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Formation of Supersonic Turbulence in the Primordial Star-forming Cloud

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that strong supersonic turbulence, with a characteristic Mach number of roughly 5.2, arises naturally during the assembly of a massive primordial minihalo, before any stars exist to drive it.

desk verdict Plausible new result undercut by a checkable box-size inconsistency and a missing resolution study; worth a referee but not ready to be taken as established. read the letter →

arxiv 2505.18964 v2 pith:HQEOZAKG submitted 2025-05-25 astro-ph.GA astro-ph.CO

Ke-Jung Chen , Meng-Yuan Ho , Pei-Cheng Tung This is my paper · ORCID
classification astro-ph.GAastro-ph.CO
keywords PopulationIIIstarsprimordialstarformationminihalosupersonicturbulencecosmologicalzoom-insimulationturbulentfragmentationMachnumberfirst
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 claims that the first star-forming clouds, which form inside dark matter minihalos before any stars exist, are churned by strongly supersonic turbulence generated purely by gravitational collapse and gas accretion, not by stellar feedback. Using a zoom-in cosmological simulation that starts from a large-volume cosmological box and refines a single minihalo by about a factor of $10^5$, it finds a characteristic Mach number near 5.2 and a kinetic-energy cascade consistent with $k^{-5/3}$ scaling. This turbulence fragments the primordial cloud into multiple clumps instead of allowing monolithic collapse, and one clump, with a mass of $8.07\,M_\odot$ and a size of $0.03$ pc, already exceeds its Jeans mass and is beginning to collapse. If true, accretion-driven supersonic turbulence is a normal part of minihalo assembly and lowers the characteristic mass scale of the first stars.

What carries the argument

The central object is the super-Lagrangian particle-splitting refinement: every gas and dark matter particle is progressively split during the first five million years of the simulation, raising the mass resolution by a factor of about $10^5$ to target masses of $0.19\,M_\odot$ for gas and $80.88\,M_\odot$ for dark matter. This lets the simulation resolve the entire minihalo rather than only its central core, which is what allows the large-scale accretion flow and its turbulence to appear. The load-bearing diagnostics are the gas Mach number distribution, peaking near 5.2, and the kinetic-energy power spectrum, whose turnover at $k \sim 1$ kpc$^{-1}$ marks the driving scale near $3 R_{\rm vir}$ and whose $k^{-5/3}$ slope marks the inertial cascade.

What would settle it

Re-run the same halo with a distinctly different particle-splitting schedule, for example halving or doubling the target gas mass resolution of $0.19\,M_\odot$, or splitting particles over a longer or shorter interval, and compare the Mach number distribution, the kinetic-energy spectrum, and the mass of the most massive bound clump. If the characteristic Mach number changes by more than the expected sampling uncertainty, or if the bound core disappears or changes mass substantially, then the reported supersonic turbulence would be a numerical artifact rather than a property of halo assembly.

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Extended reading notes

Core claim

The paper's central claim is that gravitational collapse alone, during the assembly of a massive minihalo at $z \sim 19$, naturally produces supersonic turbulence with a characteristic Mach number of approximately 5.2. The kinetic-energy power spectrum of the gas follows a $k^{-5/3}$ power law from a driving scale of about three virial radii down to roughly 2 pc, indicating an inertial turbulent cascade. This turbulence stirs the gas and fragments the star-forming cloud into dense clumps, one of which is gravitationally bound with mass $8.07\,M_\odot$, size $0.03$ pc, density $3.9\times10^6$ cm$^{-3}$, and temperature 117 K, exceeding its local Jeans mass of $1.75\,M_\odot$ and beginning to collapse. The author's interpretation is that supersonic turbulence on halo scales, rather than stellar feedback, regulates the mass scale of Population III stars by setting an upper limit on stellar mass through the masses of the collapsing clumps.

Load-bearing premise

The measurement assumes that the $10^5$-fold particle-splitting refinement reproduces the real large-scale accretion flow without injecting spurious velocity perturbations, and the paper presents no resolution study or convergence test showing that the Mach number, the $k^{-5/3}$ spectrum, or the bound-core mass are independent of the splitting schedule and numerical viscosity.

Editorial extensions

If this is right

  • Supersonic turbulence with Mach number near 5.2 forms naturally in a collapsing $10^7\,M_\odot$ minihalo without any stellar feedback.
  • The kinetic-energy spectrum follows $k^{-5/3}$ from the halo scale down to parsec scales, so the turbulence stirs the entire star-forming cloud, not just the central region.
  • The turbulence fragments the primordial cloud into multiple clumps rather than allowing monolithic collapse, lowering the characteristic mass of Population III stars.
  • The identified bound core of $8.07\,M_\odot$ exceeds its Jeans mass and is collapsing, giving an upper bound on the mass of the star that will form from it.
  • Cloud-scale fragmentation, driven by supersonic turbulence, complements disk-scale fragmentation and pushes the characteristic Population III mass down to the roughly 1 to 40 $M_\odot$ range.

Reading between the lines

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

  • Editorial extension: if the turbulent cascade with a driving scale near $3 R_{\rm vir}$ is generic, then zoom-in simulations that start inside the halo may miss the energy injection that sets the clump mass spectrum, implying some reported Population III initial mass functions are biased by their initial conditions.
  • Editorial extension: a clean numerical test would be to run the same halo with and without the early-Universe streaming velocity between baryons and dark matter; since that effect is deliberately omitted here, its inclusion would bracket the turbulence amplitude in realistic patches of the early universe.
  • Editorial extension: if cloud-scale clump masses cap the final stellar masses, then the abundance patterns of extremely metal-poor stars should be dominated by core-collapse and hypernova yields rather than pair-instability supernovae, a prediction that can be compared with stellar archaeology surveys.
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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

4 major / 6 minor

Summary. The paper presents a GIZMO zoom-in simulation of a 1.05e7 solar-mass minihalo at z~20-18.78, using initial conditions from the TNG50 simulation and a super-Lagrangian particle-splitting technique that increases resolution by ~1e5, with GRACKLE primordial chemistry and cooling. The authors report that supersonic turbulence with a characteristic Mach number of ~5.2 develops during halo assembly, that the gas kinetic-energy power spectrum follows a Kolmogorov k^-5/3 scaling, and that a gravitationally bound core of 8.07 solar masses and 0.03 pc size forms. They conclude that accretion-driven supersonic turbulence fragments primordial star-forming clouds and may lower the characteristic mass of Population III stars.

Significance. If the result is robust, it would challenge the traditional picture of quasi-spherical, quiescent collapse in minihalos and would strengthen the emerging view that the first stars can form with relatively low masses. The paper has clear strengths: it uses external large-scale cosmological initial conditions rather than idealized boxes, it couples the simulation to a detailed primordial chemistry network, and it does not fit free parameters to the target claims; the Mach number, spectral slope, and bound-core mass are all simulation outputs. These are falsifiable predictions. However, the central claim currently rests on a single simulation run with internal unit inconsistencies and no convergence testing, so the significance is conditional.

major comments (4)
  1. [§1.2, §2.2, Fig. 4] The claimed driving scale is inconsistent with the simulation volume. Section 1.2 states that the initial conditions are a cubic volume of ~14.7 ckpc per side, which at z~19-20 corresponds to a physical side of ~0.7 kpc and a half-side of ~0.35 kpc, just enough to contain Rvir~0.34 kpc. Section 2.2 and Fig. 4 identify the turbulence driving scale as ~1064 pc ~ 3Rvir ~ 1.0 kpc, which is larger than the whole box and therefore cannot be a resolved physical mode. Moreover, the two wavelength conversions in §2.2 are mutually inconsistent: if k=1 kpc^-1 maps to 1064 pc through lambda=1/k, then k=50 kpc^-1 maps to 20 pc, not the quoted 2 pc; if instead lambda=2*pi/k, then k=1 kpc^-1 corresponds to 6.3 kpc, not 1064 pc. The authors need to define the k convention, correct the unit conversions, and demonstrate that the low-k turnover is not the fundamental box mode; without this, the inertial-range and 3Rvir driving-scale interpretation is unsupported.
  2. [§1.2, §2.2] There is no resolution or convergence study. The resolution is increased by a factor of ~1e5 through super-Lagrangian particle splitting over the first 5 Myr, but the paper does not test whether the splitting schedule, splitting duration, or final mass resolution (0.19 solar masses for gas and 80.9 solar masses for dark matter) affect the measured Mach number, the k^-5/3 spectral slope, or the 8.07 solar-mass bound-core mass. Because particle splitting modifies the particle distribution and can in principle inject spurious velocity perturbations, a convergence test with a different splitting rate or final resolution is necessary before the turbulence can be claimed to 'naturally develop' rather than be a numerical artifact.
  3. [§2.3, Fig. 5] The characteristic Mach number of ~5.2 is computed from the total gas velocity, which includes coherent gravitational infall and accretion streams; indeed Fig. 3 shows supersonic accretion flows around r~5-100 pc. To support the claim of supersonic turbulence rather than supersonic accretion, the authors should separate the turbulent velocity component from the mean flow, for example by subtracting a filtered large-scale velocity field or by using scale-dependent velocity structure functions. As presented, the peak in the Mach-number distribution is not uniquely attributable to turbulence.
  4. [Abstract, §2.3, §3] The generalization that supersonic turbulence 'may be common in primordial halos' is based on a single minihalo and a single bound core. There is no variation of halo mass, spin, assembly history, or environment, and no statistical sample. The conclusion that supersonic turbulence lowers the characteristic mass of Population III stars is therefore an extrapolation; the paper should either add more halo realizations or explicitly restrict the claim to the simulated halo.
minor comments (6)
  1. [§1.2] The phrase 'spacial resolution' should be 'spatial resolution'.
  2. [Abstract, Introduction] The abstract says previous simulations used cosmological box sizes of ~1-2 Mpc, while the Introduction says ~0.3-2 Mpc; these numbers should be made consistent.
  3. [References] The reference 'Turk, Abel, & O'Shea 2009' appears twice in the reference list.
  4. [Fig. 4] Figure 4 lacks axis labels and units, and the text does not state whether E(k) is the three-dimensional spectrum or an angle-averaged one-dimensional spectrum; please specify the normalization and the definition of k.
  5. [Fig. 5] The paper shows a gas mass fraction versus Mach number distribution but does not specify whether the histogram is mass-weighted or volume-weighted, nor over which radial region or density threshold it is computed; please clarify.
  6. [§2.2] The term 'depletion radius' is used for 3Rvir with references to Cuesta et al. (2008), Fong & Han (2021), and Gao et al. (2023); since this is not a standard term, either define it explicitly or replace it with a more common term such as 'splashback radius'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the central results are simulation outputs, and self-citations are used only for external comparison or method description, not to derive the target claims.

full rationale

The paper's central claims—supersonic turbulence with Mach number ~5.2, a Kolmogorov-like k^-5/3 spectrum, and a gravitationally bound 8.07 Msun core—are direct outputs of the GIZMO simulation, not parameters fitted to those claims. The kinetic-energy power spectrum is computed from the simulated gas velocities, and the bound core is identified by a clump-finding algorithm with its mass, size, density, and Jeans mass reported from the simulation. No equation is defined in terms of the result it is supposed to predict, and no fitted parameter is renamed as a prediction. The citations to Tang & Chen (2024) and Tung & Chen (2024), both involving the authors, are not load-bearing in the derivation: Tang & Chen is used as an external interpretation of what Mach > 4 turbulence does to fragmentation, and Tung & Chen is cited alongside other works as an example of particle-splitting methodology. The comparison to Kolmogorov scaling is an external benchmark rather than an input. The absence of a convergence study and the possible inconsistency between the quoted driving scale (~1064 pc) and the simulation volume are numerical and physical concerns, not circularity. Accordingly, no specific circular step can be quoted, and the appropriate score is 0.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim is produced by a simulation rather than a derived theorem, so the ledger records the physical and numerical assumptions on which the reported turbulence and fragmentation depend. The most important uncharged assumption is that the 1e5 particle splitting reproduces the true accretion flow, and that the single TNG50 halo is representative of primordial minihalos.

free parameters (3)
  • Gas particle mass resolution after splitting = 0.19 Msun
    Chosen target resolution; no convergence study verifies that the reported turbulence statistics and bound-core mass are converged at this resolution.
  • Dark matter particle mass resolution after splitting = 80.88 Msun
    Chosen target resolution; gravitational softening scales and force accuracy parameters are not reported.
  • Particle splitting duration and rate = first ~5 Myr
    The refinement is applied during the first five million years of evolution; the influence of this refinement history on the resulting turbulent field is not tested.
assumptions (6)
  • domain assumption Primordial gas chemistry and cooling are fully described by the GRACKLE twelve-species network with no metals or dust.
    Introduced in Section 1.1. The simulation treats the halo gas as metal-free; if TNG50 gas at z=20 has nonzero metallicity or if trace amounts of metals affect cooling, the thermal and fragmentation state could change.
  • domain assumption Initial conditions extracted from TNG50 at z=20, including the FOF group and surrounding volume, provide a valid cosmological environment for a Pop III minihalo.
    Section 1.2. A single halo is selected without stated representative criteria, and the resimulation inherits all modeling choices and limitations of TNG50.
  • ad hoc to paper Super-Lagrangian particle splitting increases resolution by ~1e5 without spuriously modifying the turbulent velocity field.
    Section 1.2. No convergence test demonstrates that the measured Mach number or the k^-5/3 spectrum is independent of the splitting schedule and numerical dissipation.
  • domain assumption Uniform particle refinement is preferable to AMR for capturing volume-filling turbulence.
    Section 1.2. The paper argues that AMR refinement criteria are unreliable in fully turbulent flows, but provides no comparison test between the two approaches.
  • domain assumption Baryon-dark matter streaming velocity is negligible relative to gravitational accretion in this halo.
    Section 3. The paper acknowledges streaming is not included and attributes the supersonic motions to accretion and H2 cooling; the relative contribution of streaming is not tested.
  • domain assumption The kinetic-energy spectrum is interpreted with Kolmogorov's incompressible k^-5/3 scaling even though the flow is highly compressible and supersonic.
    Section 2.2. The paper uses Kolmogorov scaling as the benchmark without deriving or testing its validity for compressible supersonic turbulence.

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Cite this review

Pith. "Pith review of Formation of Supersonic Turbulence in the Primordial Star-forming Cloud." pith.science (2026). https://pith.science/paper/HQEOZAKG

@misc{pith2026250518964,
  author       = {Pith},
  title        = {Pith review of: Formation of Supersonic Turbulence in the Primordial Star-forming Cloud},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HQEOZAKG}},
  note         = {Machine review of arXiv:2505.18964}
}
abstract

We present new simulations of the formation and evolution of the first star-forming cloud within a massive minihalo of mass of $1.05 \times 10^7\, M_{\odot}$, carried out using the GIZMO code with detailed modeling of primordial gas cooling and chemistry. Unlike previous studies that simulated the formation of the first stars within a smaller cosmological boxsize of $\sim 1-2$ Mpc, our work adopts initial conditions from the large-scale cosmological simulations, IllustrisTNG spanning $\sim 50$ Mpc to study the formation of primordial clouds that give birth to the first stars. We increase the original resolution of IllustrisTNG by a factor of $\sim10^5$ using a particle-splitting technique, achieving an extremely high resolution that allows us to resolve turbulence driven by gravitational collapse during early structure formation. We find that strong supersonic turbulence with a characteristic Mach number of $\sim 5.2$ naturally develops within the collapsing halo. This turbulence efficiently stirs the gas, promoting fragmentation of the star-forming cloud into multiple dense clumps. Among them, we identify a gravitationally bound core with a mass of $8.07\,M_{\odot}$ and a size of $0.03$ pc, which exceeds its local Jeans mass and is on the verge of collapsing into a star. Our results indicate that supersonic turbulence may be common in primordial halos and can play a crucial role in cloud-scale fragmentation, potentially lowering the characteristic mass scale of the first stars.

Figures

Figures reproduced from arXiv: 2505.18964 by the authors.

Figure 1
Figure 1. Density evolution during the assembly of a minihalo. Panels from left to right show snapshots at different stages of the evolution. The streamlines illustrate the direction of gas flow. The initially diffuse and featureless gas distribution rapidly evolves into a concentrated gas cloud as the minihalo forms. Filamentary and clumpy structures emerge within the cloud, likely driven by anisotropic accretion flows of pr… view at source ↗
Figure 2
Figure 2. Morphology of a primordial minihalo at z = 18.78. The series of panels shows successive zoom-ins of the gas density from a scale of 40 kpc down to the inner 4 pc of the targeted halo. Clumpy structures become increasingly prominent at smaller scales. In the 4 pc panel, the central region exhibits an elongated dense clump surrounded by a tail of circularly streaming gas, highlighting the complex, anisotropic dynamics… view at source ↗
Figure 3
Figure 3. Physical properties of a primordial halo. Panels show the gas density, dark matter distribution, gas temperature, and M at the end of the simulation. The dashed circle marks the inner region of the halo with a radius of 100 pc. The gas density morphology closely traces the underlying dark matter structure, with dense gas regions coinciding with concentrations of dark matter. The central high-density gas exhibits low… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Kinetic energy power spectrum of gas in the halo. The energy spectrum has a turning point at k ≈ k1, corresponding to a physical scale of 1063 pc—approximately three times the halo’s virial radius. When k > k1, the spectrum follows the Kolmogorov power-law scaling of k…
Figure 5
Figure 5. Figure 5: The gas mass fraction as a function of M. It shows a peak at M ∼ 5.2, with a broad distribution spanning M ∼ 0.5 to 28. shock the gas, leading to the formation of clumpy structures such as giant molecular clouds in the Milky Way. When some of these compressed clumps fo…
Figure 6
Figure 6. Figure 6: Gas temperature–density phase diagram at the end of the simulations. The gas density spans from 10−5 to 106 cm−3 , corresponding to temperatures ranging from 10 to 104 K. For 10−5 < n < 10−2 cm−3 , the temperature increases with density following adiabatic compression …
Figure 7
Figure 7. Figure 7: 3D volume rendering of dense clumps at the center of the halo. Several dense clumps appear as yellow–red nuggets. At this stage, one of the clumps has surpassed the Jeans instability threshold and began to collapse into a Pop III star with a mass of approximately 8.07M…

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Forward citations

Cited by 2 Pith papers

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

  1. Supersonic Turbulence in Primordial Halos: A Comparison With and Without The Stream Velocity

    astro-ph.GA 2025-07 conditional novelty 7.0 of 10

    Stream velocity boosts turbulence in primordial halos below roughly one million solar masses and suppresses it above, with the crossover near the filtering mass.

  2. Turbulence in Primordial Dark Matter Halos and Its Impact on the First Star Formation

    astro-ph.GA 2025-05 conditional novelty 5.0 of 10

    Supersonic turbulence, with Mach numbers 1.8 to 4.2 scaling with halo mass, is common in 15 simulated minihalos and fragments their central gas into Jeans-unstable clumps.

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Works this paper leans on

99 extracted references · 49 canonical work pages · cited by 2 Pith papers

  1. [1]

    2021, MNRAS, 508, 3226

    Abe, M., Yajima, H., Khochfar, S., Dalla Vecchia, C., & Omukai, K. 2021, MNRAS, 508, 3226

    2021

  2. [2]

    L., & Norman, M

    Abel, T., Bryan, G. L., & Norman, M. L. 1998, The Formation and Fragmentation of Primordial Molecular Clouds, arXiv:astro-ph/9810215 [astro-ph]

    arXiv 1998

  3. [3]

    L., & Norman, M

    Abel, T., Bryan, G. L., & Norman, M. L. 2002, Science, 295, 93 Anglés-Alcázar, D., Quataert, E., Hopkins, P. F., et al. 2021, ApJ, 917, 53

    2002

  4. [4]

    C., Honda, S., & Lee, Y

    Aoki, W., Tominaga, N., Beers, T. C., Honda, S., & Lee, Y . S. 2014, Science, 345, 912

    2014

  5. [5]

    2020, A&A, 641, A70

    Bacchini, C., Fraternali, F., Iorio, G., et al. 2020, A&A, 641, A70

    2020

  6. [6]

    1967, Physical Review Letters, 18, 379

    Barkat, Z., Rakavy, G., & Sack, N. 1967, Physical Review Letters, 18, 379

    1967

  7. [7]

    C., & Christlieb, N

    Beers, T. C., & Christlieb, N. 2005, ARA&A, 43, 531

    2005

  8. [8]

    2013, Reports on Progress in Physics, 76, 112901

    Bromm, V . 2013, Reports on Progress in Physics, 76, 112901

    2013

Show all 99 references
  1. [9]

    Bromm, V ., & Larson, R. B. 2004, ARA&A, 42, 79

    2004

  2. [10]

    2015, ApJ, 802, 13

    Chen, K.-J., Bromm, V ., Heger, A., Jeon, M., & Woosley, S. 2015, ApJ, 802, 13

    2015

  3. [11]

    J., et al

    Chen, K.-J., Heger, A., Whalen, D. J., et al. 2017, MNRAS, 467, 4731

    2017

  4. [12]

    J., et al

    Chen, K.-J., Tang, C.-Y ., Whalen, D. J., et al. 2024, ApJ, 964, 91

    2024

  5. [13]

    2018, MNRAS, 475, 4378

    Chiaki, G., Susa, H., & Hirano, S. 2018, MNRAS, 475, 4378

    2018

  6. [14]

    2020, MNRAS, 498, 2676

    Chiaki, G., & Tominaga, N. 2020, MNRAS, 498, 2676

    2020

  7. [15]

    2022, MNRAS, 510, 5199

    Chiaki, G., & Yoshida, N. 2022, MNRAS, 510, 5199

    2022

  8. [16]

    S., Naoz, S., Burkhart, B., Marinacci, F., & V ogelsberger, M

    Chiou, Y . S., Naoz, S., Burkhart, B., Marinacci, F., & V ogelsberger, M. 2021, ApJ, 906, 25

    2021

  9. [17]

    2021, MNRAS, 508, 4175

    Chon, S., Omukai, K., & Schneider, R. 2021, MNRAS, 508, 4175

    2021

  10. [18]

    C., Glover, S

    Clark, P. C., Glover, S. C. O., Smith, R. J., et al. 2011, Science, 331, 1040 10 CHEN, HO,ANDTUNG

    2011

  11. [19]

    J., Prada, F., Klypin, A., & Moles, M

    Cuesta, A. J., Prada, F., Klypin, A., & Moles, M. 2008, MNRAS, 389, 385

    2008

  12. [20]

    G., & Scalo, J

    Elmegreen, B. G., & Scalo, J. 2004, ARA&A, 42, 211 Falceta-Gonçalves, D., Kowal, G., Falgarone, E., & Chian, A. C. L. 2014, Nonlinear Processes in Geophysics, 21, 587

    2004

  13. [21]

    2011, PhRvL, 107, 114504

    Federrath, C., Chabrier, G., Schober, J., et al. 2011, PhRvL, 107, 114504

    2011

  14. [22]

    S., Iapichino, L., & Beattie, J

    Federrath, C., Klessen, R. S., Iapichino, L., & Beattie, J. R. 2021, Nature Astronomy, 5, 365

    2021

  15. [23]

    2023, A&A, 672, A193 Ferrière, K

    Fensch, J., Bournaud, F., Brucy, N., et al. 2023, A&A, 672, A193 Ferrière, K. M. 2001, Reviews of Modern Physics, 73, 1031

    2023

  16. [24]

    2021, MNRAS, 503, 4250

    Fong, M., & Han, J. 2021, MNRAS, 503, 4250

    2021

  17. [25]

    2010, Astronomische Nachrichten, 331, 474

    Frebel, A. 2010, Astronomische Nachrichten, 331, 474

    2010

  18. [26]

    L., Woosley, S

    Fryer, C. L., Woosley, S. E., & Heger, A. 2001, ApJ, 550, 372

    2001

  19. [27]

    P., & Li, Z

    Gao, H., Han, J., Fong, M., Jing, Y . P., & Li, Z. 2023, ApJ, 953, 37

    2023

  20. [28]

    Y ., Semenov, V

    Gnedin, N. Y ., Semenov, V . A., & Kravtsov, A. V . 2018, Journal of Computational Physics, 359, 93

    2018

  21. [29]

    Greif, T. H. 2015, Computational Astrophysics and Cosmology, 2, 3

    2015

  22. [30]

    H., Springel, V ., White, S

    Greif, T. H., Springel, V ., White, S. D. M., et al. 2011, ApJ, 737, 75

    2011

  23. [31]

    Heger, A., & Woosley, S. E. 2002, ApJ, 567, 532 —. 2010, ApJ, 724, 341

    2002

  24. [32]

    2021, A&A, 655, A3

    Hennebelle, P. 2021, A&A, 655, A3

    2021

  25. [33]

    2021, ApJ, 915, 107 —

    Higashi, S., Susa, H., & Chiaki, G. 2021, ApJ, 915, 107 —. 2022, ApJ, 940, 38

    2021

  26. [34]

    2024, ApJ, 962, 158

    Higashi, S., Susa, H., Federrath, C., & Chiaki, G. 2024, ApJ, 962, 158

    2024

  27. [35]

    2017, Science, 357, 1375

    Hirano, S., Hosokawa, T., Yoshida, N., & Kuiper, R. 2017, Science, 357, 1375

    2017

  28. [36]

    Hirano, S., Hosokawa, T., Yoshida, N., Omukai, K., & Yorke, H. W. 2015, MNRAS, 448, 568

    2015

  29. [37]

    2014, ApJ, 781, 60

    Hirano, S., Hosokawa, T., Yoshida, N., et al. 2014, ApJ, 781, 60

    2014

  30. [38]

    2014, The Astrophysical Journal, 781, 60

    Hirano, S., Hosokawa, T., Yoshida, N., et al. 2014, The Astrophysical Journal, 781, 60

    2014

  31. [39]

    Hopkins, P. F. 2015, Monthly Notices of the Royal Astronomical Society, 450, 53–110

    2015

  32. [40]

    F., Wetzel, A., Kereš, D., et al

    Hopkins, P. F., Wetzel, A., Kereš, D., et al. 2018, Monthly Notices of the Royal Astronomical Society, 480, 800–863

    2018

  33. [41]

    2022, ApJL, 929, L30

    Hu, H., Qiu, Y ., Gendron-Marsolais, M.-L., et al. 2022, ApJL, 929, L30

    2022

  34. [42]

    N., Tominaga, N., Kobayashi, C., & Nomoto, K

    Ishigaki, M. N., Tominaga, N., Kobayashi, C., & Nomoto, K. 2018, ApJ, 857, 46

    2018

  35. [43]

    2012, Annual Review of Nuclear and Particle Science, 62, 407

    Janka, H.-T. 2012, Annual Review of Nuclear and Particle Science, 62, 407

    2012

  36. [44]

    C., Almgren, A., Bell, J., et al

    Joggerst, C. C., Almgren, A., Bell, J., et al. 2010, ApJ, 709, 11

    2010

  37. [45]

    E., & Heger, A

    Kasen, D., Woosley, S. E., & Heger, A. 2011, ApJ, 734, 102

    2011

  38. [46]

    C., Bessell, M

    Keller, S. C., Bessell, M. S., Frebel, A., et al. 2014, Nature, 506, 463

    2014

  39. [47]

    Kim, C.-G., & Ostriker, E. C. 2017, ApJ, 846, 133

    2017

  40. [48]

    S., & Glover, S

    Klessen, R. S., & Glover, S. C. O. 2023, ARA&A, 61, 65

    2023

  41. [49]

    S., Heitsch, F., & Mac Low, M.-M

    Klessen, R. S., Heitsch, F., & Mac Low, M.-M. 2000, ApJ, 535, 887

    2000

  42. [50]

    Kolmogorov, A. N. 1991, Proceedings: Mathematical and Physical Sciences, 434, 9

    1991

  43. [51]

    Koo, B.-C., Kim, C.-G., Park, S., & Ostriker, E. C. 2020, ApJ, 905, 35

    2020

  44. [52]

    R., & Burkhart, B

    Krumholz, M. R., & Burkhart, B. 2016, MNRAS, 458, 1671

    2016

  45. [53]

    Larson, R. B. 1979, MNRAS, 186, 479

    1979

  46. [54]

    A., Whalen, D., & Khochfar, S

    Latif, M. A., Whalen, D., & Khochfar, S. 2022, ApJ, 925, 28

    2022

  47. [55]

    2024, MNRAS, 534, 290 Mac Low, M.-M., & Klessen, R

    Liu, B., Gurian, J., Inayoshi, K., et al. 2024, MNRAS, 534, 290 Mac Low, M.-M., & Klessen, R. S. 2004, Reviews of Modern Physics, 76, 125

    2024

  48. [56]

    I., & Woosley, S

    MacFadyen, A. I., & Woosley, S. E. 1999, ApJ, 524, 262

    1999

  49. [57]

    2003, ApJ, 598, 1163

    Maeda, K., & Nomoto, K. 2003, ApJ, 598, 1163

    2003

  50. [58]

    Magg, M., Nordlander, T., Glover, S. C. O., et al. 2020, MNRAS, 498, 3703

    2020

  51. [59]

    2018, MNRAS, 480, 5113

    Marinacci, F., V ogelsberger, M., Pakmor, R., et al. 2018, MNRAS, 480, 5113

    2018

  52. [60]

    F., Stacy, A., & Li, P

    McKee, C. F., Stacy, A., & Li, P. S. 2020, MNRAS, 496, 5528

    2020

  53. [61]

    P., Pillepich, A., Springel, V ., et al

    Naiman, J. P., Pillepich, A., Springel, V ., et al. 2018, MNRAS, 477, 1206

    2018

  54. [62]

    2022, ApJL, 927, L12

    Nakazato, Y ., Chiaki, G., Yoshida, N., et al. 2022, ApJL, 927, L12

    2022

  55. [63]

    2018, MNRAS, 475, 624 —

    Nelson, D., Pillepich, A., Springel, V ., et al. 2018, MNRAS, 475, 624 —. 2019, MNRAS, 490, 3234

    2018

  56. [64]

    2006, Nuclear Physics A, 777, 424

    Nomoto, K., Tominaga, N., Umeda, H., Kobayashi, C., & Maeda, K. 2006, Nuclear Physics A, 777, 424

    2006

  57. [65]

    2001, ApJL, 561, L55

    Omukai, K., & Palla, F. 2001, ApJL, 561, L55

    2001

  58. [66]

    J., Quataert, E., & Sharma, P

    Parrish, I. J., Quataert, E., & Sharma, P. 2010, ApJL, 712, L194

    2010

  59. [67]

    2018, MNRAS, 475, 648

    Pillepich, A., Nelson, D., Hernquist, L., et al. 2018, MNRAS, 475, 648

    2018

  60. [68]

    2019, MNRAS, 490, 3196

    Pillepich, A., Nelson, D., Springel, V ., et al. 2019, MNRAS, 490, 3196

    2019

  61. [69]

    R., Clark, P

    Prole, L. R., Clark, P. C., Klessen, R. S., & Glover, S. C. O. 2022, MNRAS, 510, 4019

    2022

  62. [70]

    2024, MNRAS, 528, 3320

    Ramesh, R., & Nelson, D. 2024, MNRAS, 528, 3320

    2024

  63. [71]

    2024, A&A, 684, L16

    Ramesh, R., Nelson, D., Fielding, D., & Brüggen, M. 2024, A&A, 684, L16

    2024

  64. [72]

    Riaz, R., Bovino, S., Vanaverbeke, S., & Schleicher, D. R. G. 2018, MNRAS, 479, 667

    2018

  65. [73]

    Ruszkowski, M., & Oh, S. P. 2011, MNRAS, 414, 1493

    2011

  66. [74]

    Sharda, P., Federrath, C., & Krumholz, M. R. 2020, MNRAS, 497, 336

    2020

  67. [75]

    Shore, S. N. 1992, An introduction to astrophysical hydrodynamics Skúladóttir, Á., Vanni, I., Salvadori, S., & Lucchesi, R. 2024, A&A, 681, A44

    1992

  68. [76]

    Norman, M. L. 2009, The Astrophysical Journal, 691, 441

    2009

  69. [77]

    D., Bryan, G

    Smith, B. D., Bryan, G. L., Glover, S. C. O., et al. 2017, MNRAS, 466, 2217 PRIMORDIALTURBULENCE11

    2017

  70. [78]

    2003, MNRAS, 339, 289

    Springel, V ., & Hernquist, L. 2003, MNRAS, 339, 289

    2003

  71. [79]

    Springel, V ., White, S. D. M., Tormen, G., & Kauffmann, G. 2001, MNRAS, 328, 726

    2001

  72. [80]

    2018, MNRAS, 475, 676

    Springel, V ., Pakmor, R., Pillepich, A., et al. 2018, MNRAS, 475, 676

    2018

  73. [81]

    H., & Bromm, V

    Stacy, A., Greif, T. H., & Bromm, V . 2010, MNRAS, 403, 45

    2010

  74. [82]

    F., Lee, A

    Stacy, A., McKee, C. F., Lee, A. T., Klein, R. I., & Li, P. S. 2022, MNRAS, 511, 5042

    2022

  75. [83]

    2014, ApJ, 792, 32

    Susa, H., Hasegawa, K., & Tominaga, N. 2014, ApJ, 792, 32

    2014

  76. [84]

    2024, MNRAS, 529, 4248

    Tang, C.-Y ., & Chen, K.-J. 2024, MNRAS, 529, 4248

    2024

  77. [85]

    J., et al

    Tegmark, M., Silk, J., Rees, M. J., et al. 1997, The Astrophysical Journal, 474, 1–12

    1997

  78. [86]

    2009, ApJ, 690, 526

    Tominaga, N. 2009, ApJ, 690, 526

    2009

  79. [87]

    2007, ApJ, 660, 516

    Tominaga, N., Umeda, H., & Nomoto, K. 2007, ApJ, 660, 516

    2007

  80. [88]

    2010, Phys

    Tseliakhovich, D., & Hirata, C. 2010, Phys. Rev. D, 82, 083520

    2010

  81. [89]

    2024, arXiv e-prints, arXiv:2412.16440

    Tung, P.-C., & Chen, K.-J. 2024, arXiv e-prints, arXiv:2412.16440

    2024 arXiv

  82. [91]

    J., Abel, T., & O’Shea, B

    Turk, M. J., Abel, T., & O’Shea, B. 2009, Science, 325, 601

    2009

  83. [92]

    2002, ApJ, 565, 385

    Umeda, H., & Nomoto, K. 2002, ApJ, 565, 385

    2002

  84. [93]

    Wollenberg, K. M. J., Glover, S. C. O., Clark, P. C., & Klessen, R. S. 2020, MNRAS, 494, 1871

    2020

  85. [94]

    Woosley, S. E. 1993, ApJ, 405, 273 —. 2017, ApJ, 836, 244

    1993

  86. [95]

    E., Blinnikov, S., & Heger, A

    Woosley, S. E., Blinnikov, S., & Heger, A. 2007, Nature, 450, 390

    2007

  87. [96]

    E., Heger, A., & Weaver, T

    Woosley, S. E., Heger, A., & Weaver, T. A. 2002, Reviews of Modern Physics, 74, 1015

    2002

  88. [97]

    2023, Nature, 618, 712

    Xing, Q.-F., Zhao, G., Liu, Z.-W., et al. 2023, Nature, 618, 712

    2023

  89. [98]

    2008, Science, 321, 669

    Yoshida, N., Omukai, K., & Hernquist, L. 2008, Science, 321, 669

    2008

  90. [99]

    H., Ho, K

    Yuen, K. H., Ho, K. W., Law, C. Y ., Chen, A., & Lazarian, A. 2022, Turbulent universal galactic Kolmogorov velocity cascade over 6 decades,arXiv:2204.13760 [astro-ph.GA]

    2022 arXiv

  91. [100]

    E., & Heger, A

    Zhang, W., Woosley, S. E., & Heger, A. 2008, ApJ, 679, 639

    2008

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