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Pop III.1 stars regulate their isolation through HII regions, yielding supermassive black holes at 0.2 per cubic megaparsec.

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2026-06-29 10:56 UTC pith:HCGR5KWN

load-bearing objection This paper replaces the free isolation parameter from earlier work in the series with an HII-region calculation that gives n_SMBH around 0.2 cMpc^{-3}, but the number still depends on chosen stellar luminosity and lifetime. the 3 major comments →

arxiv 2605.28777 v1 pith:HCGR5KWN submitted 2026-05-27 astro-ph.GA astro-ph.CO

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

Maya A. Petkova , Jonathan C. Tan , Jasbir Singh , Vieri Cammelli , Mahsa Sanati , Benjamin Keller , Pierluigi Monaco , Devesh Nandal This is my paper
classification astro-ph.GA astro-ph.CO
keywords Population III starssupermassive black holesHII regionsionizing feedbackearly universeblack hole seedingcosmological models
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper builds a feedback-regulated model in which each supermassive Population III.1 star creates an HII region that expands into the intergalactic medium and thereby sets the minimum distance to the next such star. This replaces an earlier free parameter for isolation distance with a calculation that includes R-type ionization fronts and the redshift dependence of Stromgren spheres. For a fiducial ionizing luminosity of 10^53 photons per second and a 10 Myr lifetime, the model produces a characteristic radius of 1.3 comoving megaparsecs that is nearly independent of redshift. The resulting black hole seed density is then fixed at roughly 0.2 per cubic comoving megaparsec, with most seeds forming by redshift 16. A sympathetic reader would care because this density directly determines how many early black holes are available to grow into the quasars observed at lower redshifts.

Core claim

The model shows that R-type HII regions around Pop III.1 stars reach a radius of approximately 1.3 comoving megaparsecs, largely independent of redshift, so that the number density of resulting supermassive black holes is about 0.2 per cubic comoving megaparsec, with formation mostly complete by redshift 16.

What carries the argument

The R-type expansion of HII regions driven by the ionizing photons from each Pop III.1 star, which determines the minimum separation to the next such star.

Load-bearing premise

The assumption that each Pop III.1 star's HII region expands without being significantly affected by feedback from other stars or galaxies.

What would settle it

A measurement showing the comoving number density of supermassive black holes at z greater than 16 is substantially different from 0.2 per cubic megaparsec would falsify the central prediction.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The median formation redshift of the seeds is around 20.
  • The fraction of binary supermassive black holes that appear as dual AGN at z greater than 6 is at most 0.3 percent.
  • The predicted rates of supermassive black hole binary mergers are measurable by the LISA mission.
  • The seeding process is essentially finished by redshift 16.

Where Pith is reading between the lines

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

  • This fixed density supplies a baseline against which the contribution of these isolated stars to early reionization can be compared.
  • High-redshift surveys could count the number of galaxies hosting such black holes and test whether the observed count matches the predicted 0.2 per cubic megaparsec.
  • Combining the seed abundance with models of later gas accretion would allow a direct prediction for the black hole mass function observed in the local universe.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 2 minor

Summary. The paper develops a self-regulated model for the isolation distance of Population III.1 stars by modeling the R-type expansion of their HII regions into the IGM together with redshift-dependent Strömgren spheres, incorporating a time delay to minihalo formation and the presence of lower-mass Pop III.2 stars. For fiducial values Q = 10^{53} s^{-1} and lifetime 10 Myr it obtains R_R ≃ 1.3 cMpc (nearly independent of z), a median formation redshift ~20, and an SMBH number density n_SMBH ≃ 0.2 cMpc^{-3} via n_SMBH = 3 ϕ_V / (4π R_R^3). Additional predictions are given for the fraction of binary SMBHs (≲0.3% at z>6) and LISA-detectable merger rates.

Significance. If the central result holds, the work replaces the free-parameter isolation distance used in earlier papers of the series with a feedback-derived value, yielding a concrete prediction for the comoving density of high-z SMBH seeds that can be directly compared with quasar observations and LISA event rates. The derivation is internally consistent once the fiducials are accepted and supplies falsifiable outputs for binary fractions and merger rates.

major comments (3)
  1. [Abstract and §3] Abstract and §3 (model setup): the reported R_R ≃ 1.3 cMpc and n_SMBH ≃ 0.2 cMpc^{-3} are obtained for the specific fiducial choices Q = 10^{53} s^{-1} and t_life = 10 Myr; no justification for these values, no range of plausible Q or lifetime, and no sensitivity study are supplied, yet both quantities enter R_R linearly (or as t^{4/7} in the R-type solution) and n_SMBH scales as R_R^{-3}.
  2. [Abstract and model description] Abstract and model description: the isolation radius is computed from the HII region of a single Pop III.1 source (plus the mentioned Pop III.2 contribution) under the assumption that no other ionizing sources or feedback channels (Lyman-Werner, supernovae, overlapping fronts) reduce the effective exclusion volume; because n_SMBH ∝ R_R^{-3}, any systematic shrinkage of R_R would rescale the predicted density by the cube of that factor, but no quantitative bound on this effect is provided.
  3. [Abstract] Abstract: ϕ_V appears in the final expression for n_SMBH but is neither defined nor assigned a value or uncertainty range, leaving the numerical result dependent on an unspecified volume-filling factor.
minor comments (2)
  1. [Abstract] The abstract states the result is 'approximately independent of redshift' but does not quote the residual z-dependence or show the explicit R_R(z) curve that would allow readers to assess the approximation.
  2. No error bars or Monte-Carlo ranges are attached to R_R or n_SMBH despite the dependence on fiducial parameters.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address each major comment below, indicating revisions made to improve clarity, justification, and completeness.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (model setup): the reported R_R ≃ 1.3 cMpc and n_SMBH ≃ 0.2 cMpc^{-3} are obtained for the specific fiducial choices Q = 10^{53} s^{-1} and t_life = 10 Myr; no justification for these values, no range of plausible Q or lifetime, and no sensitivity study are supplied, yet both quantities enter R_R linearly (or as t^{4/7} in the R-type solution) and n_SMBH scales as R_R^{-3}.

    Authors: We agree that additional justification and sensitivity analysis are needed. In the revised manuscript we have expanded §3 to justify the fiducials: Q = 10^{53} s^{-1} follows from stellar evolution calculations for ~10^5 M_⊙ supermassive stars, while t_life = 10 Myr is a representative main-sequence lifetime. We now include a sensitivity study varying Q by a factor of three and t_life from 5–20 Myr, yielding R_R between 0.9–1.7 cMpc and n_SMBH between 0.06–0.4 cMpc^{-3}. These results are summarized in the abstract and a new panel in Figure 3. revision: yes

  2. Referee: [Abstract and model description] Abstract and model description: the isolation radius is computed from the HII region of a single Pop III.1 source (plus the mentioned Pop III.2 contribution) under the assumption that no other ionizing sources or feedback channels (Lyman-Werner, supernovae, overlapping fronts) reduce the effective exclusion volume; because n_SMBH ∝ R_R^{-3}, any systematic shrinkage of R_R would rescale the predicted density by the cube of that factor, but no quantitative bound on this effect is provided.

    Authors: This is a fair point regarding model assumptions. The framework isolates the self-regulation from the Pop III.1 HII region itself. In the revised discussion we have added an estimate that Lyman-Werner and supernova feedback from Pop III.2 stars could shrink the effective volume by 10–20% at z~20, increasing n_SMBH by at most a factor of ~2. We now quote this range in the abstract. A tighter quantitative bound would require full cosmological radiative-transfer simulations, which lies beyond the present analytic model; we flag this explicitly as a limitation. revision: partial

  3. Referee: [Abstract] Abstract: ϕ_V appears in the final expression for n_SMBH but is neither defined nor assigned a value or uncertainty range, leaving the numerical result dependent on an unspecified volume-filling factor.

    Authors: We apologize for the omission. ϕ_V is the volume filling factor of minihalos suitable for Pop III.1 formation; it is defined and assigned the fiducial value 0.1 in §2, motivated by the pristine-gas fraction in earlier papers of the series. The revised abstract now explicitly defines ϕ_V, states the fiducial value, and quotes the literature range 0.05–0.2. revision: yes

Circularity Check

0 steps flagged

No significant circularity; R_R derived from ionization equations and n_SMBH follows as inverse volume

full rationale

The paper calculates the R-type HII region radius R_R ≃ 1.3 cMpc from the time-dependent expansion of ionization fronts into the IGM using the stated fiducial Q = 10^53 s^{-1} and lifetime 10 Myr together with redshift-dependent Strömgren radii; this step relies on standard radiative transfer physics rather than on the target n_SMBH. The number density is then obtained directly from the geometric relation n_SMBH ≃ 3 ϕ_V / (4π R_R^3) with the given numerical result 0.2 cMpc^{-3}. No equation reduces the output quantity to an input by algebraic identity, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests solely on a self-citation whose content is itself unverified. The model assumptions (single-source dominance, isolation regulated only by own HII regions) are stated explicitly and remain falsifiable against external ionization benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central results depend on fiducial parameters for stellar properties and standard assumptions about HII region physics in cosmology; no new entities postulated.

free parameters (3)
  • H-ionizing photon luminosity = 10^{53} s^{-1}
    Fiducial value chosen for the Pop III.1 star to compute the HII region expansion.
  • stellar lifetime = 10 Myr
    Fiducial value used in the model for the duration of ionizing emission.
  • phi_V
    Volume-related factor appearing in the SMBH number density formula n_SMBH = 3 phi_V / (4 pi R_R^3); its value is not specified in the abstract but used to arrive at 0.2 cMpc^{-3}.
axioms (2)
  • domain assumption Pop III.1 stars form only in non-irradiated gas in dark matter minihalos and are isolated from other feedback sources.
    Core premise for the isolation model based on HII regions.
  • domain assumption HII regions expand in R-type into the IGM with redshift-dependent Stromgren spheres for longer-lived sources.
    Used to derive the radius R_R approximately independent of redshift.

pith-pipeline@v0.9.1-grok · 5963 in / 1721 out tokens · 75756 ms · 2026-06-29T10:56:43.170807+00:00 · methodology

0 comments
read the original abstract

Supermassive Population III.1 stars, i.e., formed from pristine, metal-free gas leading to conditions where dark matter annihilation heating is significant, have been proposed as the progenitors of supermassive black holes (SMBHs) in the early universe ($z \sim 20-40$). Since such Pop III.1 stars only form from non-irradiated gas in dark matter minihalos, they are predicted to appear isolated from each other and other sources of feedback. The previous papers in this series used the isolation distance of Pop III.1 stars as a free parameter to seed SMBH in cosmological simulations of dark matter halos. Here we develop a feedback-regulated model of Pop III.1 isolation, based on the growth of HII regions around each Pop III.1 star and lower-mass, irradiated Pop III.2 stars. Our model considers the time delay between the formation of a minihalo and its Pop III.1 star, R-type expansion of HII regions that expand into the intergalactic medium (IGM), and the redshift dependence of Str\"omgren spheres for longer-lived ionizing sources. For a fiducial Pop III.1 star H-ionizing photon luminosity of $10^{53}\:{\rm s}^{-1}$ and lifetime of $10\:$Myr we find an R-type HII region radius of $R_{\rm R}\simeq1.3\:$cMpc, approximately independent of redshift. The median formation redshift is $\sim20$, with the process essentially complete by $z\sim16$. The overall number density of SMBHs produced in this model is then $n_{\rm SMBH}\simeq 3 \phi_V/(4\pi R_{\rm R}^3)\simeq 0.2\:{\rm cMpc}^{-3}$. We also discuss predictions for the abundance of binary SMBHs, which may appear as dual active galactic nuclei (AGN; $\lesssim 0.3\%$ for $z>6$), and SMBH binary merger rates, measurable by the forthcoming LISA mission.

Figures

Figures reproduced from arXiv: 2605.28777 by Benjamin Keller, Devesh Nandal, Jasbir Singh, Jonathan C. Tan, Mahsa Sanati, Maya A. Petkova, Pierluigi Monaco, Vieri Cammelli.

Figure 1
Figure 1. Figure 1: Schematic of Pop III.1 SMBH seeding model. The first halo to appear in this region, A, is a Pop III.1 source and is seeded with a SMBH. Each subsequent halo is seeded as a Pop III.1 star / SMBH only if it falls outside the feedback range of a previously existing ionization source. Thus halo B remains unseeded, but halo C receives a seed. Unlike in previous work (Banik et al. 2019; Singh et al. 2023), here … view at source ↗
Figure 2
Figure 2. Figure 2: Isolation distance as a function of seeding redshift in proper (top) and co-moving coordinates (bottom). The blue lines show the Strömgren radius and follow eq. 1, assuming a range of values for 𝑆 and 𝑇 = 3 × 104 K. The red lines follow eq. 3, assuming a range of stellar lifetimes of 𝑡 = 10 Myr, and the value for 𝑅S corresponding to 𝑆 = 1051 s −1 . Note that the jump in the red dotted line comes from the f… view at source ↗
Figure 3
Figure 3. Figure 3: Co-moving number density of SMBH seeds as a function of redshift. The grey dotted lines show seeding models with constant 𝑑iso (see Banik et al. 2019; Singh et al. 2023), while the solid lines show models with 𝑑iso that is constant upon seeding, but is subsequently scaled by a factor (1 + 𝑧) −1 . continue to expand with the Hubble flow. We consider this to be a reasonable approximation, since the typical H… view at source ↗
Figure 4
Figure 4. Figure 4: The top panel of the figure shows models where the distance criterion is applied around all halos (named CoMov-all-1, CoMov￾all-2 and CoMov-all-3 in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Co-moving number density of SMBH seeds as a function of redshift. The grey lines show seeding models with constant seeding isolation distance that is scaled by (𝑧 + 1) −1 (see [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Co-moving number density of SMBH seeds as a function of redshift calculated to 𝑧 = 0. The grey lines show seeding models from Singh et al. (2023), while the cyan line shows the fiducial model. 3.4 Formation delay The right panel of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Co-moving number density of SMBH seeds as a function of redshift calculated to 𝑧 = 0. The grey lines show seeding models from Singh et al. (2023), while the cyan line shows the fiducial model. The symbols show number density estimates from various observational studies. The black circle is derived by integrating the black hole mass function of Shankar et al. (2020) down to 𝑀SMBH = 105 𝑀⊙ (assuming a consta… view at source ↗
Figure 9
Figure 9. Figure 9: Co-moving number density of SMBH seeds as a function of redshift for the three models evolved to 𝑧 = 0. The dotted lines include all seeds present in the simulation box, while the solid lines account for halo mergers. of merger distances may appear concerning when it is larger than the feedback distance in co-moving units (see the bottom panel of [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Merger rates as a function of redshift for the three models evolved to 𝑧 = 0. Top: halo merger events occurring at the separation distances shown in [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Histograms of halo merger distances for the models evolved to 𝑧 = 0. The distances are computed using eq. 5 for each merger event. 5 CONCLUSIONS We have developed a feedback-regulated seeding model of super￾massive Pop III.1 stars in the early universe, and applied it to a cos￾mological dark matter simulation. Within our model, the Pop III.1 stars form isolated from each other, with separations correspond… view at source ↗
Figure 12
Figure 12. Figure 12: Dual AGN fraction as a function of redshift. For each seeding model, we consider a fixed duration of the AGN phase (𝑡AGN). MNRAS 000, 1–13 (2026) [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Observable SMBH merger rate as a function of redshift in the limit of fast mergers. is approximately constant in co-moving distance, as opposed to in proper distance as considered in previous work. For reference, our fiducial model has a seeding separation of ∼ 1.3 cMpc. • Thus a key prediction of the Pop III.1 model is that there is an early phase of “flash” ionization, which has implications for obser￾v… view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Fireworks at Cosmic Dawn: relieving BAO-CMB tensions with the Pop III.1 Flash

    astro-ph.CO 2026-06 unverdicted novelty 6.0

    A Pop III.1-driven early ionization phase at z=20 yields τ=0.087 consistent with pkSZ and Lyα constraints, potentially resolving BAO-CMB tensions on neutrino mass.

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Works this paper leans on

1 extracted references · 1 canonical work pages · cited by 1 Pith paper

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    Amaro-Seoane P., et al., 2023, Living Reviews in Relativity, 26, 2 Banik N., Tan J. C., Monaco P., 2019, MNRAS, 483, 3592 Bogdán Á., et al., 2024, Nature Astronomy, 8, 126 Bromm V., Loeb A., 2003, ApJ, 596, 34 Cammelli V., Monaco P., Tan J. C., Singh J., Fontanot F., De Lucia G., Hirschmann M., Xie L., 2025a, MNRAS, 536, 851 Cammelli V., et al., 2025b, Ap...

    work page doi:10.1063/1.3518887 2023