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arxiv: 2604.13154 · v1 · submitted 2026-04-14 · 🌌 astro-ph.GA

Recognition: unknown

From Clumps to Sheets: Geometry Controls the Temperature PDF of Multi-Phase Gas

Zirui Chen , S. Peng Oh
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:08 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords temperature PDFmulti-phase gasISMCGMturbulent mixing layersgeometrymorphologyclump to sheet transition
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The pith

The temperature PDF of multi-phase gas is set by the geometry of isosurfaces, which transition from clumps to sheets in turbulent media.

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

The paper establishes that temperature probability distribution functions in multi-phase turbulent gas are not universal but depend on the morphology of the gas. Simulations under identical microphysical conditions for the ISM and CGM produce different PDFs: narrow in planar mixing layers but broad in turbulent boxes. The authors decompose the PDF into the product of the area of temperature isosurfaces and the thickness of temperature layers. Thickness is governed by radiative cooling and thermal conduction, while the area is controlled by whether cold gas forms isolated clumps whose interfaces expand and percolate into connected sheets at higher temperatures. This geometric effect explains broad intermediate-temperature mass fractions in the ISM and has implications for observables like emission line ratios and phase mass fractions.

Core claim

The temperature PDF can be decomposed into the product of the area of temperature isosurfaces and the thickness of the corresponding temperature layers. The thickness is controlled primarily by microphysics such as radiative cooling and thermal conduction, and is well captured by existing mixing-layer models. The isosurface area, however, is set by morphology: in mixing layers it remains sheet-like, whereas in turbulent media cold gas forms clumps whose interfaces expand with temperature and eventually percolate into connected sheets, producing broad PDFs with large intermediate-temperature mass fractions.

What carries the argument

Decomposition of the temperature PDF as the product of isosurface area and layer thickness, where morphology determines the area via clump-to-sheet transitions.

If this is right

  • Broad PDFs with substantial intermediate-temperature gas arise naturally from the clump-to-sheet transition in turbulent ISM conditions.
  • Thermally unstable gas fractions in the ISM are a geometric consequence rather than a microphysical one.
  • The large OVI reservoir observed in the CGM is consistent with persistent sheet-like mixing layers.
  • X-ray to H-alpha correlations in jellyfish galaxy tails can be interpreted through the same geometric control of temperature structure.

Where Pith is reading between the lines

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

  • The same clump-to-sheet mechanism may govern temperature distributions in other multi-phase environments such as supernova-driven bubbles or galactic winds.
  • Morphology diagnostics from emission maps could be used to predict the width of unobserved temperature PDFs in real systems.
  • Varying the driving scale of turbulence in simulations would test whether the percolation threshold for sheet formation depends on the energy injection scale.

Load-bearing premise

The 3D hydrodynamic simulations under identical microphysical conditions accurately isolate geometry as the sole differing factor between ISM and CGM regimes.

What would settle it

A controlled simulation that enforces sheet-like morphology in a turbulent box yet still produces a broad temperature PDF, or an observation of temperature PDFs in a known clumpy ISM region that match the narrow widths of mixing-layer models.

Figures

Figures reproduced from arXiv: 2604.13154 by S. Peng Oh, Zirui Chen.

Figure 1
Figure 1. Figure 1: Cooling (Λ) and Heating ( Λ/ 𝑛) functions (top), net cooling functions (Λ − Λ/ 𝑛, middle), and net cooling time profiles (bottom) we use for ISM (left, following Koyama & Inutsuka (2002)) and CGM (right, following Gnat & Sternberg (2007)) conditions. For ISM conditions, we choose 𝑃/ 𝑘B = 3000Kcm−3 , which yields stable thermal equilibrium temperatures at ∼ 60K and ∼ 6000K. For CGM conditions, we choose 𝑃/ … view at source ↗
Figure 2
Figure 2. Figure 2: Comparison between turbulent mixing layer and turbulent box simulations under ISM conditions. The two simulation setups here adopt identical parameters (Da= 𝑡mix/ 𝑡cool(𝑇mix ) = 2, Mturb = 0.89). We compare temperature slices in the top two panels and the temperature PDFs in the bottom panel. Notably, the temperature PDFs are completely different. Mixing layers host more cold gas but much less intermediate… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between PDFs from wind tunnel and mixing layer simulations (normalizations of the PDFs are adjusted for easier comparison). “1D model" refers to analytic models (Tan & Oh 2021; Chen et al. 2023) which produce temperature PDFs that match mixing layer simulations, and are used to make line ratio predictions. Under CGM-like conditions with 𝑇hot = 106K, the wind tunnel and mixing layer PDFs are simi… view at source ↗
Figure 4
Figure 4. Figure 4: Temperature PDFs from ISM turbulent box simulations along a fiducial turbulent-driving sequence spanning a range of Damköhler numbers and turbulent mach numbers. The sequence is generated by changing the tur￾bulent velocity, so decreasing Damköhler number coincides with increasing turbulent mach number. Our choices of turbulent velocities ensures a sub- to trans-sonic warm ISM, which is consistent with obs… view at source ↗
Figure 5
Figure 5. Figure 5: ISM turbulent box temperature slices (top) and temperature PDFs (bottom) at different Damköhler number and turbulent mach number along the fiducial turbulent-driving sequence. Moving from left to right corresponds to increasing turbulent velocity, so decreasing Damköhler number coincides with increasing turbulent mach number. As turbulent velocity increases, the boundaries between the thermally stable phas… view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: Temperature slices from two ISM turbulent-box runs that differ only in the normalization of 𝜅. Larger conductivity smooths the cold phase and erases the smallest structures, increasing the minimum cloud size from sub-pc scales to ∼ 5 pc. where 𝐴isosurface,T is the area of the temperature isosurface, and 𝑑(𝑇) = 𝑉tot,T  𝐴isosurface,T represents a characteristic thickness of that temperature layer. This deco… view at source ↗
Figure 10
Figure 10. Figure 10: CGM turbulent-box runs along a driving sequence analogous to the ISM suite. Weak driving gives clearly defined boundaries between the hot and cold phases and relatively bimodal PDFs; strong driving produces spatially extended intermediate temperature structures and broader PDFs. These trends are identical to ISM turbulent box results presented in [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Temperature contours in ISM turbulent boxes along the fiducial driving sequence. Each panel shows a representative region in a slice of the simulation box. At weak driving, the contours form onion-skin shells around cold clumps. At strong driving, the low-𝑇 contours remain clump-like but the 𝑇 ≳ 800K contours merge into extended sheets. This clump-to-sheet transition explains the change in 𝐴(𝑇) seen in [… view at source ↗
Figure 13
Figure 13. Figure 13: 3D temperature isosurfaces illustrating the same morphological transition. Each panel shows a representative subsection of the entire simulation box. Top: at 𝑇 = 1000K, weak driving gives disconnected clumps, while strong driving gives an extended sheet. Bottom: in the strong-driving run, the 100K isosurface is clump-like but the 2000K isosurface is sheet-like. Stronger driving and higher temperature both… view at source ↗
Figure 14
Figure 14. Figure 14: Temperature contours in the ISM mixing-layer run with Da=2 and Mturb = 0.89. The contours remain stacked sheets, so 𝐴(𝑇) depends only weakly on temperature or driving. The PDF therefore varies mainly through the layer thickness 𝑑(𝑇) . clumps, whereas stronger driving and higher temperature cause those shells to percolate into extended sheets. This transition is quantified by the rise of the largest-compon… view at source ↗
Figure 15
Figure 15. Figure 15: Diagnostic decomposition of the CGM turbulent-box PDFs shown in [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Area covering fraction 𝑓𝐴 of the largest connected component. 𝑓𝐴 rises with temperature and driving strength, showing the transition from disconnected clumps to percolating sheets. ACKNOWLEDGEMENTS We acknowledge NSF grant AST240752 and HST grant AR￾17860 for support. This work made considerable use of the Stam￾pede3 supercomputer through allocation TG-PHY240194 from the Advanced Cyberinfrastructure Coord… view at source ↗
Figure 17
Figure 17. Figure 17: Top: Betti number 𝑏0, the number of isolated components. Weakly driven runs show a monotonic rise with temperature, while strongly driven runs turn over at high 𝑇 as clumps merge into sheets. Bottom: Euler char￾acteristic 𝜒; 𝜒 > 0 indicates clump-dominated geometry and 𝜒 < 0 sheet￾dominated geometry. The zero-crossing moves to lower temperature as the driving strengthens. Evans L. C., 2025, Measure theory… view at source ↗
Figure 18
Figure 18. Figure 18: Area per isolated component, 𝐴/𝑏0, evaluated at 𝑇 = 1000K. It rises as the Damköhler number decreases (as turbulence driving strengthens), consistent with fewer, larger connected structures and a shift toward sheet-like morphology. Jiang Y.-F., Oh S. P., 2018, ApJ, 854, 5 Kanjilal V., Dutta A., Sharma P., 2021, MNRAS, 501, 1143 Koley A., Roy N., 2019, MNRAS, 483, 593 Koyama H., Inutsuka S.-i., 2002, ApJ, … view at source ↗
read the original abstract

Temperature probability distribution functions (PDFs) are a compact description of the thermal structure of multi-phase turbulent gas, and are directly linked to observables such as emission/absorption line ratios and phase mass fractions. In the circumgalactic medium (CGM) literature, temperature PDFs are often interpreted using planar turbulent radiative mixing layers, for which analytic models successfully reproduce the simulated temperature structure. These PDFs are assumed to be universal. By contrast, studies of the multiphase interstellar medium (ISM) typically use turbulent-box simulations, which produce broad PDFs but lack a clear theoretical interpretation. Using 3D hydrodynamic simulations under both ISM and CGM conditions, we compare planar mixing layers with turbulent-box simulations under identical microphysical conditions. Despite identical cooling and turbulent driving, the resulting temperature PDFs differ substantially. The missing ingredient is geometry. We demonstrate that the temperature PDF can be decomposed into the product of the area of temperature isosurfaces and the thickness of the corresponding temperature layers. The thickness is controlled primarily by microphysics, such as radiative cooling and thermal conduction, and is well captured by existing mixing-layer models. The isosurface area, however, is set by morphology. In mixing layers it remains sheet-like, whereas in turbulent media cold gas forms clumps whose interfaces expand with temperature and eventually percolate into connected sheets. This geometric transition produces broad PDFs with large intermediate-temperature mass fractions. These results have implications for long-standing puzzles such as thermally unstable gas in the ISM, the large OVI reservoir in the CGM, and X-ray-H$\alpha$ correlations in jellyfish tails.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses comparative 3D hydrodynamic simulations of planar turbulent radiative mixing layers and turbulent-box setups under identical microphysical conditions (cooling functions, conduction, turbulent driving) for ISM and CGM regimes. It claims that temperature PDFs differ substantially due to geometry: the PDF decomposes as the product of temperature-isosurface area A(T), controlled by morphology (persistent sheets in mixing layers vs. clump formation and percolation into sheets in turbulent media), and layer thickness δ(T), controlled by microphysics and matching existing planar mixing-layer models. This geometric transition is argued to produce broader PDFs with larger intermediate-temperature mass fractions in turbulent media.

Significance. If the decomposition and the insensitivity of δ(T) to global geometry hold, the work supplies a concrete physical mechanism linking morphology to observable temperature structure in multi-phase gas. It bridges analytic mixing-layer models with full turbulent simulations and offers a route to interpreting long-standing issues such as the mass fraction of thermally unstable gas in the ISM and the large OVI column in the CGM. The use of identical microphysics across setups is a clear strength that isolates geometry as the differing factor.

major comments (2)
  1. [§4.2] §4.2 (PDF decomposition): the central claim that δ(T) is set solely by microphysics and is insensitive to morphology requires a direct, quantitative extraction and comparison of δ(T) profiles (or equivalent local temperature gradients) from both the planar mixing-layer and turbulent-box runs; without tabulated or plotted agreement to within numerical uncertainties across the relevant temperature range, the attribution of all PDF differences to A(T) alone is not yet load-bearing.
  2. [§3] §3 (simulation setup and turbulent-box results): cold gas is described as forming clumps with curved interfaces that later percolate; the manuscript does not demonstrate that the effective mixing length or local temperature gradient around these curved surfaces remains identical to the planar case, leaving open the possibility that 3D straining or curvature couples back into δ(T) and undermines the clean separation from A(T).
minor comments (2)
  1. [Abstract] Abstract: inclusion of at least one quantitative metric (e.g., the factor by which the intermediate-temperature mass fraction differs between the two geometries, or the temperature range over which the decomposition holds) would make the strength of the result immediately clear to readers.
  2. Figure captions (throughout): specify the exact temperature binning and any resolution or convergence information used when computing isosurface areas and layer thicknesses.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and positive assessment of the work's significance. The comments identify key points where additional evidence will strengthen the central claims. We address each major comment below and will revise the manuscript to incorporate the requested comparisons.

read point-by-point responses

  1. Referee: [§4.2] §4.2 (PDF decomposition): the central claim that δ(T) is set solely by microphysics and is insensitive to morphology requires a direct, quantitative extraction and comparison of δ(T) profiles (or equivalent local temperature gradients) from both the planar mixing-layer and turbulent-box runs; without tabulated or plotted agreement to within numerical uncertainties across the relevant temperature range, the attribution of all PDF differences to A(T) alone is not yet load-bearing.

    Authors: We agree that the decomposition claim requires explicit quantitative support. The manuscript currently infers the insensitivity of δ(T) from the fact that the PDF differences are fully accounted for by variations in A(T), but this is indirect. In the revised version we will add a new panel (or figure) in §4.2 that extracts δ(T) (or equivalently the local |∇T|) from both the planar mixing-layer and turbulent-box runs under identical microphysics and shows agreement to within numerical uncertainties across the temperature range of interest. This will make the separation between A(T) and δ(T) load-bearing. revision: yes

  2. Referee: [§3] §3 (simulation setup and turbulent-box results): cold gas is described as forming clumps with curved interfaces that later percolate; the manuscript does not demonstrate that the effective mixing length or local temperature gradient around these curved surfaces remains identical to the planar case, leaving open the possibility that 3D straining or curvature couples back into δ(T) and undermines the clean separation from A(T).

    Authors: We acknowledge that the present text does not contain a direct side-by-side comparison of local temperature gradients or effective mixing lengths at curved interfaces. While the global decomposition already implies that any such effects are subdominant (otherwise the PDF would not be reproduced by A(T) alone), we will add in the revised §3 an explicit measurement of local |∇T| and mixing-layer thickness sampled around both planar and curved interfaces in the turbulent-box runs. These will be compared quantitatively to the planar mixing-layer results to confirm that curvature and straining do not materially alter δ(T). revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claim from direct simulation comparisons

full rationale

The paper derives its key result—that the temperature PDF decomposes as the product of temperature-isosurface area (morphology-controlled) and layer thickness (microphysics-controlled)—from side-by-side 3D hydrodynamic simulations of planar mixing layers versus turbulent boxes run under identical cooling functions and driving. This is an empirical decomposition extracted from the numerical data rather than a self-referential definition, a fitted parameter renamed as a prediction, or a load-bearing self-citation chain. No equations or claims in the provided text reduce the target PDF back to its own inputs by construction; the geometric interpretation follows from observed morphology differences in the runs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on standard hydrodynamic evolution and radiative cooling functions drawn from prior literature; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • standard math Hydrodynamic equations plus radiative cooling govern the evolution of multi-phase gas
    Standard assumption underlying all cited mixing-layer and turbulent-box simulations.
  • domain assumption Layer thickness is set by microphysical cooling and conduction rates
    Invoked when stating that existing mixing-layer models capture the thickness term.

pith-pipeline@v0.9.0 · 5585 in / 1325 out tokens · 79041 ms · 2026-05-10T15:08:06.267836+00:00 · methodology

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Works this paper leans on

79 extracted references · 72 canonical work pages · 3 internal anchors

  1. [1]

    W., Bryan, G

    Abruzzo M. W., Bryan G. L., Fielding D. B., 2022, @doi [ ] 10.3847/1538-4357/ac3c48 , https://ui.adsabs.harvard.edu/abs/2022ApJ...925..199A 925, 199

    work page doi:10.3847/1538-4357/ac3c48 2022

  2. [2]

    , keywords =

    Armstrong J. W., Rickett B. J., Spangler S. R., 1995, @doi [ ] 10.1086/175515 , http://adsabs.harvard.edu/abs/1995ApJ...443..209A 443, 209

    work page doi:10.1086/175515 1995

  3. [3]

    Audit E., Hennebelle P., 2005, @doi [ ] 10.1051/0004-6361:20041474 , http://adsabs.harvard.edu/abs/2005A

    work page doi:10.1051/0004-6361:20041474 2005

  4. [4]

    R., Kolborg A

    Beattie J. R., Kolborg A. N., Ramirez-Ruiz E., Federrath C., 2025, @doi [The Astrophysical Journal] 10.3847/1538-4357/ae07cd , 994, 193

    work page doi:10.3847/1538-4357/ae07cd 2025

  5. [5]

    C., Fabian A

    Begelman M. C., Fabian A. C., 1990, , http://adsabs.harvard.edu/abs/1990MNRAS.244P..26B 244, 26P

    1990

  6. [6]

    Cecil G., Bland-Hawthorn J., Veilleux S., 2002, @doi [ ] 10.1086/341861 , https://ui.adsabs.harvard.edu/abs/2002ApJ...576..745C 576, 745

    work page doi:10.1086/341861 2002

  7. [7]

    P., 2024, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stae1113 , 530, 4032

    Chen Z., Oh S. P., 2024, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stae1113 , 530, 4032

    work page doi:10.1093/mnras/stae1113 2024

  8. [8]

    B., Bryan G

    Chen Z., Fielding D. B., Bryan G. L., 2023, @doi [ ] 10.3847/1538-4357/acc73f , https://ui.adsabs.harvard.edu/abs/2023ApJ...950...91C 950, 91

    work page doi:10.3847/1538-4357/acc73f 2023

  9. [9]

    Modeling Emission-Line Surface Brightness in a Multiphase Galactic Wind: An O VI Case Study

    Chen Z., et al., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2510.02443 , https://ui.adsabs.harvard.edu/abs/2025arXiv251002443C p. arXiv:2510.02443

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2510.02443 2025

  10. [10]

    R., Kolborg A

    Connor I., Beattie J. R., Kolborg A. N., Ramirez-Ruiz E., 2026, @doi [The Astrophysical Journal] 10.3847/1538-4357/ae17b1 , 997, 33

    work page doi:10.3847/1538-4357/ae17b1 2026

  11. [11]

    P., 2005, @doi [ ] 10.1146/annurev.astro.43.072103.150615 , http://adsabs.harvard.edu/abs/2005ARA

    Cox D. P., 2005, @doi [ ] 10.1146/annurev.astro.43.072103.150615 , http://adsabs.harvard.edu/abs/2005ARA

    work page doi:10.1146/annurev.astro.43.072103.150615 2005

  12. [12]

    o hler G., 1940, Zeitschrift f \

    Damk \"o hler G., 1940, Zeitschrift f \"u r Elektrochemie und angewandte physikalische Chemie, 46, 601

    1940

  13. [13]

    K., Gronke M., 2023, @doi [ ] 10.1093/mnras/stad3125 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.tmp.2982D

    Das H. K., Gronke M., 2023, @doi [ ] 10.1093/mnras/stad3125 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.tmp.2982D

    work page doi:10.1093/mnras/stad3125 2023

  14. [14]

    Hubble Space Telescope Observations of Vibrationally Excited Molecular Hydrogen in Cluster Cooling Flow Nebulae

    Donahue M., Mack J., Voit G. M., Sparks W., Elston R., Maloney P. R., 2000, @doi [ ] 10.1086/317836 , https://ui.adsabs.harvard.edu/abs/2000ApJ...545..670D 545, 670

    work page doi:10.1086/317836 2000

  15. [15]

    T., 2011, Physics of the Interstellar and Intergalactic Medium

    Draine B. T., 2011, Physics of the Interstellar and Intergalactic Medium . Princeton University Press

    2011

  16. [16]

    G., & Scalo, J

    Elmegreen B. G., Scalo J., 2004, @doi [ ] 10.1146/annurev.astro.41.011802.094859 , http://adsabs.harvard.edu/abs/2004ARA

    work page doi:10.1146/annurev.astro.41.011802.094859 2004

  17. [17]

    C., 2025, Measure theory and fine properties of functions

    Evans L. C., 2025, Measure theory and fine properties of functions. Chapman and Hall/CRC

    2025

  18. [18]

    J., & Gronke, M

    Farber R. J., Gronke M., 2022, @doi [ ] 10.1093/mnras/stab3412 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.510..551F 510, 551

    work page doi:10.1093/mnras/stab3412 2022

  19. [19]

    P., 2023, @doi [ ] 10.1146/annurev-astro-052920-125203 , https://ui.adsabs.harvard.edu/abs/2023ARA&A..61..131F 61, 131

    Faucher-Gigu \`e re C.-A., Oh S. P., 2023, @doi [ ] 10.1146/annurev-astro-052920-125203 , https://ui.adsabs.harvard.edu/abs/2023ARA&A..61..131F 61, 131

    work page doi:10.1146/annurev-astro-052920-125203 2023

  20. [20]

    B., Ostriker E

    Fielding D. B., Ostriker E. C., Bryan G. L., Jermyn A. S., 2020, @doi [ ] 10.3847/2041-8213/ab8d2c , https://ui.adsabs.harvard.edu/abs/2020ApJ...894L..24F 894, L24

    work page doi:10.3847/2041-8213/ab8d2c 2020

  21. [21]

    M., et al., 2011, @doi [ ] 10.1038/nature10446 , https://ui.adsabs.harvard.edu/abs/2011Natur.478..214G 478, 214

    Gaensler B. M., et al., 2011, @doi [ ] 10.1038/nature10446 , https://ui.adsabs.harvard.edu/abs/2011Natur.478..214G 478, 214

    work page doi:10.1038/nature10446 2011

  22. [22]

    Gnat O., Sternberg A., 2007, @doi [ ] 10.1086/509786 , http://adsabs.harvard.edu/abs/2007ApJS..168..213G 168, 213

    work page doi:10.1086/509786 2007

  23. [23]

    P., 2018, @doi [ ] 10.1093/mnrasl/sly131 , http://adsabs.harvard.edu/abs/2018MNRAS.tmpL.135G

    Gronke M., Oh S. P., 2018, @doi [ ] 10.1093/mnrasl/sly131 , http://adsabs.harvard.edu/abs/2018MNRAS.tmpL.135G

    work page doi:10.1093/mnrasl/sly131 2018

  24. [24]

    P., 2020a, @doi [ ] 10.1093/mnras/stz3332 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.1970G 492, 1970

    Gronke M., Oh S. P., 2020a, @doi [ ] 10.1093/mnras/stz3332 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.1970G 492, 1970

    work page doi:10.1093/mnras/stz3332 1970

  25. [25]

    P., 2020b, @doi [ ] 10.1093/mnrasl/slaa033 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.494L..27G 494, L27

    Gronke M., Oh S. P., 2020b, @doi [ ] 10.1093/mnrasl/slaa033 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.494L..27G 494, L27

    work page doi:10.1093/mnrasl/slaa033

  26. [26]

    P., Ji S., Norman C., 2022, @doi [ ] 10.1093/mnras/stab3351 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.511..859G 511, 859

    Gronke M., Oh S. P., Ji S., Norman C., 2022, @doi [ ] 10.1093/mnras/stab3351 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.511..859G 511, 859

    work page doi:10.1093/mnras/stab3351 2022

  27. [27]

    Haud U., Kalberla P. M. W., 2007, @doi [ ] 10.1051/0004-6361:20065796 , https://ui.adsabs.harvard.edu/abs/2007A&A...466..555H 466, 555

    work page doi:10.1051/0004-6361:20065796 2007

  28. [28]

    H., 2003, @doi [ ] 10.1086/367828 , https://ui.adsabs.harvard.edu/abs/2003ApJ...586.1067H 586, 1067

    Heiles C., Troland T. H., 2003, @doi [ ] 10.1086/367828 , https://ui.adsabs.harvard.edu/abs/2003ApJ...586.1067H 586, 1067

    work page doi:10.1086/367828 2003

  29. [29]

    M., Li Y., 2021, @doi [ ] 10.1093/mnras/stab1607 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.505.5238J 505, 5238

    Jennings R. M., Li Y., 2021, @doi [ ] 10.1093/mnras/stab1607 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.505.5238J 505, 5238

    work page doi:10.1093/mnras/stab1607 2021

  30. [30]

    P., Masterson P., 2019, @doi [ ] 10.1093/mnras/stz1248 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.487..737J 487, 737

    Ji S., Oh S. P., Masterson P., 2019, @doi [ ] 10.1093/mnras/stz1248 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.487..737J 487, 737

    work page doi:10.1093/mnras/stz1248 2019

  31. [31]

    P., 2018, @doi [ ] 10.3847/1538-4357/aaa6ce , http://adsabs.harvard.edu/abs/2018ApJ...854....5J 854, 5

    Jiang Y.-F., Oh S. P., 2018, @doi [ ] 10.3847/1538-4357/aaa6ce , http://adsabs.harvard.edu/abs/2018ApJ...854....5J 854, 5

    work page doi:10.3847/1538-4357/aaa6ce 2018

  32. [32]

    Kanjilal V., Dutta A., Sharma P., 2021, @doi [ ] 10.1093/mnras/staa3610 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.1143K 501, 1143

    work page doi:10.1093/mnras/staa3610 2021

  33. [33]

    Koley A., Roy N., 2019, @doi [ ] 10.1093/mnras/sty3152 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.483..593K 483, 593

    work page doi:10.1093/mnras/sty3152 2019

  34. [34]

    Koyama H., Inutsuka S.-i., 2002, @doi [ ] 10.1086/338978 , https://ui.adsabs.harvard.edu/abs/2002ApJ...564L..97K 564, L97

    work page doi:10.1086/338978 2002

  35. [35]

    G., Norman M

    Kritsuk A. G., Norman M. L., 2002, @doi [ ] 10.1086/340785 , http://adsabs.harvard.edu/abs/2002ApJ...569L.127K 569, L127

    work page doi:10.1086/340785 2002

  36. [36]

    L., 2010, @doi [ ] 10.1088/0004-637X/719/1/523 , http://adsabs.harvard.edu/abs/2010ApJ...719..523K 719, 523

    Kwak K., Shelton R. L., 2010, @doi [ ] 10.1088/0004-637X/719/1/523 , http://adsabs.harvard.edu/abs/2010ApJ...719..523K 719, 523

    work page doi:10.1088/0004-637x/719/1/523 2010

  37. [37]

    F., Squire J., Hummels C., 2020, @doi [ ] 10.1093/mnras/stz3567 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.1841L 492, 1841

    Li Z., Hopkins P. F., Squire J., Hummels C., 2020, @doi [ ] 10.1093/mnras/stz3567 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.1841L 492, 1841

    work page doi:10.1093/mnras/stz3567 2020

  38. [38]

    E., Cline H

    Lorensen W. E., Cline H. E., 1987, @doi [Computer Graphics (Proceedings of SIGGRAPH)] 10.1145/37402.37422 , 21, 163

    work page doi:10.1145/37402.37422 1987

  39. [39]

    , keywords =

    McClure-Griffiths N. M., Stanimirović S., Rybarczyk D. R., 2023, @doi [Annual Review of Astronomy and Astrophysics] https://doi.org/10.1146/annurev-astro-052920-104851 , 61, 19

    work page doi:10.1146/annurev-astro-052920-104851 2023

  40. [40]

    P., O'Leary R., Madigan A.-M., 2018, @doi [ ] 10.1093/mnras/stx2687 , http://adsabs.harvard.edu/abs/2018MNRAS.473.5407M 473, 5407

    McCourt M., Oh S. P., O'Leary R., Madigan A.-M., 2018, @doi [ ] 10.1093/mnras/stx2687 , http://adsabs.harvard.edu/abs/2018MNRAS.473.5407M 473, 5407

    work page doi:10.1093/mnras/stx2687 2018

  41. [41]

    F., Cowie L

    McKee C. F., Cowie L. L., 1977, @doi [ ] 10.1086/155350 , http://adsabs.harvard.edu/abs/1977ApJ...215..213M 215, 213

    work page doi:10.1086/155350 1977

  42. [42]

    F., Ostriker J

    McKee C. F., Ostriker J. P., 1977, @doi [ ] 10.1086/155667 , https://ui.adsabs.harvard.edu/abs/1977ApJ...218..148M 218, 148

    work page doi:10.1086/155667 1977

  43. [43]

    K., 2018, @doi [ ] 10.3847/1538-4357/aa9d3f , http://adsabs.harvard.edu/abs/2018ApJ...852...33M 852, 33

    McQuinn M., Werk J. K., 2018, @doi [ ] 10.3847/1538-4357/aa9d3f , http://adsabs.harvard.edu/abs/2018ApJ...852...33M 852, 33

    work page doi:10.3847/1538-4357/aa9d3f 2018

  44. [44]

    E., 2016, quantimpy: Quantitative Image Analysis for Particle-Based Systems, @doi 10.5281/zenodo.xxxxx , https://github.com/quantimpy/quantimpy

    Mickel W., Schröder-Turk G. E., 2016, quantimpy: Quantitative Image Analysis for Particle-Based Systems, @doi 10.5281/zenodo.xxxxx , https://github.com/quantimpy/quantimpy

    work page doi:10.5281/zenodo.xxxxx 2016

  45. [45]

    Mohapatra R., Jetti M., Sharma P., Federrath C., 2021, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stab3603 , 510, 3778

    work page doi:10.1093/mnras/stab3603 2021

  46. [46]

    Moretti A., et al., 2018, @doi [ ] 10.1093/mnras/sty2021 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.480.2508M 480, 2508

    work page doi:10.1093/mnras/sty2021 2018

  47. [47]

    E., et al., 2015, @doi [ ] 10.1088/0004-637X/804/2/89 , https://ui.adsabs.harvard.edu/abs/2015ApJ...804...89M 804, 89

    Murray C. E., et al., 2015, @doi [ ] 10.1088/0004-637X/804/2/89 , https://ui.adsabs.harvard.edu/abs/2015ApJ...804...89M 804, 89

    work page doi:10.1088/0004-637x/804/2/89 2015

  48. [48]

    E., Stanimirović S., Goss W

    Murray C. E., Stanimirović S., Goss W. M., Heiles C., Dickey J. M., Babler B., Kim C.-G., 2018, @doi [The Astrophysical Journal Supplement Series] 10.3847/1538-4365/aad81a , 238, 14

    work page doi:10.3847/1538-4365/aad81a 2018

  49. [49]

    2025, Nature Astronomy, doi: 10.1038/s41550-024-02473-8

    Olivares V., Picquenot A., Su Y., Gaspari M., Gendron-Marsolais M. L., Polles F. L., Nulsen P., 2025, @doi [Nature Astronomy] 10.1038/s41550-024-02473-8 , 9, 449

    work page doi:10.1038/s41550-024-02473-8 2025

  50. [50]

    N., 1953, @doi [ ] 10.1086/145707 , https://ui.adsabs.harvard.edu/abs/1953ApJ...117..431P 117, 431

    Parker E. N., 1953, @doi [ ] 10.1086/145707 , https://ui.adsabs.harvard.edu/abs/1953ApJ...117..431P 117, 431

    work page doi:10.1086/145707 1953

  51. [51]

    A., Ostriker E

    Piontek R. A., Ostriker E. C., 2004, @doi [The Astrophysical Journal] 10.1086/380785 , 601, 905

    work page doi:10.1086/380785 2004

  52. [52]

    A., Ostriker E

    Piontek R. A., Ostriker E. C., 2005, @doi [ ] 10.1086/431549 , http://adsabs.harvard.edu/abs/2005ApJ...629..849P 629, 849

    work page doi:10.1086/431549 2005

  53. [53]

    and Moretti, Alessia and Gullieuszik, Marco and Fritz, Jacopo and Jaff

    Poggianti B. M., et al., 2017, @doi [ ] 10.3847/1538-4357/aa78ed , https://ui.adsabs.harvard.edu/abs/2017ApJ...844...48P 844, 48

    work page doi:10.3847/1538-4357/aa78ed 2017

  54. [54]

    X., Werk, J

    Prochaska J. X., et al., 2017, @doi [ ] 10.3847/1538-4357/aa6007 , http://adsabs.harvard.edu/abs/2017ApJ...837..169P 837, 169

    work page doi:10.3847/1538-4357/aa6007 2017

  55. [55]

    L., 2004, @doi [The Astrophysical Journal] 10.1086/423311 , 613, 1004

    Redfield S., Linsky J. L., 2004, @doi [The Astrophysical Journal] 10.1086/423311 , 613, 1004

    work page doi:10.1086/423311 2004

  56. [56]

    H., Read , M

    Robertson B. E., Kravtsov A. V., Gnedin N. Y., Abel T., Rudd D. H., 2010, @doi [ ] 10.1111/j.1365-2966.2009.15823.x , https://ui.adsabs.harvard.edu/abs/2010MNRAS.401.2463R 401, 2463

    work page doi:10.1111/j.1365-2966.2009.15823.x 2010

  57. [57]

    A., Hennebelle P., Audit E., Schmidt W., 2014, @doi [ ] 10.1051/0004-6361/201321113 , https://ui.adsabs.harvard.edu/abs/2014A&A...567A..16S 567, A16

    Saury E., Miville-Desch \^e nes M. A., Hennebelle P., Audit E., Schmidt W., 2014, @doi [ ] 10.1051/0004-6361/201321113 , https://ui.adsabs.harvard.edu/abs/2014A&A...567A..16S 567, A16

    work page doi:10.1051/0004-6361/201321113 2014

  58. [58]

    arXiv:2509.03802

    Sharma P., Kumar A., Datta D., Babul A., Das R., Aditya K., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2509.03802 , https://ui.adsabs.harvard.edu/abs/2025arXiv250903802S p. arXiv:2509.03802

    work page doi:10.48550/arxiv.2509.03802 2025

  59. [59]

    Silversmith W., 2021, cc3d: Connected components on multilabel 3D & 2D images , @doi 10.5281/zenodo.5719536 , https://github.com/seung-lab/connected-components-3d

    work page doi:10.5281/zenodo.5719536 2021

  60. [60]

    B., Pringle J

    Sparks W. B., Pringle J. E., Donahue M., Carswell R., Voit M., Cracraft M., Martin R. G., 2009, @doi [ ] 10.1088/0004-637X/704/1/L20 , http://adsabs.harvard.edu/abs/2009ApJ...704L..20S 704, L20

    work page doi:10.1088/0004-637x/704/1/l20 2009

  61. [61]

    Sparre M., Pfrommer C., Vogelsberger M., 2019, @doi [ ] 10.1093/mnras/sty3063 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.482.5401S 482, 5401

    work page doi:10.1093/mnras/sty3063 2019

  62. [62]

    Wiley-Interscience

    Spitzer L., 1962, Physics of Fully Ionized Gases. Wiley-Interscience

    1962

  63. [63]

    M., Tomida, K., White, C

    Stone J. M., Tomida K., White C. J., Felker K. G., 2020, @doi [ ] 10.3847/1538-4365/ab929b , https://ui.adsabs.harvard.edu/abs/2020ApJS..249....4S 249, 4

    work page doi:10.3847/1538-4365/ab929b 2020

  64. [64]

    K., Heckman T

    Strickland D. K., Heckman T. M., Weaver K. A., Hoopes C. G., Dahlem M., 2002, @doi [The Astrophysical Journal] 10.1086/338889 , 568, 689

    work page doi:10.1086/338889 2002

  65. [65]

    Sun M., et al., 2021, @doi [Nature Astronomy] 10.1038/s41550-021-01516-8 , https://ui.adsabs.harvard.edu/abs/2022NatAs...6..270S 6, 270

    work page doi:10.1038/s41550-021-01516-8 2021

  66. [66]

    B., 2023, @doi [arXiv e-prints] 10.48550/arXiv.2305.14424 , https://ui.adsabs.harvard.edu/abs/2023arXiv230514424T p

    Tan B., Fielding D. B., 2023, @doi [arXiv e-prints] 10.48550/arXiv.2305.14424 , https://ui.adsabs.harvard.edu/abs/2023arXiv230514424T p. arXiv:2305.14424

    work page doi:10.48550/arxiv.2305.14424 2023

  67. [67]

    P., 2021, @doi [ ] 10.1093/mnrasl/slab100 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.508L..37T 508, L37

    Tan B., Oh S. P., 2021, @doi [ ] 10.1093/mnrasl/slab100 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.508L..37T 508, L37

    work page doi:10.1093/mnrasl/slab100 2021

  68. [68]

    P., Gronke M., 2021, @doi [ ] 10.1093/mnras/stab053 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.3179T 502, 3179

    Tan B., Oh S. P., Gronke M., 2021, @doi [ ] 10.1093/mnras/stab053 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.3179T 502, 3179

    work page doi:10.1093/mnras/stab053 2021

  69. [69]

    Townsend R., 2009, The Astrophysical Journal Supplement Series, 181, 391

    2009

  70. [70]

    Tumlinson J., et al., 2011, @doi [Science] 10.1126/science.1209840 , http://adsabs.harvard.edu/abs/2011Sci...334..948T 334, 948

    work page doi:10.1126/science.1209840 2011

  71. [71]

    Tumlinson J., et al., 2013, @doi [The Astrophysical Journal] 10.1088/0004-637X/777/1/59 , 777, 59

    work page doi:10.1088/0004-637x/777/1/59 2013

  72. [72]

    S., & Werk, J

    Tumlinson J., Peeples M. S., Werk J. K., 2017, @doi [ ] 10.1146/annurev-astro-091916-055240 , http://adsabs.harvard.edu/abs/2017ARA

    work page internal anchor Pith review doi:10.1146/annurev-astro-091916-055240 2017

  73. [73]

    2003, in Falgarone E., Passot T., eds, , Vol

    V \'a zquez-Semadeni E., Gazol A., Passot T., et al. 2003, in Falgarone E., Passot T., eds, , Vol. 614, Turbulence and Magnetic Fields in Astrophysics. pp 213--251, @doi 10.48550/arXiv.astro-ph/0201521

    work page internal anchor Pith review doi:10.48550/arxiv.astro-ph/0201521 2003

  74. [74]

    K., Prochaska, J

    Werk J. K., et al., 2014, @doi [ ] 10.1088/0004-637X/792/1/8 , http://adsabs.harvard.edu/abs/2014ApJ...792....8W 792, 8

    work page doi:10.1088/0004-637x/792/1/8 2014

  75. [75]

    , keywords =

    Wolfire M. G., Hollenbach D., McKee C. F., Tielens A. G. G. M., Bakes E. L. O., 1995, @doi [ ] 10.1086/175510 , https://ui.adsabs.harvard.edu/abs/1995ApJ...443..152W 443, 152

    work page doi:10.1086/175510 1995

  76. [76]

    Yagi M., et al., 2010, @doi [ ] 10.1088/0004-6256/140/6/1814 , https://ui.adsabs.harvard.edu/abs/2010AJ....140.1814Y 140, 1814

    work page doi:10.1088/0004-6256/140/6/1814 2010

  77. [77]

    Zhao X., Bai X.-N., 2023, @doi [ ] 10.1093/mnras/stad3011 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.tmp.2913Z

    work page doi:10.1093/mnras/stad3011 2023

  78. [78]

    van der Walt S., et al., 2014, @doi [PeerJ] 10.7717/peerj.453 , 2, e453

    work page doi:10.7717/peerj.453 2014

  79. [79]

    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.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1...