidate haloes. Accordingly, no self-definitional step, fitted-input-called-prediction, or author-imported uniqueness argument is present.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claims depend on several chosen IMFs, SEDs, and physical thresholds, all taken from prior work or idealized assumptions. The key free parameter is the popIII SED in the powerful case: if real first stars are closer to the weak 10^4 K case, the paper's own simulations find no DCBH candidates.

free parameters (6)

Critical metallicity Zcrit = 10^-4 Z_sun
Threshold separating popIII from popII-I star formation; sets which stellar population contributes the light BH seeds and affects the timing of the light-seed formation rate.
PopIII IMF = Top-heavy, 100-500 M_sun, Salpeter slope
Mass range for population III stars; in the powerful case it yields BH remnants of ~100 M_sun and is one of the two conditions for producing DCBH candidates.
PopII-I IMF = Salpeter, 0.1-100 M_sun
Standard IMF for enriched populations; produces 1-10 M_sun BH remnants that dominate the light seed population.
PopIII SED in powerful case = 10^5 K black body
The strong radiation case that produces DCBH candidates. The entire direct-collapse conclusion depends on this spectral assumption.
PopIII SED in weak case = 10^4 K black body
Used as contrast; no DCBH candidates form, showing the sensitivity of the result to the assumed stellar spectrum.
Kinetic wind velocity = 500 km/s
Strength of mechanical feedback from SNe; influences metal spreading and photo-evaporation that can suppress or enable DCBH formation in nearby halos.

assumptions (5)

domain assumption The Lambda CDM cosmological model with the adopted parameters is correct.
The simulations assume a flat Lambda CDM universe with h=0.7, Omega_m=0.27-0.3, Omega_Lambda=0.7-0.73, as stated in Sections 2 and 3.
domain assumption The sub-grid models for star formation, feedback, and metal spreading capture the essential physics of the early universe.
These prescriptions (Tornatore et al. 2007, Maio et al. 2007) are adopted without convergence tests in this paper.
domain assumption The Eddington tensor radiative transfer approximation is accurate enough for the DCBH problem.
The RT scheme is coupled to non-equilibrium chemistry, but it is an approximate method; see Section 3 and Maio et al. 2019.
domain assumption The literature criteria for DCBH formation (virial temperature ~10^4 K, JLW in 1-1000 J21) are applicable to the simulated halos.
Used to select candidate halos in Section 3; these thresholds come from idealized models cited in the text.
domain assumption The simulation resolution (2 x 256^3 particles in a 0.5 Mpc/h box) is sufficient to resolve the halos relevant for DCBH.
The paper states this is a trade-off configuration, but does not demonstrate numerical convergence.

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Cite this review

Pith. "Pith review of Early black-hole seeds in the first billion years." pith.science (2026). https://pith.science/paper/6QMP5RRO

@misc{pith2026190804823,
  author       = {Pith},
  title        = {Pith review of: Early black-hole seeds in the first billion years},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6QMP5RRO}},
  note         = {Machine review of arXiv:1908.04823}
}

read the original abstract

Supermassive black holes with billion solar masses are in place already within the first Gyr, however, their origin and growth in such a short lapse of time is extremely challenging to understand. Here, we discuss the formation paths of early black-hole seeds, showing the limits of light black-hole seeds from stellar origin and the expected characteristics of heavy/massive black-hole seeds originated by gas direct collapse in peculiar primordial conditions. To draw conclusions on the possible candidates and the role of the ambient medium, we use results from N-body hydrodynamic simulations including atomic and molecular non-equilibrium abundance calculations, cooling, star formation, feedback mechanisms, stellar evolution, metal spreading of several heavy elements from SNII, AGB and SNIa, and multifrequency radiative transfer over 150 frequencies coupled to chemistry and SED emission for popII-I and popIII stellar sources. Standard stellar-origin light black holes are unlikely to be reliable seeds of early supermassive black holes, because, under realistic assumptions, they cannot grow significantly in less than a billion years. Alternatively, massive black-hole seeds might originate from direct collapse of pristine gas in primordial quiescent mini-haloes that are exposed to stellar radiation from nearby star forming regions. The necessary conditions required to form these heavy seeds must be complemented with information on the complex features of local environments and the fine balance between chemistry evolution and radiative transfer.

Figures

Figures reproduced from arXiv: 1908.04823 by the authors.

**Figure 1.** Simulated H2-driven gas collapse and inflow of a primordial star forming halo displayed through the projection of gas overdensity, δ, on a 128×128 pixel grid. The region corresponds to 600 kpc (comoving) at redshift z ≃ 7 and the following 0.4, 0.8 and 1.4 Gyr, respectively, from left to right [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** which shows how, simultaneously in the same time span, early gas clumps host first episodes of star formation accompanied by shock heating and metal enrichment in the neighbouring regions. Highly non-linear effects related to the underlying structure evolution (e.g. development of knots and filaments) are evident. In these chaotic environments, where star formation, feedback and photon production coexist, the first… view at source ↗

**Figure 3.** Stellar-origin BHs for different populations, as expected from the primordial cosmic star formation rate. The BH formation rate density for popII-I (solid line) and popIII (dash-dotted line) is plotted, as derived from simulated SFR densities for popII-I (dashed line) and popIII (dotted line) regimes. and 260-500 M⊙ after a rapid evolution of roughly 2 Myr. Stars in the intermediate mass range of 140-260 M⊙ die as p… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Temperature maps at z = 9 for a run with a top-heavy IMF and a powerful SED corresponding to 105 K black-body emission (left) and for a run with a Salpeter IMF and a weaker SED corresponding to 104 K black-body emission (right). The black bullets on the left map highli…

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[Maio(2011)] Maio, U

2011
[3067]

10 BH seeds [Bifﬁ and Maio(2013)] Bifﬁ, V ., Maio, U

2013
[3130]

L., Dijkstra, M

[Johnson and Dijkstra(2017)] Johnson, J. L., Dijkstra, M. 2

2017
[3532]

[Bañados et al.(2018)] Bañados, E., and 17 colleagues

2018
[3733]

[Mancini et al.(2016)] Mancini, M., and 6 colleagues

2016
[3798]

[Maio and Viel(2015)] Maio, U., Viel, M

2015
[3825]

M., and 9 colleagues 20

[Belotsky et al.(2019)] Belotsky, K. M., and 9 colleagues 20

2019
[4244]

E., Weaver, T

[Woosley and Weaver(1995)] Woosley, S. E., Weaver, T. A. 199

1995

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

[Rees(1984)] Rees, M. J

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Monthly Notices of the Royal Astronomical Society 412, L40

The impact of primordial supersonic ﬂows on early structure formation, reionization and the low est-mass dwarf galaxies. Monthly Notices of the Royal Astronomical Society 412, L40. [Maio et al.(2011)] Maio, U., Khochfar, S., Johnson, J. L., C iardi, B

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[Hutter et al.(2019)] Hutter, A., and 28 colleagues

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Astronomy and Astrophysics 601, A138

Enhanced direct collapse due to Lyman α feedback. Astronomy and Astrophysics 601, A138. [Ma et al.(2017)] Ma, Q., Maio, U., Ciardi, B., Salvaterra, R

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Monthly Notices of the Royal Astronomical Socie ty 451, L70

T he dust mass in z > 6 normal star-forming galaxies.. Monthly Notices of the Royal Astronomical Socie ty 451, L70. [Habouzit et al.(2016)] Habouzit, M., V olonteri, M., Latif , M., Dubois, Y ., Peirani, S

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