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REVIEW 2 major objections 4 minor 65 references

Spectral Evolution of Rotating Population III Stars

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Rotation and aging make the most massive first stars detectable with lensing magnifications of only 10–100 at z<7, orders of magnitude below earlier estimates.

desk verdict Useful extension of Pop III spectral templates, but the headline magnification claim depends on wind-free non-rotating models that may not survive to TAMS. read the letter →

arxiv 2505.21463 v1 pith:IAOTDNDY submitted 2025-05-27 astro-ph.GA astro-ph.SR

Jake Hassan , Rosalba Perna , Matteo Cantiello , Tyler Parsotan , Davide Lazzati , Nathan Walker This is my paper
classification astro-ph.GAastro-ph.SR
keywords PopulationIIIstarsstellarrotationchemicallyhomogeneousevolutionspectraJamesWebbSpaceTelescopegravitationallensingearlyuniversemain-sequence
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

Population III stars—the first stars, born from metal-free gas—have never been directly observed because they are short-lived and far away. This paper asks whether rotation and ordinary main-sequence aging make them easier for JWST to catch than earlier non-rotating, zero-age main-sequence models suggested. The authors evolve 64 models spanning 10 to 800 solar masses and four rotation rates, synthesize their spectra, and place them in JWST bands. They find that rotation alone barely changes a star's zero-age brightness, but evolution brightens stars; the most massive ($M \gtrsim 500\,M_\odot$) can become visible at $z \lesssim 7$ with lensing magnifications of only about $\mu \sim 10$ at the end of the main sequence and $\mu \sim 10^2$ at the intermediate-age stage. If correct, this shrinks the required lensing amplification by one to three orders of magnitude relative to the previous picture.

What carries the argument

The machinery is a grid of 64 one-dimensional stellar evolution tracks computed with the MESA code: 16 initial masses from 10 to 800 solar masses crossed with four initial rotation rates expressed as fractions of the critical velocity ($\Omega = 0.0, 0.2, 0.4, 0.6$). The load-bearing physical ingredient is rotationally induced mixing; when it is efficient the star undergoes chemically homogeneous evolution, keeping a uniform composition, staying blue and compact, and becoming more luminous and helium-enriched at the surface. For each track, ATLAS-based atmosphere synthesis generates the emitted spectrum at the zero-age, intermediate-age, and terminal-age main sequence, and the fluxes are folded through JWST NIRCam and MIRI filter efficiencies with limiting magnitudes from the JWST exposure-time calculations. This chain turns the stellar-structure question—how bright and hot the surface is at a given mass, rotation, and age—into an observational answer: which JWST band, redshift, and lensing magnification would reveal it.

What would settle it

Run the same 64-model grid with the rotational mixing efficiency reduced by a factor of two (or with an independently calibrated mixing scheme) and check whether chemically homogeneous tracks survive; if they vanish, so does the prediction of $\mu \lesssim 10$–$10^2$ detections. Observationally, a targeted JWST search at $z \lesssim 7$ for lensed stars with zero-metallicity, helium-enriched spectra—strong helium lines and no metal lines—would test the brightest end of the predicted population directly.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that stellar rotation and post-zero-age main-sequence evolution change the predicted JWST observability of Population III stars in a specific way: rotation has almost no effect at the zero-age main sequence, but evolution does. Slowly rotating models swell into red supergiants and grow redder and brighter, while rapidly rotating models can undergo chemically homogeneous evolution, staying compact and hot with helium and metals dragged to the surface. In both channels the late main-sequence stars are more luminous, and for the most massive models ($M \gtrsim 500\,M_\odot$) this lowers the required caustic lensing amplification to $\mu \lesssim 10^2$ at intermediate-age and $\mu \lesssim 10$ at terminal-age main sequence for $z \lesssim 7$. The paper thereby extends earlier non-rotating zero-age predictions and identifies the JWST bands and redshifts where a first-star detection is most plausible.

Load-bearing premise

The load-bearing premise is that rotationally induced mixing in the stellar models is as efficient as the adopted published prescription; if real mixing is weaker, chemically homogeneous evolution would not occur and the predicted post-main-sequence brightening of moderately massive stars would disappear, pushing required lensing magnifications back up.

Editorial extensions

If this is right

  • The most massive Pop III stars ($M \gtrsim 500\,M_\odot$) at $z \lesssim 7$ would be detectable with lensing magnifications of about 10–100, roughly one to three orders of magnitude smaller than the amplifications previously estimated for non-rotating zero-age stars.
  • At any given redshift, nearly all stars—across mass, rotation, and main-sequence stage—are best observed in the same JWST band, so a single filter choice covers most of the parameter space; only massive, slowly rotating stars near the end of the main sequence need redder filters at $z \lesssim 7$.
  • Rotation by itself does not change the zero-age main-sequence spectrum appreciably, so previously published non-rotating zero-age templates remain valid for the youngest first stars.
  • If the models are right, helium-enriched surfaces on chemically homogeneous and blue-supergiant tracks produce distinctive spectral signatures—helium lines and a drop at the helium photoionization edge—that could distinguish evolved Pop III stars from other hot stellar populations.
  • Pop III clusters of roughly 70 stars could be detectable at magnifications below $\mu \sim 10^3$ up to $z = 7$, offering a second route to detection that does not require extremely massive single stars.

Reading between the lines

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

  • Editorial inference: the same brightening mechanism implies that a lensed Pop III star caught near the end of its main sequence should look distinctly helium-rich in its spectrum; this offers a specific spectroscopic confirmation test that the paper does not itself develop.
  • Editorial inference: the cluster calculation assumed all members sit on the zero-age main sequence simultaneously, which the paper notes understates the light; a cluster with evolved massive members would be brighter still, so the magnification thresholds for cluster detection are upper limits rather than central values.
  • Editorial inference: the model grid could be extended to the helium-burning and pre-supernova phases the authors deliberately excluded; their own HR diagrams show red supergiants with enormous radii, so such stars might be visible in the mid-infrared even if main-sequence templates are not.
  • Editorial inference: the rotation-grid results imply that the detectability of Pop III stars is sensitive to the unknown initial rotation distribution; if most first stars rotate near the critical velocity, the bright chemically homogeneous tracks dominate the observable population, whereas a slowly rotating population would need stronger lensing.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper presents new evolutionary and synthetic-spectral models of Population III stars. The authors compute 64 MESA tracks with initial masses 10–800 M☉ and four initial rotation rates (Ω = v/v_crit = 0.0, 0.2, 0.4, 0.6), generate ATLAS/SYNTHE spectra at ZAMS, IAMS, and TAMS, and predict JWST NIRCam/MIRI photometry using Pandeia limiting magnitudes. Their central finding is that post-ZAMS evolution can substantially brighten the most massive stars: for M ≳ 500 M☉, magnifications of μ ≲ 10² at IAMS and μ ≲ 10 at TAMS are claimed at z ≲ 7, improving on previous ZAMS-only estimates. The paper also computes photometry for model star clusters drawn from the Reinoso et al. (2025) IMF and discusses implications for high-redshift GRBs.

Significance. If the central claim is correct, this work would improve the feasibility of detecting Pop III stars with JWST and provide quantitative color–magnitude predictions that can be compared to lensed-star candidates. The paper's main contribution is the systematic inclusion of rotation and post-ZAMS evolution in spectral synthesis, extending Larkin et al. (2023). The modeling is transparent and reproducible in structure: the Appendix A tables list full MESA inputs and outputs, the photometric calculations are fully specified, and no fitting to observational data is involved. However, the headline detection claim rests on a physically uncertain assumption about mass loss in extremely extended, near-Eddington TAMS models, and the summary statements are not fully consistent with the paper's own Appendix B. These issues need resolution before the central claim can be accepted.

major comments (2)
  1. [Section 6 and Appendix B] The headline claim that M ≳ 500 M☉ Pop III stars are detectable at μ ≲ 10 at TAMS rests on the non-rotating and slowly rotating models reaching R_TAMS ≈ 7000–9000 R☉ and T_eff ≈ 4400 K (e.g., Table 2: 800 M☉, Ω=0.0 gives R_TAMS = 9032 R☉, L_TAMS = 2.87×10⁷ L☉). Section 2.1 states that mass loss is "neglected entirely for nonrotating models," citing Krtička & Kubát (2006) for hot metal-free stars. Those TAMS models, however, are cool, extremely extended red supergiants close to the Eddington limit (for electron scattering, L/L_Edd ≈ 1.1 for the 800 M☉ model), a regime where continuum-driven or super-Eddington winds are expected rather than negligible. The authors themselves list mass loss as a needed future refinement in Section 6. A sensitivity test with a plausible super-Eddington wind, or a quantitative argument that such winds are absent at Z=0 for these cool supergiants, is required before the μ ≲ 10 TAMS claim can be accepted as robust.
  2. [Section 6 and Appendix B] The detectability claims are not internally consistent. Section 6 states that M ≳ 500 M☉ stars "could be detected with moderate lensing amplifications of μ ≲ 10² at IAMS and μ ≲ 10 at TAMS, for distances z ≲ 7." Appendix B, however, says that at z = 7 "the most massive models in our study do not see a significant improvement, and the lower bound on μ needed to detect Population III stars is not substantially improved." This implies the μ ≲ 10 TAMS claim is not valid over the full quoted range z ≲ 7, and the summary should either be restricted to z ≈ 3 or state the z = 7 limits explicitly. In addition, Section 3.2's statement that 800 M☉ stars at z ∼ 3 "could almost be directly detected without lensing in the MIRI bands of JWST" is not supported by Appendix B, which reports detection at magnifications below μ ∼ 10 (not μ ∼ 1), and Table 5 lists NIRCam bands F277W/F356W, not MIRI bands, at z = 3.
minor comments (4)
  1. [Section 3.2] The phrase "in the MIRI bands of JWST" is incorrect for z ∼ 3; Table 5 shows the optimal bands at z = 3 are NIRCam F277W/F356W. The same sentence should also be reworded to avoid implying detection without lensing when Appendix B gives μ < 10.
  2. [Section 4] The statement that large clusters are comparable to "the largest stable Pop III mass (∼820 M☉) predicted by (Larkin et al. 2023)" is inaccurate: Larkin et al. (2023) modeled masses up to 800 M☉ and did not predict a stability limit. Rephrase to "the most massive model considered by Larkin et al. (2023)" or provide a proper citation for a stability limit.
  3. [Table 4 caption] The caption contains a stray period after "bands" in the last entry; remove it.
  4. [Section 2.2] The sentence beginning "As in Larkin et al. (2023), the same two sets of ODFs..." has a grammatical break; consider revising for clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's predictions are forward-modeled outputs of MESA/ATLAS stellar models with no parameter fitting to the claimed JWST observables.

full rationale

The claimed derivation chain runs from adopted input physics (Yoon et al. 2012 rotational mixing and mass-loss treatment; Reinoso et al. 2025 IMF) through MESA evolutionary models, ATLAS/SYNTHE synthetic spectra, and Pandeia JWST limiting magnitudes to the final magnification thresholds. No step fits a parameter to the quantity that is later presented as a prediction. The ZAMS/IAMS/TAMS definitions are operational bookkeeping, not restatements of the result. The non-rotating models' neglect of wind mass loss is a stated physical assumption, and the headline claim for M ≳ 500 M⊙ at TAMS follows from the tabulated model outputs (e.g., 800 M⊙, Ω = 0.0: R_TAMS ≈ 9032 R⊙, Teff ≈ 4444 K) rather than from a fitted parameter. The paper does not invoke a uniqueness theorem, does not smuggle an ansatz in via self-citation, and does not rename a known empirical pattern as a new derivation. The self-citations (Perna et al. 2014; Perna et al. 2018; Walker et al., in preparation) appear in contextual or forward-looking remarks and are not load-bearing for the spectral or lensing predictions. Concerns about wind mass loss or mixing efficiency altering the RSG tracks are physical robustness/correctness risks, not circularity: the outputs would change under different assumptions, but that is a property of any forward model and does not make the derivation equivalent to its inputs. The paper is self-contained against external benchmarks in the sense that its predictions are computed, not fitted, and therefore no significant circularity is present.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The paper does not fit data and introduces no new entities. It relies on prior stellar physics and astrophysical assumptions: the existence and mass range of Pop III stars, the Yoon et al. mixing prescription, the Meiksin IGM transmission extrapolation, and the Reinoso IMF for clusters. The cluster multiplicity is explicitly treated as a free parameter, making the cluster predictions a conditioned result.

free parameters (1)
  • cluster multiplicity n = None (grid 5 to 80)
    Explicitly treated as a free parameter in Section 4. Cluster photometry depends on it, but the paper scans a range rather than fitting it to data.
assumptions (5)
  • domain assumption Population III stars exist with masses up to 800 M_sun and rotation rates up to 0.6 v_crit
    The grid covers 10-800 M_sun and v/v_crit = 0-0.6 based on theoretical expectations (Stacy et al. 2013); the high-mass end is uncertain.
  • domain assumption The overshooting and mixing prescriptions from Yoon et al. (2012) are adopted unchanged
    These control whether chemically homogeneous evolution occurs, which drives the predicted brightening; Section 2.1.
  • domain assumption The Meiksin (2006) IGM transmission approximation is valid at z < 7
    They extend the z>7 formula to lower redshifts despite the original validity range; Section 3.2, Eq. 10.
  • domain assumption The Reinoso et al. (2025) IMF applies to Pop III clusters
    Used to sample cluster masses; alternative IMFs would change cluster photometry; Section 4.
  • standard math MESA and ATLAS codes correctly model the stellar physics and atmospheres
    Accepted community codes, but their accuracy for extreme Pop III stars is not independently verified here.

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Cite this review

Pith. "Pith review of Spectral Evolution of Rotating Population III Stars." pith.science (2026). https://pith.science/paper/IAOTDNDY

@misc{pith2026250521463,
  author       = {Pith},
  title        = {Pith review of: Spectral Evolution of Rotating Population III Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IAOTDNDY}},
  note         = {Machine review of arXiv:2505.21463}
}
read the original abstract

Population III (Pop III) stars, the first generation of stars formed from primordial gas, played a fundamental role in shaping the early universe through their influence on cosmic reionization, early chemical enrichment, and the formation of the first galaxies. However, to date they have eluded direct detection due to their short lifetimes and high redshifts. The launch of the James Webb Space Telescope (JWST) has revolutionized observational capabilities, providing the opportunity to detect Pop~III stars via caustic lensing, where strong gravitational lensing magnifies individual stars to observable levels. This prospect makes it compelling to develop accurate models for their spectral characteristics to distinguish them from other stellar populations. Previous studies have focused on computing the spectral properties of non-rotating, zero-age main sequence (ZAMS) Pop III stars. In this work, we expand upon these efforts by incorporating the effects of stellar rotation and post-ZAMS evolution into spectral calculations. We use the JWST bands and magnitude limits to identify the optimal observing conditions, both for isolated stars, as well as for small star clusters. We find that, while rotation does not appreciably change the observability at ZAMS, the subsequent evolution can significantly brighten the stars, making the most massive ones potentially visible with only moderate lensing.

Figures

Figures reproduced from arXiv: 2505.21463 by the authors.

Figure 1
Figure 1. HR-diagrams showing evolutionary tracks from the beginning of hydrogen burning to the end of the calculation for models of Pop III stars with different initial masses and rotational velocities. Circle symbols mark the position at which X = 0.3, while the end points of hydrogen burning and helium burning are marked with a square and cross, respectively. spend a very small fraction of their life in post-MS stages as a… view at source ↗
Figure 2
Figure 2. Change in surface rotational velocity in units of the critical velocity (left panel) and mass loss rate (right panel) from pre-MS to helium exhaustion, for a 50 M⊙ model with varying initial velocities. Lines of constant radius are shown in gray. use the wind scheme described in Yoon et al. (2012), neglecting wind entirely for nonrotating models. This is motivated by the fact that mass loss from stellar winds in met… view at source ↗
Figure 3
Figure 3. Comparison of spectral fluxes and evolutionary tracks for Pop III stars with different initial masses and rotational velocities. Spectral fluxes are shown at ZAMS (blue), IAMS (green), and TAMS (red), which are the points indicated in the H-R diagram of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Color-magnitude diagrams at different redshifts and rotational velocities. Results are shown for ZAMS (blue), IAMS (green) and TAMS (red). The models from [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Color magnitude diagrams for clusters of varying multiplicities. The plotted values for each cluster were obtained by summing the fluxes for the cluster’s individual stars, computing the total magnitude and color index for the cluster, and then averaging the cluster’s …
Figure 6
Figure 6. Figure 6: Color-magnitude diagrams in the optimal bands for massive stars near TAMS, at redshifts z = 3 and z = 7 [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

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Works this paper leans on

65 extracted references · 15 canonical work pages

  1. [1]

    L., & Norman, M

    Abel, T., Bryan, G. L., & Norman, M. L. 2002, Science, 295, 93, doi: 10.1126/science.1063991 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068

    doi:10.1126/science.1063991 2002

  2. [2]

    S., & Larson, R

    Bromm, V., Coppi, P. S., & Larson, R. B. 2002, ApJ, 564, 23, doi: 10.1086/323947

    doi:10.1086/323947 2002

  3. [3]

    L., Norman, M

    Bryan, G. L., Norman, M. L., O’Shea, B. W., et al. 2014, The Astrophysical Journal Supplement Series, 211, 19, doi: 10.1088/0067-0049/211/2/19

    doi:10.1088/0067-0049/211/2/19 2014

  4. [4]

    2005, Memorie della Societa Astronomica Italiana Supplementi, 8, 34

    Castelli, F. 2005, Memorie della Societa Astronomica Italiana Supplementi, 8, 34

    work page 2005

  5. [5]

    2000, Astrophysical Journal, 540, 687, doi: 10.1086/309374

    Ciardi, B., & Loeb, A. 2000, Astrophysical Journal, 540, 687, doi: 10.1086/309374

    doi:10.1086/309374 2000

  6. [6]

    C., Glover, S

    Clark, P. C., Glover, S. C. O., & Klessen, R. S. 2008, The Astrophysical Journal, 672, 757, doi: 10.1086/523842

    work page doi:10.1086/523842 2008

  7. [7]

    C., et al

    Clark, P. C., et al. 2011, Science, 331, 1040, doi: 10.1126/science.1198027 de Souza, R. S., Mesinger, A., Ferrara, A., et al. 2013, M.N.R.A.S., 432, 3218, doi: 10.1093/mnras/stt674

    doi:10.1126/science.1198027 2011

  8. [8]

    Diego, J. M. 2019, Astronomy & Astrophysics, 625, A84, doi: 10.1051/0004-6361/201935351

    work page doi:10.1051/0004-6361/201935351 2019

Show all 65 references
  1. [9]

    S., & Larkin, M

    Gerasimov, R., Zhou, T. S., & Larkin, M. 2022, Roman-UCSD/BasicATLAS: v1.0.0, v1.0.0, Zenodo, doi: 10.5281/zenodo.7145514

    2022 doi

  2. [10]

    S., Fialkov, A., et al

    Gessey-Jones, T., Sartorio, N. S., Fialkov, A., et al. 2022, Monthly Notices of the Royal Astronomical Society, 516, 841, doi: 10.1093/mnras/stac2049

    2022 doi

  3. [11]

    J., M´ esz´ aros, P., Abel, T., & Zhang, B

    Gou, L. J., M´ esz´ aros, P., Abel, T., & Zhang, B. 2004, Astrophysical Journal, 604, 508, doi: 10.1086/381979

    2004 doi

  4. [12]

    H., Springel, V., White, S

    Greif, T. H., Springel, V., White, S. D. M., et al. 2011, The Astrophysical Journal, 737, 75, doi: 10.1088/0004-637X/737/2/75

    2011 doi

  5. [13]

    S., & Glover, S

    Hartwig, T., Bromm, V., Klessen, R. S., & Glover, S. C. O. 2015, M.N.R.A.S., 447, 3892, doi: 10.1093/mnras/stu2740

    2015 doi

  6. [14]

    2000, ApJ, 544, 1016, doi: 10.1086/317239

    Heger, A., & Langer, N. 2000, ApJ, 544, 1016, doi: 10.1086/317239

    2000 doi

  7. [15]

    2014, The Astrophysical Journal, 781, 60, doi: 10.1088/0004-637X/781/2/60

    Hirano, S., Hosokawa, T., Yoshida, N., et al. 2014, The Astrophysical Journal, 781, 60, doi: 10.1088/0004-637X/781/2/60

    2014 doi

  8. [16]

    Hosokawa, T., Omukai, K., Yoshida, N., & Yorke, H. W. 2011, Science, 334, 1250, doi: 10.1126/science.1207433

    2011 doi

  9. [17]

    Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90, doi: 10.1109/MCSE.2007.55

    2007 doi

  10. [18]

    2007, Monthly Notices of the Royal Astronomical Society, 380, 1715, doi: 10.1111/j.1365-2966.2007.12246.x

    Inoue, S., Omukai, K., & Ciardi, B. 2007, Monthly Notices of the Royal Astronomical Society, 380, 1715, doi: 10.1111/j.1365-2966.2007.12246.x

    2007

  11. [19]

    2005, Astrophysical Journal, 619, 684, doi: 10.1086/426679

    Ioka, K., & M´ esz´ aros, P. 2005, Astrophysical Journal, 619, 684, doi: 10.1086/426679

    2005 doi

  12. [20]

    2016, ApJ, 826, 9, doi: 10.3847/0004-637X/826/1/9

    Ishiyama, T., Sudo, K., Yokoi, S., et al. 2016, ApJ, 826, 9, doi: 10.3847/0004-637X/826/1/9

    2016 doi

  13. [21]

    2022, Monthly Notices of the Royal Astronomical Society, 512, 116, doi: 10.1093/mnras/stac514

    Jaura, O., et al. 2022, Monthly Notices of the Royal Astronomical Society, 512, 116, doi: 10.1093/mnras/stac514

    2022 doi

  14. [22]

    Potekhin, A. Y. 2021, ApJ, 913, 72, doi: 10.3847/1538-4357/abf48e

    2021 doi

  15. [23]

    Johnson, J. L. 2010, M.N.R.A.S., 404, 1425, doi: 10.1111/j.1365-2966.2010.16351.x Krtiˇ cka, J., & Kub´ at, J. 2006, Astronomy & Astrophysics, 446, 1039, doi: 10.1051/0004-6361:20053957

    2010

  16. [24]

    Kurucz, R. L. 1970, SAO Special Report, 309 —. 2014, Determination of Atmospheric Parameters of B-,

    1970

  17. [25]

    A-, F- and G-Type Stars, 471, doi: 10.1007/978-3-319-06956-2 41

    doi

  18. [26]

    L., & Avrett, E

    Kurucz, R. L., & Avrett, E. H. 1981, SAO Special Report, 391

    1981

  19. [27]

    Q., & Reichart, D

    Lamb, D. Q., & Reichart, D. E. 2000, Astrophysical Journal, 536, 1, doi: 10.1086/308918

    2000 doi

  20. [28]

    M., Gerasimov, R., & Burgasser, A

    Larkin, M. M., Gerasimov, R., & Burgasser, A. J. 2023, AJ, 165, 2, doi: 10.3847/1538-3881/ac9b43

    2023 doi

  21. [29]

    Levan, A. J. 2015, Journal of High Energy Astrophysics, 7, 44, doi: 10.1016/j.jheap.2015.05.004

    2015 doi

  22. [30]

    2020, Monthly Notices of the Royal Astronomical Society, 497, 2839, doi: 10.1093/mnras/staa2127

    Liu, B., et al. 2020, Monthly Notices of the Royal Astronomical Society, 497, 2839, doi: 10.1093/mnras/staa2127

    2020 doi

  23. [31]

    2025, arXiv e-prints, arXiv:2503.14452, doi: 10.48550/arXiv.2503.14452

    Louis, T., La Posta, A., Atkins, Z., et al. 2025, arXiv e-prints, arXiv:2503.14452, doi: 10.48550/arXiv.2503.14452

    2025 doi arXiv

  24. [32]

    1987, Astronomy & Astrophysics, 178, 159 18 Hassan et al

    Maeder, A. 1987, Astronomy & Astrophysics, 178, 159 18 Hassan et al

    1987

  25. [33]

    2011, Monthly Notices of the Royal Astronomical Society, 414, 1145, doi: 10.1111/j.1365-2966.2011.18470.x

    Maio, U., et al. 2011, Monthly Notices of the Royal Astronomical Society, 414, 1145, doi: 10.1111/j.1365-2966.2011.18470.x

    2011

  26. [34]

    2006, Monthly Notices of the Royal Astronomical Society, 365, 807, doi: 10.1111/j.1365-2966.2005.09764.x

    Meiksin, A. 2006, Monthly Notices of the Royal Astronomical Society, 365, 807, doi: 10.1111/j.1365-2966.2005.09764.x

    2006

  27. [35]

    2005, ApJ, 623, 1, doi: 10.1086/428770 Miralda-Escud´ e, J

    Mesinger, A., Perna, R., & Haiman, Z. 2005, ApJ, 623, 1, doi: 10.1086/428770 Miralda-Escud´ e, J. 1991, The Astrophysical Journal, 379, 94, doi: 10.1086/170498

    2005 doi

  28. [36]

    L., Gnedin, O

    Muratov, A. L., Gnedin, O. Y., Gnedin, N. Y., & Zemp, M. 2013, The Astrophysical Journal, 773, 19, doi: 10.1088/0004-637X/773/1/19

    2013 doi

  29. [38]

    2012, The Astrophysical Journal, 754, 85, doi: 10.1088/0004-637X/754/2/85

    Nagakura, H., Suwa, Y., & Ioka, K. 2012, The Astrophysical Journal, 754, 85, doi: 10.1088/0004-637X/754/2/85

    2012 doi

  30. [39]

    B., & Gunn, J

    Oke, J. B., & Gunn, J. E. 1983, The Astrophysical Journal, 266, 713, doi: 10.1086/160817

    1983 doi

  31. [40]

    2011, The Astrophysical Journal Supplement Series, 192, 3, doi: 10.1088/0067-0049/192/1/3

    Paxton, B., Bildsten, L., Dotter, A., et al. 2011, The Astrophysical Journal Supplement Series, 192, 3, doi: 10.1088/0067-0049/192/1/3

    2011 doi

  32. [41]

    2013, The Astrophysical Journal Supplement Series, 208, 4, doi: 10.1088/0067-0049/208/1/4

    Paxton, B., Cantiello, M., Arras, P., et al. 2013, The Astrophysical Journal Supplement Series, 208, 4, doi: 10.1088/0067-0049/208/1/4

    2013 doi

  33. [42]

    2015, The Astrophysical Journal Supplement Series, 220, 15, doi: 10.1088/0067-0049/220/1/15

    Paxton, B., Marchant, P., Schwab, J., et al. 2015, The Astrophysical Journal Supplement Series, 220, 15, doi: 10.1088/0067-0049/220/1/15

    2015 doi

  34. [43]

    B., et al

    Paxton, B., Schwab, J., Bauer, E. B., et al. 2018, The Astrophysical Journal Supplement Series, 234, 34, doi: 10.3847/1538-4365/aaa5a8

    2018 doi

  35. [44]

    2019, The Astrophysical Journal Supplement Series, 243, 10, doi: 10.3847/1538-4365/ab2241

    Paxton, B., Smolec, R., Schwab, J., et al. 2019, The Astrophysical Journal Supplement Series, 243, 10, doi: 10.3847/1538-4365/ab2241

    2019 doi

  36. [45]

    Perna, R., Duffell, P., Cantiello, M., & MacFadyen, A. I. 2014, ApJ, 781, 119, doi: 10.1088/0004-637X/781/2/119

    2014 doi

  37. [46]

    2018, ApJ, 859, 48, doi: 10.3847/1538-4357/aabcc1

    Perna, R., Lazzati, D., & Cantiello, M. 2018, ApJ, 859, 48, doi: 10.3847/1538-4357/aabcc1

    2018 doi

  38. [47]

    M., Pickering, T

    Pontoppidan, K. M., Pickering, T. E., Laidler, V. G., et al. 2016, 9910, 991016, doi: 10.1117/12.2231768

    2016 doi

  39. [48]

    A., & Schleicher, D

    Reinoso, B., Latif, M. A., & Schleicher, D. R. G. 2025, arXiv e-prints, arXiv:2503.20415, doi: 10.48550/arXiv.2503.20415

    2025 doi arXiv

  40. [49]

    2013, Monthly Notices of the Royal Astronomical Society, 429, 3658, doi: 10.1093/mnras/sts589

    Rydberg, C.-E., Zackrisson, E., Lundqvist, P., & Scott, P. 2013, Monthly Notices of the Royal Astronomical Society, 429, 3658, doi: 10.1093/mnras/sts589

    2013 doi

  41. [50]

    Stacy, A., Bromm, V., & Lee, A. T. 2016, M.N.R.A.S., 462, 1307, doi: 10.1093/mnras/stw1728

    2016 doi

  42. [51]

    H., & Bromm, V

    Stacy, A., Greif, T. H., & Bromm, V. 2012, Monthly Notices of the Royal Astronomical Society, 422, 290, doi: 10.1111/j.1365-2966.2012.20605.x

    2012

  43. [52]

    H., Klessen, R

    Stacy, A., Greif, T. H., Klessen, R. S., Bromm, V., & Loeb, A. 2013, M.N.R.A.S., 431, 1470, doi: 10.1093/mnras/stt264

    2013 doi

  44. [53]

    2014, The Astrophysical Journal, 792, 32, doi: 10.1088/0004-637X/792/1/32

    Susa, H., Hasegawa, K., & Tominaga, N. 2014, The Astrophysical Journal, 792, 32, doi: 10.1088/0004-637X/792/1/32

    2014 doi

  45. [54]

    2010, The Astrophysical Journal, 726, 107, doi: 10.1088/0004-637X/726/2/107

    Suwa, Y., & Ioka, K. 2010, The Astrophysical Journal, 726, 107, doi: 10.1088/0004-637X/726/2/107

    2010 doi

  46. [55]

    2011, Astrophysical Journal, 731, 127, doi: 10.1088/0004-637X/731/2/127

    Toma, K., Sakamoto, T., & M´ esz´ aros, P. 2011, Astrophysical Journal, 731, 127, doi: 10.1088/0004-637X/731/2/127

    2011 doi

  47. [56]

    Trenti, M., Stiavelli, M., & Shull, J. M. 2009, The Astrophysical Journal, 700, 1672, doi: 10.1088/0004-637X/700/2/1672

    2009 doi

  48. [57]

    J., Abel, T., & O’Shea, B

    Turk, M. J., Abel, T., & O’Shea, B. 2009, Science, 325, 601, doi: 10.1126/science.1173540

    2009 doi

  49. [58]

    L., & Haiman, Z

    Visbal, E., Bryan, G. L., & Haiman, Z. 2017, M.N.R.A.S., 469, 1456, doi: 10.1093/mnras/stx909

    2017 doi

  50. [59]

    2022, Monthly Notices of the Royal Astronomical Society, 515, 5106, doi: 10.1093/mnras/stac2043

    Wang, L., Tanikawa, A., & Fujii, M. 2022, Monthly Notices of the Royal Astronomical Society, 515, 5106, doi: 10.1093/mnras/stac2043

    2022 doi

  51. [60]

    A., Timmes, F

    Windhorst, R. A., Timmes, F. X., Wyithe, J. S. B., et al. 2018, ApJ Supp., 234, 41, doi: 10.3847/1538-4365/aaa760

    2018 doi

  52. [61]

    Wollenberg, K. M. J., et al. 2020, Monthly Notices of the Royal Astronomical Society, 494, 1871, doi: 10.1093/mnras/staa760

    2020 doi

  53. [62]

    E., & Heger, A

    Woosley, S. E., & Heger, A. 2006, The Astrophysical Journal, 637, 914, doi: 10.1086/498500

    2006 doi

  54. [63]

    2025, Pair-Instability Gap Black Holes in Population III Star Clusters: Pathways, Dynamics, and Gravitational Wave Implications

    Wu, W., Wang, L., Liu, S., et al. 2025, Pair-Instability Gap Black Holes in Population III Star Clusters: Pathways, Dynamics, and Gravitational Wave Implications. https://arxiv.org/abs/2504.20392

    2025 arXiv

  55. [64]

    2012, A&A, 542, A113, doi: 10.1051/0004-6361/201117769

    Yoon, S.-C., Dierks, A., & Langer, N. 2012, A&A, 542, A113, doi: 10.1051/0004-6361/201117769

    2012 doi

  56. [65]

    2005, Astronomy & Astrophysics, 443, 643, doi: 10.1051/0004-6361:20054030

    Yoon, S.-C., & Langer, N. 2005, Astronomy & Astrophysics, 443, 643, doi: 10.1051/0004-6361:20054030

    2005 doi

  57. [66]

    2015, Monthly Notices of the Royal Astronomical Society, 449, 3057, doi: 10.1093/mnras/stv467

    Zackrisson, E., Gonzalez, J., Eriksson, S., et al. 2015, Monthly Notices of the Royal Astronomical Society, 449, 3057, doi: 10.1093/mnras/stv467

    2015 doi

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