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On the origin of compressive turbulence in protoclumps in high redshift disks

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Giant clumps in high-redshift disks can be born from compressive tides and stream-disk collisions, not only from classic Toomre instability.

desk verdict Solid correlational extension to eight galaxies, but the tidal tensor's self-gravity contamination undercuts the causal claim; worth reviewing with a demand to address it. read the letter →

arxiv 2501.07097 v2 pith:STIPLNCK submitted 2025-01-13 astro-ph.GA

Omry Ginzburg , Avishai Dekel , Nir Mandelker , Dhruba Dutta Chowdhury , Frederic Bournaud , Daniel Ceverino , Joel Primack This is my paper · ORCID
classification astro-ph.GA
keywords high-redshiftgalaxiesgiantclumpscompressiveturbulencetidaltensorcoldstreamsdiskinstabilityToomreQcosmologicalsimulations
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

High-redshift galactic disks form giant star-forming clumps, and the standard explanation is Toomre instability: the disk fragments where its stability parameter Q drops below unity. This paper argues that in realistic cosmological settings clumps can instead form in regions where Q is well above unity, because the surrounding environment can do the squeezing. Using zoom-in cosmological simulations, it shows that protoclump regions systematically sit in compressive tidal fields, with about 25% of them fully compressive, and at sites where cold streams hit the disk carrying 2-10 times the average stream mass. These environmental drivers correlate with the excess of converging turbulence measured in protoclumps, so the paper proposes them as the origin of the compressive modes that let collapse start before self-gravity takes over. If right, this replaces the linear Toomre picture with a non-linear, environmentally driven mode of violent disk instability.

What carries the argument

The analysis rests on three local diagnostics computed on a 0.2 kpc grid. fconv is the fraction of turbulent kinetic energy in converging modes, defined as the negative-divergence part of the velocity field divided by the full divergence and curl contributions, specifically |∇·v|²_neg over |∇·v|² plus |∇×v|². ftides is defined as (λ2+λ3)/λ1 using the eigenvalues of the tidal tensor T_ij = ∂²φ/∂r_i∂r_j, where positive eigenvalues mean compression, so positive ftides indicates substantially compressive tides and λ3 > 0 indicates fully compressive tides. fstr is the mass of stream material in a protoclump's angular bin divided by the mean stream mass in the surrounding annulus, with stream material identified by backtracking gas cells along streamlines over a dynamical time. Protoclumps are defined as the 0.5 kpc regions from which tracked clumps collapse, and each protoclump is compared against a random patch at the same galactocentric radius.

What would settle it

A simulation with tracer particles that follows protoclumps backward in time could settle the order of events: if the excess converging turbulence and compressive tides appear only after the protoclump's own density enhancement starts to grow, rather than before, the proposed environmental drivers are consequences, not causes. Alternatively, recomputing the tidal Hessian after masking out the protoclump's own mass, and finding that most protoclump regions then have the smallest eigenvalue λ3 below zero, would falsify the claim that external compressive tides precede clump formation.

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Extended reading notes

Core claim

Protoclump regions in the VELA cosmological simulations are not random disk patches. Almost all of them have a positive tidal compression parameter ftides, averaging about 0.32, meaning the local tidal field is substantially compressive along at least two directions, and in about 25% of protoclumps the tidal field is fully compressive, with all three eigenvalues of the tidal tensor positive. No random patch shows fully compressive tides. About 70% of protoclumps reside in stream-disk interaction sites, with stream mass fractions 2-10 times the angular average at the same galactocentric radius, while random patches cluster near a fraction of about 0.8. The fraction of turbulent kinetic energy in converging modes is correspondingly high in protoclumps, with a median fconv near 0.5 versus about 0.21 in random patches, and it rises with both ftides and fstr, with Spearman correlation coefficients of about 0.46 and 0.3 respectively. The paper concludes that compressive tides and inflowing streams can drive the excess compressive turbulence that initiates clump formation, constituting a new non-linear mode of violent disk instability in high-redshift galaxies.

Load-bearing premise

The load-bearing assumption is that the measured squeeze-and-stretch forces around a protoclump come from the galaxy and its surroundings, not from the protoclump's own mass or a nearby disk feature; if local self-gravity dominates the signal, the compressive tides would be a result of collapse rather than its cause.

Editorial extensions

If this is right

  • Clump formation in high-redshift disks can proceed where the Toomre Q parameter is much larger than unity, so linear Toomre stability is not a sufficient criterion in cosmological disks.
  • The contrast between cosmological and isolated simulations is explained: external tides and streams are present only in the cosmological case, matching the observed excess of compressive turbulence in cosmological protoclumps.
  • The positive correlations of converging turbulence with both ftides and fstr identify two concrete environmental drivers that a future theory of disk fragmentation must include.
  • Protoclumps can be recognized by compressive tidal fields and stream-impact sites rather than by low Q alone, which gives simulations and observations a new way to find clump formation sites.
  • A complementary non-linear theory of violent disk instability, balancing converging modes against solenoidal and shear modes, is needed in place of the Toomre-based picture.

Reading between the lines

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

  • If the causal ordering holds, clump formation should be predictable from maps of the tidal tensor and stream geometry alone, before any density threshold is crossed; this could be tested in simulations that mask the protoclump's own mass when computing the Hessian.
  • Tracking protoclump trajectories with tracer particles would distinguish whether compressive tides or stream impacts lead the process, since the current diagnostics are measured at a single formation snapshot.
  • Observationally, giant clumps at high redshift should preferentially lie near the projected intersections of cold inflows with the disk, and their internal velocity fields should show an excess of converging relative to solenoidal power.
  • Because compressive driving raises star formation efficiency, the same environmental drivers may boost star formation inside protoclumps even before collapse, linking this formation channel to the measured clump contribution to total star formation.
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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

3 major / 5 minor

Summary. This paper studies protoclump regions in eight VELA3 cosmological zoom-in simulations, testing two candidate external drivers of the excess compressive turbulence found earlier in these protoclumps: compressive gravitational tides from the cosmological environment and direct driving by inflowing gas streams. The authors define three diagnostics: fconv, the local fraction of kinetic energy in converging modes of turbulence; ftides, a dimensionless measure of how compressive the gravitational tidal tensor is; and fstr, the local excess of stream material relative to the azimuthal average at the same galactocentric radius. They compare protoclumps to matched random disk patches and report that protoclumps have higher fconv, preferentially positive ftides (median ~0.33, with ~25% fully compressive), and enhanced fstr (median ~2.5), with Spearman correlations of 0.46 (ftides vs fconv) and 0.30 (fstr vs fconv). The paper concludes that compressive tides and stream-disk interactions can drive the compressive turbulence that initiates clump formation in disks where Toomre Q is high.

Significance. If the causal interpretation were established, the paper would provide a new, plausible mechanism for giant clump formation in high-z disks that is complementary to classical Toomre instability, and it would connect clump formation to cosmological processes (tides and cold streams). The work extends the earlier single-galaxy analysis of Mandelker et al. (2025) to eight galaxies and introduces a quantitative, local definition of tidal compressiveness (ftides) that is clearly explained. The authors are transparent about many caveats, including the absence of tracer particles in the stream analysis and the correlational nature of the analysis. However, the central evidence for the tidal mechanism is weakened by a selection effect that has not been controlled for, as detailed below; the stream analysis is more robust but still crude. The paper is clearly written and would be of interest to the community if the tidal result can be made self-contamination-free.

major comments (3)
  1. [§2.4, §3.2.2, Fig. 5] The tidal tensor is defined as the Hessian of the full gravitational potential, so through Poisson's equation it necessarily contains the local density enhancement of the protoclump itself. Since protoclumps are defined as δ > 10 density peaks, their self-gravity contributes positive eigenvalues in all three directions (a uniform sphere gives λ1=λ2=λ3=4πGρ/3 and ftides=2). Therefore the median ftides > 0 and the 25% fully compressive fraction may be a direct consequence of the density selection used to identify protoclumps, not evidence of external compressive tides. The argument in §3.2.2 that Q >> 1 implies the protoclump is not self-gravitating does not address this, because Toomre Q is a stability criterion involving velocity dispersion and surface density, not a measure of the local density contribution to the Hessian. The random-patch comparison is also not a valid control, since random patches are not selected to be density peaks. The isolated-simulation comparison in Fig. 8 still shows a positive median ftides ~ 0.2 in protoclumps, which is consistent with a self-gravity floor, and the absence of λ3 > 0 there may reflect different density contrasts or simulation setups rather than the absence of external tides. The authors should recompute the tidal tensor after removing or smoothing the protoclump's own mass (e.g., using a potential computed from the density field smoothed on scales larger than RPC) or quantify and subtract the self term.
  2. [§3.3, Fig. 7, Conclusions] The causal language in the abstract and conclusions ("can thus serve as the drivers of excessive compressive turbulence") goes beyond what the correlations establish. A compressive converging flow (which is exactly what a high fconv means) compresses gas and raises the local density, which in turn raises the self-gravity contribution to ftides; thus the ftides-fconv correlation may be partly a physical consequence of the same converging motion rather than evidence that tides drive that motion. The paper states in §3.3 that causality is not straightforward to establish, but the concluding sections present the correlation as support for a driver role. Please either soften the causal claims or add a time-lagged test, e.g., measuring ftides at an earlier snapshot before the converging flow develops, or comparing regions with similar density but different ftides.
  3. [§2.5, §3.2.3] The stream indicator fstr relies on approximating fluid-element trajectories with a snapshotted velocity field held constant over a disk dynamical time, and it is a mass-based proxy without tracer particles. The paper acknowledges these limitations, but the quantitative claims (70% of protoclumps are stream-interaction sites, fstr = 2–10) are sensitive to the choices of the 10% disk-radius threshold, the backtracking time, and the angular bin size, none of which are varied here. Since protoclumps are dense and may be associated with slow, non-circular flows, the streamline method could systematically misclassify a fraction of the dense gas as 'stream' material. Please report a sensitivity test over these parameters, and ideally compare with a tracer-based identification if any such testbed is available.
minor comments (5)
  1. [Fig. 5 caption] The right-panel caption and x-axis label contain an apparent typo ('log (20 3)' instead of 'log(20λ3)'), and the explanation of how negative λ3 values are encoded on the logarithmic axis is hard to follow; consider plotting λ3 directly or using a two-panel presentation for positive and negative values.
  2. [§2.1] The phrase 'maximal resolution' should be 'maximum resolution' for standard English usage.
  3. [§3.2.2 and Fig. 5] The text reports a median ftides of 0.32 for protoclumps and −0.26 for random patches, while the figure caption quotes 0.33 and −0.27; please make the numbers consistent.
  4. [§3.3] The p-values for the Spearman correlations appear only in the Fig. 7 caption and are missing from the body text; include them in the text where the correlation coefficients are reported.
  5. [§2.5] The term 'disk dynamical time' is used but not explicitly defined; give the formula or reference used for this timescale.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the three diagnostics (fconv, ftides, fstr) are measured from independent simulation fields, the paper is explicitly correlational, and the one self-gravity confound is flagged and partially controlled by an isolated simulation.

full rationale

The paper's central claims are correlations, not derivations: fconv comes from the velocity divergence and curl (eqs. 8-9 and Sect. 2.3.2), ftides from the Hessian of the gravitational potential (Sect. 2.4, eq. 14), and fstr from streamline back-tracing (Sect. 2.5, eq. 15). No fitted parameter is constructed from the target quantity, and no equation makes a diagnostic equal to the protoclump-selection criterion by construction. The closest concern is that the tidal tensor includes the protoclump's own density through trace(T) = 4πGρ, so positive ftides may partly reflect self-gravity rather than external tides. However, the paper explicitly acknowledges this possibility in Sect. 3.2.2, and it performs an isolated-galaxy control (Sect. 4.1, Fig. 8) in which protoclumps do not show fully compressive tides, weakening the claim that the signal is a pure selection artifact. Self-citations to M25 and Inoue et al. (2016) provide prior simulation measurements and are not used as uniqueness theorems or to forbid alternatives. The remaining caveats about tracerless stream identification and tidal-source ambiguity are stated as limitations, not hidden as predictions. The derivation chain is therefore self-contained rather than circular.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

No fitted parameters are used; the analysis is correlational. The main analysis choices are the protoclump radius and the streamline back-tracing interval. Background assumptions concern the reliability of the simulations, the local turbulence decomposition, and the stream identification.

free parameters (2)
  • Protoclump radius RPC = 0.5 kpc (0.8 kpc check)
    Defines the region for all local measurements; chosen from clump radii and contraction factors, not fitted. The authors state results are qualitatively unchanged at 0.8 kpc.
  • Stream tracing lookback time = one disk dynamical time
    Fixed by the streamline method of Dutta Chowdhury et al. 2024; only one value is used and it is not fitted. The fstr indicator is sensitive to this choice.
assumptions (3)
  • domain assumption The VELA simulations resolve the physical processes relevant to protoclump formation at ~0.2 kpc scales, despite not resolving the full turbulence cascade.
    Invoked throughout Sections 2.1-2.3; the authors acknowledge in Section 2.3.2 that the turbulence cascade is not properly resolved and that the converging flows lie near the beginning of the inertial range.
  • domain assumption Local turbulent kinetic energy in a protoclump can be represented by |div v|^2 and |curl v|^2, with the shearing term neglected.
    This is the basis for fconv in Section 2.3.2. The authors justify it qualitatively in Section 4.3 by finding |div v| ~ 2 mu_1 in protoclumps, but the assumption is not formally proven.
  • domain assumption Single-snapshot streamline back-tracing with a frozen velocity field correctly identifies accreted stream material in the absence of tracer particles.
    Used to define fstr in Section 2.5; the authors flag it as crude and noisy in Section 3.3, and note that tracer particles are needed for a proper isolation of accreted material.

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Pith. "Pith review of On the origin of compressive turbulence in protoclumps in high redshift disks." pith.science (2026). https://pith.science/paper/STIPLNCK

@misc{pith2026250107097,
  author       = {Pith},
  title        = {Pith review of: On the origin of compressive turbulence in protoclumps in high redshift disks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/STIPLNCK}},
  note         = {Machine review of arXiv:2501.07097}
}
abstract

The giant, star forming clumps in gas-rich, high redshift disks are commonly assumed to form due to gravitational instabilities, in which protoclumps have a Toomre-$Q$ parameter less than unity. However, some cosmological simulations show that clumps can form in regions where $Q\gg1$. In these simulations, there is an excess of compressive modes of turbulence that lead to gravitational collapse of regions that were not supposed to gravitationally collapse, according to linear theory. In contrast, sites of clump formation in isolated simulations do not show this excess, hinting that the origin may be external. We explore two external mechanisms that can induce compressive modes of disk turbulence in protoclumps, namely, compressive tides exerted by the cosmological environment and the direct driving by inflowing streams. We correlate the local strength of compressive tides and the amount of fresh stream material with protoclump regions in zoom-in cosmological simulations. The local strength of compressive tides is derived from the tidal tensor. The local strength of incoming streams is derived from the fractional presence of the stream compared to the average. We find that the tidal field in protoclumps tends to be over-compressive while random patches in the disk show diverging tides. In particular, in $25\%$ of the protoclumps, the tidal field is fully compressive, while no random patch resides in regions of fully compressive tides. In addition, protoclumps tend to reside in regions where the fraction of incoming stream mass is 2-10 times larger than the average at the same galactocentric radius. Both compressive tides and inflowing streams are correlated with the protoclumps and can thus serve as the drivers of excessive compressive turbulence that can initiate clump formation. This constitutes a new, non-linear mode of violent disk instabilities in high-$z$ galaxies.

Figures

Figures reproduced from arXiv: 2501.07097 by the authors.

Figure 1
Figure 1. Proof of concept for fstr. The background color shows the pro￾jected surface density of gas in V07 at z ∼ 2 (top) and in V08 at z ∼ 1 (bottom). The contours are of fstr in angular bins at a radius of 8 kpc in both panels. We can see how fstr increases in regions where the stream interacts with the disk. compressive along at least two directions (those of λ1 and λ2), and potentially fully compressive. If ftides < 0, … view at source ↗
Figure 2
Figure 2. The temporal evolution of the global fraction of turbulent energy in converging and diverging (blue curve) and only converging (i.e. only cells with ∇ · v < 0; red curve) flows, for three galaxies from our suite. The vertical black line indicates the moment of the blue nugget phase in each galaxy (Lapiner et al. 2023). The horizontal solid (dashed) lines indicate one third (sixth) of the total energy, values expecte… view at source ↗
Figure 3
Figure 3. Correlation of fconv with gas density in protoclump regions. In the left panels, we show the projected surface density of the gas. The top row represents V07 at z ∼ 2 while the bottom row represents V08 at z ∼ 1, as in figure 1. The black circles indicate the location of a protoclump region. The white circle is the disk radius, defined as the radius that contains 85% of the cold gas in the disk. In the right panels,… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: The probability distribution of fconv in protoclump regions (green histogram) and random patches (orange histogram) over all eight galax￾ies. The vertical lines of each color indicate the median of the corre￾sponding distribution. We can see that protoclump regions hav…
Figure 5
Figure 5. Figure 5: Probability distributions of ftides (left) and λ3 (right) in protoclump regions (green histograms) and random patches (orange histograms). Left: The vertical lines of each color indicate the median of the corresponding distribution, 0.33 and −0.27 for protoclumps and r…
Figure 6
Figure 6. Figure 6: Same as figure 4, but for fstr, which measures the amount of stream mass in a given region (see text). The vertical black line is at fstr = 1. We can see that protoclump regions tend to have larger fstr than random patches, indicating that they reside in regions with i…
Figure 7
Figure 7. Figure 7: Correlations between fconv (x-axis) and ftides (left) or fstr (right). Each point is either a protoclump (green points) or a random patch (orange points). The histograms are the projected distributions of the corresponding quantity. The vertical black lines correspond …
Figure 8
Figure 8. Figure 8: The same as figure 5, but for the protoclumps in the isolated galaxy simulation. We can see that the protoclumps in the isolated galaxy simulation are in regions where the tidal field is only weakly compressive, and are not much different than the random patches. Furth…

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Works this paper leans on

120 extracted references · 55 canonical work pages

  1. [1]

    2009 a , , 392, 294

    Agertz , O., Lake , G., Teyssier , R., et al. 2009 a , , 392, 294

    2009

  2. [2]

    2009 b , , 397, L64

    Agertz , O., Teyssier , R., & Moore , B. 2009 b , , 397, L64

    2009

  3. [3]

    2013, Physica D Nonlinear Phenomena, 247, 54

    Aluie , H. 2013, Physica D Nonlinear Phenomena, 247, 54

    2013

  4. [4]

    2025, , 695, A155

    Arora , R., Federrath , C., Krumholz , M., & Banerjee , R. 2025, , 695, A155

    2025

  5. [5]

    2024, , 532, 2965

    Aung , H., Mandelker , N., Dekel , A., et al. 2024, , 532, 2965

    2024

  6. [6]

    2019, , 490, 181

    Aung , H., Mandelker , N., Nagai , D., Dekel , A., & Birnboim , Y. 2019, , 490, 181

    2019

  7. [7]

    & Tremaine , S

    Binney , J. & Tremaine , S. 2008, Galactic Dynamics: Second Edition

    2008

  8. [8]

    & Elmegreen , B

    Bournaud , F. & Elmegreen , B. G. 2009, , 694, L158

    2009

Show all 120 references
  1. [9]

    G., Teyssier , R., Block , D

    Bournaud , F., Elmegreen , B. G., Teyssier , R., Block , D. L., & Puerari , I. 2010, , 409, 1088

    2010

  2. [10]

    2014, , 780, 57

    Bournaud , F., Perret , V., Renaud , F., et al. 2014, , 780, 57

    2014

  3. [11]

    Brunt , C. M. & Federrath , C. 2014, , 442, 1451

    2014

  4. [12]

    2018, Nature Astronomy, 2, 76

    Cava , A., Schaerer , D., Richard , J., et al. 2018, Nature Astronomy, 2, 76

    2018

  5. [13]

    2010, , 404, 2151

    Ceverino , D., Dekel , A., & Bournaud , F. 2010, , 404, 2151

    2010

  6. [14]

    2012, , 420, 3490

    Ceverino , D., Dekel , A., Mandelker , N., et al. 2012, , 420, 3490

    2012

  7. [15]

    & Klypin , A

    Ceverino , D. & Klypin , A. 2009, , 695, 292

    2009

  8. [16]

    S., et al

    Ceverino , D., Klypin , A., Klimek , E. S., et al. 2014, , 442, 1545

    2014

  9. [17]

    F., et al

    Ceverino , D., Mandelker , N., Snyder , G. F., et al. 2023, , 522, 3912

    2023

  10. [18]

    1961, Hydrodynamic and hydromagnetic stability

    Chandrasekhar , S. 1961, Hydrodynamic and hydromagnetic stability

    1961

  11. [19]

    2018, , 479, 973

    Codis , S., Pogosyan , D., & Pichon , C. 2018, , 479, 973

    2018

  12. [20]

    2012, , 422, 1732

    Danovich , M., Dekel , A., Hahn , O., & Teyssier , R. 2012, , 422, 1732

    2012

  13. [21]

    & Burkert , A

    Dekel , A. & Burkert , A. 2014, , 438, 1870

    2014

  14. [22]

    2003, , 341, 326

    Dekel , A., Devor , J., & Hetzroni , G. 2003, , 341, 326

    2003

  15. [23]

    2020, , 493, 4126

    Dekel , A., Ginzburg , O., Jiang , F., et al. 2020, , 493, 4126

    2020

  16. [24]

    2022, , 511, 316

    Dekel , A., Mandelker , N., Bournaud , F., et al. 2022, , 511, 316

    2022

  17. [25]

    2009, , 703, 785

    Dekel , A., Sari , R., & Ceverino , D. 2009, , 703, 785

    2009

  18. [26]

    C., et al

    Dekel , A., Tziperman , O., Sarkar , K. C., et al. 2023, , 521, 4299

    2023

  19. [27]

    & Perrier, V

    Deriaz, E. & Perrier, V. 2009, Applied and Computational Harmonic Analysis, 26, 249

    2009

  20. [28]

    2024, arXiv e-prints, arXiv:2409.01589

    Dutta Chowdhury , D., Dekel , A., Mandelker , N., Ginzburg , O., & Genzel , R. 2024, arXiv e-prints, arXiv:2409.01589

    2024

  21. [29]

    a rn , T., Agertz , O., \

    Ejdetj \"a rn , T., Agertz , O., \"O stlin , G., Renaud , F., & Romeo , A. B. 2022, , 514, 480

    2022

  22. [30]

    Elmegreen , B. G. 2011, , 737, 10

    2011

  23. [31]

    Elmegreen , B. G. & Burkert , A. 2010, , 712, 294

    2010

  24. [32]

    1992, Annual Review of Fluid Mechanics, 24, 395

    Farge , M. 1992, Annual Review of Fluid Mechanics, 24, 395

    1992

  25. [33]

    2018, Physics Today, 71, 38

    Federrath , C. 2018, Physics Today, 71, 38

    2018

  26. [34]

    & Klessen , R

    Federrath , C. & Klessen , R. S. 2012, , 761, 156

    2012

  27. [35]

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

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

    2021

  28. [36]

    M., Longmore , S

    Federrath , C., Rathborne , J. M., Longmore , S. N., et al. 2017, in IAU Symposium, Vol. 322, The Multi-Messenger Astrophysics of the Galactic Centre, ed. R. M. Crocker , S. N. Longmore , & G. V. Bicknell , 123--128

    2017

  29. [37]

    S., Schmidt , W., & Mac Low , M

    Federrath , C., Roman-Duval , J., Klessen , R. S., Schmidt , W., & Mac Low , M. M. 2010, , 512, A81

    2010

  30. [38]

    & Bournaud , F

    Fensch , J. & Bournaud , F. 2020, arXiv e-prints, arXiv:2011.12966

    2020 arXiv

  31. [39]

    2023, , 672, A193

    Fensch , J., Bournaud , F., Brucy , N., et al. 2023, , 672, A193

    2023

  32. [40]

    B., Glazebrook , K., Abraham , R

    Fisher , D. B., Glazebrook , K., Abraham , R. G., et al. 2017, , 839, L5

    2017

  33. [41]

    Folini , D., Walder , R., & Favre , J. M. 2014, , 562, A112

    2014

  34. [42]

    C., Emami , R., Somerville , R

    Forbes , J. C., Emami , R., Somerville , R. S., et al. 2023, , 948, 107

    2023

  35. [43]

    M., Shapley , A

    F \"o rster Schreiber , N. M., Shapley , A. E., Genzel , R., et al. 2011, , 739, 45

    2011

  36. [44]

    o rster Schreiber , N. M., \

    F \"o rster Schreiber , N. M., \"U bler , H., Davies , R. L., et al. 2019, , 875, 21

    2019

  37. [45]

    2024, arXiv e-prints, arXiv:2402.18543

    Fujimoto , S., Ouchi , M., Kohno , K., et al. 2024, arXiv e-prints, arXiv:2402.18543

    2024 arXiv

  38. [46]

    Gabor , J. M. & Bournaud , F. 2014, , 437, L56

    2014

  39. [47]

    2009, Large Eddy Simulation for Compressible Flows

    Garnier , E., Adams , N., & Sagaut , P. 2009, Large Eddy Simulation for Compressible Flows

    2009

  40. [48]

    2008, , 687, 59

    Genzel , R., Burkert , A., Bouch \'e , N., et al. 2008, , 687, 59

    2008

  41. [49]

    M., Lang , P., et al

    Genzel , R., F \"o rster Schreiber , N. M., Lang , P., et al. 2014, , 785, 75

    2014

  42. [50]

    B., Liu , D., et al

    Genzel , R., Jolly , J. B., Liu , D., et al. 2023, , 957, 48

    2023

  43. [51]

    2011, , 733, 101

    Genzel , R., Newman , S., Jones , T., et al. 2011, , 733, 101

    2011

  44. [52]

    Ginzburg , O., Dekel , A., Mandelker , N., & Krumholz , M. R. 2022, , 513, 6177

    2022

  45. [53]

    2021, , 501, 730

    Ginzburg , O., Huertas-Company , M., Dekel , A., et al. 2021, , 501, 730

    2021

  46. [54]

    J., Krumholz , M

    Goldbaum , N. J., Krumholz , M. R., & Forbes , J. C. 2015, , 814, 131

    2015

  47. [55]

    & Lynden-Bell , D

    Goldreich , P. & Lynden-Bell , D. 1965, , 130, 97

    1965

  48. [56]

    & Gedalin , M

    Griv , E. & Gedalin , M. 2012, , 422, 600

    2012

  49. [57]

    C., Bell , E

    Guo , Y., Ferguson , H. C., Bell , E. F., et al. 2015, , 800, 39

    2015

  50. [58]

    F., et al

    Guo , Y., Rafelski , M., Bell , E. F., et al. 2018, , 853, 108

    2018

  51. [59]

    & Falgarone , E

    Hennebelle , P. & Falgarone , E. 2012, , 20, 55

    2012

  52. [60]

    Hopkins , P. F. & Christiansen , J. L. 2013, , 776, 48

    2013

  53. [61]

    F., Kere s , D., & Murray , N

    Hopkins , P. F., Kere s , D., & Murray , N. 2013, , 432, 2639

    2013

  54. [62]

    F., Quataert , E., & Murray , N

    Hopkins , P. F., Quataert , E., & Murray , N. 2012, , 421, 3488

    2012

  55. [63]

    2020, , 499, 814

    Huertas-Company , M., Guo , Y., Ginzburg , O., et al. 2020, , 499, 814

    2020

  56. [64]

    2004, , 611, 20

    Immeli , A., Samland , M., Westera , P., & Gerhard , O. 2004, , 611, 20

    2004

  57. [65]

    2016, , 456, 2052

    Inoue , S., Dekel , A., Mandelker , N., et al. 2016, , 456, 2052

    2016

  58. [66]

    & Yoshida , N

    Inoue , S. & Yoshida , N. 2018, , 474, 3466

    2018

  59. [67]

    Jim \'e nez , E., Lagos , C. d. P., Ludlow , A. D., & Wisnioski , E. 2023, , 524, 4346

    2023

  60. [68]

    Jog , C. J. 2014, , 147, 132

    2014

  61. [69]

    S., Silverman , J

    Kalita , B. S., Silverman , J. D., Daddi , E., et al. 2024, , 960, 25

    2024

  62. [70]

    A., Weiner , B

    Kassin , S. A., Weiner , B. J., Faber , S. M., et al. 2012, , 758, 106

    2012

  63. [71]

    & Orszag , S

    Kida , S. & Orszag , S. A. 1990, Journal of Scientific Computing, 5, 85

    1990

  64. [72]

    Klessen , R. S. & Hennebelle , P. 2010, , 520, A17

    2010

  65. [73]

    V., Klypin , A

    Kravtsov , A. V., Klypin , A. A., & Khokhlov , A. M. 1997, , 111, 73

    1997

  66. [74]

    G., Nordlund , A ., Collins , D., et al

    Kritsuk , A. G., Nordlund , A ., Collins , D., et al. 2011, , 737, 13

    2011

  67. [75]

    G., Norman , M

    Kritsuk , A. G., Norman , M. L., Padoan , P., & Wagner , R. 2007, , 665, 416

    2007

  68. [76]

    & Burkert , A

    Krumholz , M. & Burkert , A. 2010, , 724, 895

    2010

  69. [77]

    R., Burkhart , B., Forbes , J

    Krumholz , M. R., Burkhart , B., Forbes , J. C., & Crocker , R. M. 2018, , 477, 2716

    2018

  70. [78]

    2023, , 522, 4515

    Lapiner , S., Dekel , A., Freundlich , J., et al. 2023, , 522, 4515

    2023

  71. [79]

    L., et al

    Li , H., Vogelsberger , M., Bryan , G. L., et al. 2022, , 514, 265

    2022

  72. [80]

    C., Jones , T

    Livermore , R. C., Jones , T. A., Richard , J., et al. 2015, , 450, 1812

    2015

  73. [81]

    Lovelace , R. V. E. & Hohlfeld , R. G. 1978, , 221, 51

    1978

  74. [82]

    2017, , 464, 635

    Mandelker , N., Dekel , A., Ceverino , D., et al. 2017, , 464, 635

    2017

  75. [83]

    2025, , 538, L9

    Mandelker , N., Ginzburg , O., Dekel , A., et al. 2025, , 538, L9

    2025

  76. [84]

    2020, , 494, 2641

    Mandelker , N., Nagai , D., Aung , H., et al. 2020, , 494, 2641

    2020

  77. [85]

    G., Brodie , J

    Mandelker , N., van Dokkum , P. G., Brodie , J. P., van den Bosch , F. C., & Ceverino , D. 2018, , 861, 148

    2018

  78. [86]

    2016, , 830, L13

    Mayer , L., Tamburello , V., Lupi , A., et al. 2016, , 830, L13

    2016

  79. [87]

    & Gnedin , O

    Meng , X. & Gnedin , O. Y. 2020, , 494, 1263

    2020

  80. [88]

    L., Kere s , D., Faucher-Gigu \`e re , C.-A., et al

    Muratov , A. L., Kere s , D., Faucher-Gigu \`e re , C.-A., et al. 2015, , 454, 2691

    2015

  81. [89]

    2024, arXiv e-prints, arXiv:2402.08911

    Nakazato , Y., Ceverino , D., & Yoshida , N. 2024, arXiv e-prints, arXiv:2402.08911

    2024

  82. [90]

    1999, , 514, 77

    Noguchi , M. 1999, , 514, 77

    1999

  83. [91]

    & Nagai , D

    Ogiya , G. & Nagai , D. 2022, , 514, 555

    2022

  84. [92]

    F., Feldmann , R., et al

    Oklop c i \'c , A., Hopkins , P. F., Feldmann , R., et al. 2017, , 465, 952

    2017

  85. [93]

    & Nordlund , A

    Padoan , P. & Nordlund , A . 2002, , 576, 870

    2002

  86. [94]

    Rafikov , R. R. 2001, , 323, 445

    2001

  87. [95]

    Renaud , F., Agertz , O., & Romeo , A. B. 2024, , 687, A91

    2024

  88. [96]

    M., Naab , T., & Theis , C

    Renaud , F., Boily , C. M., Naab , T., & Theis , C. 2009, , 706, 67

    2009

  89. [97]

    Renaud , F., Bournaud , F., Kraljic , K., & Duc , P. A. 2014, , 442, L33

    2014

  90. [98]

    B., & Agertz , O

    Renaud , F., Romeo , A. B., & Agertz , O. 2021, , 508, 352

    2021

  91. [99]

    2022, , 516, 4922

    Renaud , F., Segovia Otero , \'A ., & Agertz , O. 2022, , 516, 4922

    2022

  92. [100]

    Romeo , A. B. 1994, , 286, 799

    1994

  93. [101]

    Romeo , A. B. & Falstad , N. 2013, , 433, 1389

    2013

  94. [102]

    Romeo , A. B. & Wiegert , J. 2011, , 416, 1191

    2011

  95. [103]

    E., Hodge , J., Bouwens , R., et al

    Rowland , L. E., Hodge , J., Bouwens , R., et al. 2024, arXiv e-prints, arXiv:2405.06025

    2024 arXiv

  96. [104]

    2023, , 951, 147

    Sattari , Z., Mobasher , B., Chartab , N., et al. 2023, , 951, 147

    2023

  97. [105]

    2014, Numerical Modelling of Astrophysical Turbulence

    Schmidt , W. 2014, Numerical Modelling of Astrophysical Turbulence

    2014

  98. [106]

    C., & Hillebrandt , W

    Schmidt , W., Niemeyer , J. C., & Hillebrandt , W. 2006, , 450, 265

    2006

  99. [107]

    Semenov , V. A. 2024, arXiv e-prints, arXiv:2410.23339

    2024

  100. [108]

    2016, , 821, 72

    Shibuya , T., Ouchi , M., Kubo , M., & Harikane , Y. 2016, , 821, 72

    2016

  101. [109]

    M., Smail , I., Sobral , D., et al

    Swinbank , A. M., Smail , I., Sobral , D., et al. 2012, , 760, 130

    2012

  102. [110]

    1964, , 139, 1217

    Toomre , A. 1964, , 139, 1217

    1964

  103. [111]

    M., Genzel , R., et al

    Wuyts , S., F \"o rster Schreiber , N. M., Genzel , R., et al. 2012, , 753, 114

    2012

  104. [112]

    2024, , 685, A80

    Zanella , A., Iani , E., Dessauges-Zavadsky , M., et al. 2024, , 685, A80

    2024

  105. [113]

    M., et al

    Zanella , A., Le Floc'h , E., Harrison , C. M., et al. 2019, , 489, 2792

    2019

  106. [114]

    2015, , 450, 2327

    Zolotov , A., Dekel , A., Mandelker , N., et al. 2015, , 450, 2327

    2015

  107. [115]

    , " * write output.state after.block = add.period write newline

    ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sent...

  108. [116]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

  109. [117]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

  110. [118]

    @esa (Ref

    \@ifclassloaded aguplus natbib The aguplus class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command natbib from the document \@ifclassloaded nlinproc natbib The nlinproc class already includes natbib cod...

  111. [119]

    @stdbsttrue NAT@ctr \@lbibitem[ NAT@ctr ] \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 [ @natanchorstart #2\@extra@b@citeb \@biblabel @num @natanchorend] @ifc...

  112. [120]

    e-prints

    @open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifundefined NAT@sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifundefined bib@heading @heading NAT@ctr thebibliography [1] @ \@biblabel NAT@ctr \@bib...

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.