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Turbulence inference from CO spectral observations

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read CO spectral lines inflate turbulent velocity dispersions; a factor of 0.88 corrects them.

desk verdict A useful first RT-aware correction factor for CO turbulence inference, but the blanket application to all prior CO measurements is broader than the single-simulation evidence supports. read the letter →

arxiv 2509.04818 v2 pith:67IBV77N submitted 2025-09-05 astro-ph.GA astro-ph.SR

Jayashree Narayan , Aris Tritsis , Christoph Federrath This is my paper · ORCID
classification astro-ph.GAastro-ph.SR
keywords turbulencemolecularcloudsCOspectrallinesvelocitydispersionradiativetransferfirst-momentmapsMHDsimulationsstarformation
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

Astronomers reading cloud turbulence from CO line widths must contend with the fact that CO is not an optically thin tracer: opacity, excitation, and chemistry can distort the measured velocity dispersion. This paper removes those distortions in synthetic observations by post-processing a magnetohydrodynamic (MHD) chemo-dynamical simulation of a collapsing cloud with a radiative transfer code and comparing CO(1-0) and CO(2-1) first-moment maps with an optically-thin 'Ideal' case. The result is a single conversion factor, $R_{\rm CO}\approx 0.88$, by which the CO-measured turbulent velocity dispersion must be multiplied to recover the optically-thin value. If the factor is correct, previous CO-based dispersions were overestimated by about 10-15% on average and up to about 40% at the 1-$\sigma$ tail, and the corrected values can be inserted directly into the existing 3D turbulence reconstruction pipeline. The factor is calibrated for typical solar-neighbourhood conditions and may differ elsewhere.

What carries the argument

The load-bearing object is the correction factor $R_{\rm CO} = \sigma_{v,1D}(\mathrm{Ideal})/\sigma_{v,1D}(\mathrm{CO})$, the ratio of the turbulence-isolated 1D velocity dispersion in the optically-thin, density-weighted 'Ideal' case to the value measured from CO. To isolate turbulence, the method subtracts a Gaussian-smoothed version of each first-moment map, with a kernel FWHM of $L/2$ chosen so that the largest turbulent mode ($k=2$) is preserved while in-fall and rotation are removed; the standard deviation of the residual map supplies $\sigma_{v,1D}$. The comparison is made possible by non-LTE (not assuming local thermodynamic equilibrium) radiative transfer post-processing of a chemo-dynamical MHD cloud simulation, which produces CO spectral-line data cubes and moment maps in which opacity, excitation, and chemical depletion are the only differences from the Ideal case encoded in $R_{\rm CO}$.

What would settle it

Compare the turbulence-isolated 1D velocity dispersion from $^{12}$CO(1-0) with that from a genuinely optically thin tracer (or dust-based velocities) in the same cloud, across a range of metallicities and densities; if the ratio departs systematically from $0.88^{+0.09}_{-0.08}$, the universal correction is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that 1D turbulent velocity dispersions measured from CO(1-0) and CO(2-1) first-moment maps are systematically larger than the optically-thin reference value, and that the CO value must be multiplied by $R_{\rm CO}=0.88^{+0.09}_{-0.08}$ (both lines agree within uncertainties) to recover the 'Ideal' value. This gives the corrected 3D pipeline $\sigma_{v,3D} = C_{\rm SF} R_{\rm CO} \sigma_{v,1D}(\mathrm{CO})$, where $C_{\rm SF}$ is the reconstruction coefficient from the earlier optically-thin method. Consequently previous CO-based estimates of $\sigma_v$ were overestimated by $\sim10$-$15\%$ on average, with up to $\sim40\%$ overestimation at the 1-$\sigma$ tail. The average factor is derived for solar-neighbourhood interstellar medium conditions; along the collapse axis at late times CO depletion can push $R_{\rm CO}$ above unity.

Load-bearing premise

The single average correction $R_{\rm CO}=0.88$ rests on the assumption that one simulated collapsing, magnetised cloud at two ages and three viewing angles is representative of CO emission in real molecular clouds across the solar neighbourhood.

Editorial extensions

If this is right

  • Published CO-based 1D turbulent velocity dispersions should be multiplied by $R_{\rm CO}\approx 0.88$, lowering them by about 10-15% on average and up to about 40% at the 1-sigma tail.
  • Observers can now go from a CO first-moment map to a corrected 3D dispersion using $\sigma_{v,3D} = C_{\rm SF} R_{\rm CO} \sigma_{v,1D}(\mathrm{CO})$, where $C_{\rm SF}$ comes from the earlier optically-thin method.
  • Turbulent Mach numbers derived from CO decrease by the same factor, while turbulence driving parameters that scale as $b \propto \mathcal{M}^{-1}$ increase by roughly $1/R_{\rm CO}\simeq 1.14$.
  • With the current $0.08$-$0.10$ uncertainty in $R_{\rm CO}$, the correction is modest but systematic and matters for high-precision comparisons.
  • The factor is not universal: $R_{\rm CO}$ can exceed unity for lines of sight along the collapse axis at late times, when CO freezes onto dust grains, so applying 0.88 is only safe for typical solar-neighbourhood conditions.

Reading between the lines

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

  • Not tested in this paper: applying the calibration to optically thinner isotopologues such as $^{13}$CO or C$^{18}$O would probably give correction factors closer to unity, a prediction testable with the same pipeline.
  • Not tested in this paper: because the turbulence-isolation step removes structure on scales below $k=2$, varying the smoothing kernel would show whether $R_{\rm CO}$ depends on the assumed driving scale of turbulence.
  • If the bias is generic, published CO-based turbulent Mach numbers are systematically high, and models relating turbulence to star formation rates would shift toward less turbulent support once corrected.
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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 / 4 minor

Summary. The paper investigates how opacity, radiative transfer, and chemistry affect measurements of the three-dimensional turbulent velocity dispersion from CO spectral-line observations. The authors post-process a chemo-dynamical MHD simulation of a collapsing, turbulent molecular cloud (L=2 pc, ~240 Msun, sonic Mach ~3, B=7.5 uG) with the non-LTE radiative-transfer code PyRaTE to produce synthetic PPV cubes for CO(1-0), CO(2-1), and an optically-thin "Ideal" case. They isolate turbulent velocity fluctuations in first-moment maps using Gaussian smoothing with FWHM=L/2, compute the 1D velocity dispersion sigma_v from the residual maps, and define a correction factor R_CO = sigma_v,Ideal / sigma_v,CO. The time- and line-of-sight-averaged values are R_CO,1-0 = 0.88 (+0.09/-0.08) and R_CO,2-1 = 0.88 (+0.10/-0.08). The paper argues that previous CO-based estimates of sigma_v were overestimated by about 10-15% on average, with potential 1-sigma overestimates up to 40%, and proposes combining R_CO with the Stewart & Federrath (2022a) factor C_SF to obtain corrected 3D dispersions.

Significance. If the proposed correction is robust, it would provide a simple rescaling that can be applied to a large body of CO-based turbulence measurements, affecting inferred Mach numbers and turbulence driving parameters in molecular-cloud studies. The paper has notable strengths: it uses a realistic chemo-dynamical simulation, a non-LTE RT treatment, direct measurements rather than fitted parameters, and bootstrap uncertainty estimates. The authors are also transparent about some limitations. However, the significance of the universal 0.88 correction hinges on external validity that is not yet established: the measurement comes from one simulation, one filtering scale, and two timesteps, and the paper recommends applying that correction to observations analyzed with a different turbulence-isolation method. The central numerical claim is internally consistent, but its generality is not yet demonstrated.

major comments (3)
  1. [Sec. 3.2 and Eq. (6)] R_CO is calibrated on a single turbulence-isolation choice, the Gaussian low-pass filter with FWHM = L/2 (k = 2), and no sensitivity test is provided. Because sigma_v,1D is measured from the residual map after filtering, the ratio R_CO can depend on the filter scale; Appendix D in fact shows that the post-filter power spectra of the Ideal and CO cases are not identical (slopes -3.1 vs -3.0). The bootstrap errors in Table 2 only sample noise within a fixed map and do not cover this choice. I request a test with several filter scales or kernel widths (e.g., k = 1, 2, 3, or a range of FWHM values) showing how R_CO changes, or an explicit argument for why R_CO should be independent of the filter scale.
  2. [Sec. 4.2 and Table 2] The application of R_CO to previous CO studies (e.g., Menon et al. 2021, Sharda et al. 2022, Gerrard et al. 2023, 2024) assumes that the correction is transferable across different turbulence-isolation methods. Many of the cited studies used linear-gradient subtraction rather than the Gaussian smoothing used here. Since the measured sigma_v,1D is defined with respect to the adopted isolation procedure, R_CO could be method-dependent. The manuscript should either add a comparison of R_CO obtained with linear-gradient subtraction on the same synthetic maps, or explicitly restrict the recommendation to measurements made with the same Gaussian-filter approach.
  3. [Sec. 4.3.1 and Abstract] The abstract's general statement that previous measurements were overestimated by 10-15% goes beyond what the single simulation supports. Table 2 shows R_CO ranging from 0.74 to 1.08 across line of sight and time, and Sec. 4.3.1 states that the correction factors 'strictly only apply to the conditions studied'. To support a general correction, the authors should either expand the simulation sample to cover different metallicities, radiation fields, Mach numbers, and column densities, or proportionally soften the abstract and conclusion claims to 'conditions similar to those simulated'. As written, the quantitative claim is presented as a universal correction factor.
minor comments (4)
  1. [Sec. 3.1] The phrase 'small-scal variations' should be corrected to 'small-scale variations'.
  2. [References] Stewart & Federrath (2022a) and Stewart & Federrath (2022b) are listed with identical journal, volume, and page numbers (MNRAS, 509, 5237); please clarify whether these are distinct papers or a duplicated reference entry.
  3. [Appendix D] The power-spectrum analysis would benefit from a sentence describing how the 2D power spectra are computed and azimuthally averaged, including any windowing or tapering applied before the transform.
  4. [Table 2] The 'Time average of LOS averages' row reports arithmetic means, but it would be useful to state explicitly that this average is unweighted and to note that the quoted uncertainties correspond to the bootstrap percentiles rather than the scatter across LOS.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: R_CO is a directly measured ratio against an explicitly defined optically-thin Ideal case, with no fitted parameter or definitional identity; shared authorship of the simulation and the Stewart & Federrath baseline is present but not load-bearing for the central result.

full rationale

The central result R_CO is defined in Eq. 6 as R_CO = sigma_v,1D(Ideal)/sigma_v,1D(CO), where both quantities are measured from the authors' own synthetic observations and turbulence-isolated first-moment maps. R_CO is not fitted to any external data and is not obtained by assuming the desired conclusion; it is a plain ratio of two independently computed dispersions. The Ideal case is explicitly defined in Sec. 2.3.2 as density-weighted (optically thin) moment construction, i.e., it is a benchmark the authors actually compute, not merely a label imported from Stewart & Federrath (2022a). Equation 7 is algebraically derived by substituting Eq. 6 into the Stewart & Federrath formula; it is a chain-rule identity, not a fitting procedure. The claimed 10-15% overestimate is a direct arithmetic consequence of the measured ratio and carries no additional assumption beyond applying the ratio to external measurements. Several inputs do come from works with overlapping authorship: the MHD simulation from Tritsis et al. (2025a), the Gaussian smoothing approach from Gerrard et al. (2024), the kernel motivation from Federrath et al. (2016), and the C_SF calibration from Stewart & Federrath (2022a). These are methodological or input dependencies, but none of them forces the value of R_CO, which is measured from the authors' own CO and Ideal moment maps in this paper. Concerns about kernel-size sensitivity, the use of a single simulation, and generalizability to other ISM conditions are legitimate external-validity and correctness risks, not circularity. The paper itself acknowledges in Sec. 4.3.1 that the correction strictly applies only to the simulated conditions, which further indicates that the claim is not being smuggled in by definition. Overall, the derivation chain is self-contained and the central quantitative result does not reduce to its inputs by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central result is a calibration, not a derivation. Its inputs are a single hydro simulation with adopted chemical parameters, an RT model, a hand-chosen smoothing scale, and an Ideal benchmark from prior co-authored work. No new physical entities are introduced; the only new 'object' is the measured correction factor R_CO.

free parameters (3)
  • Gaussian smoothing kernel FWHM = L/2 (k=2)
    Sec. 3.2: kernel size chosen as FWHM L/2 because largest turbulent modes are at k=2; filtering scale directly sets which large-scale motions are removed and therefore affects sigma_v,1D.
  • Projection angles and averaging set = LOS (0,0,1), (1,0,1)/sqrt(2), (1,0,0); times t_ff and 1.2 t_ff
    Sec. 2.3 and Tab. 2: R_CO is averaged over these LOS and times; the diagonal LOS was chosen to maximize collapse gradients. This averaging set affects the quoted 0.88.
  • Chemical and grain parameters = n_g/n_H2=1e-12; NH2/Av=9.4e20 cm^-2 mag^-1; Hasegawa sticking; CR ionization rate
    Sec. 2.1: adopted from prior literature, they set CO depletion and abundance distribution, which directly change the CO moment maps and hence R_CO. These are inputs, not fitted to the result.
assumptions (5)
  • domain assumption The non-LTE escape-probability radiative transfer in PyRaTE, together with LAMDA coefficients, accurately computes CO line excitation and emergent spectra.
    Sec. 2.2: the RT calculation is the core of the CO moment maps; any systematic error in escape probabilities or collision rates propagates into R_CO.
  • domain assumption The Ideal case, defined as density-weighted emission in velocity channels exactly as in Stewart & Federrath (2022a), is the correct optically-thin reference for intrinsic turbulent velocity dispersion.
    Sec. 2.3.2 and Eq. 7: the correction factor is defined relative to this benchmark; if the Ideal estimator is biased, R_CO does not correct to true 3D turbulence.
  • domain assumption Subtracting a Gaussian-smoothed first-moment map with FWHM L/2 cleanly separates turbulent from systematic (infall/rotation) motions without removing turbulent power.
    Sec. 3.2: the measured sigma_v,1D values after isolation depend on this decomposition; no sensitivity test to kernel size is provided.
  • domain assumption The single FLASH MHD simulation with the chemical network produces a realistic molecular cloud whose CO abundance and velocity fields are representative of solar-neighborhood clouds.
    Sec. 2.1 and Sec. 4.3.1: generalization of R_CO to observations relies on this representativeness.
  • standard math Bootstrap resampling of the moment maps yields valid uncertainties on sigma_v,1D.
    Tab. 2: errors are quoted as bootstrap ranges; this is a standard nonparametric procedure.

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Cite this review

Pith. "Pith review of Turbulence inference from CO spectral observations." pith.science (2026). https://pith.science/paper/67IBV77N

@misc{pith2026250904818,
  author       = {Pith},
  title        = {Pith review of: Turbulence inference from CO spectral observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/67IBV77N}},
  note         = {Machine review of arXiv:2509.04818}
}
read the original abstract

Turbulence influences the structure and dynamics of molecular clouds, and plays a key role in regulating star formation. We therefore need methods to accurately infer turbulence properties of molecular clouds from position-position-velocity (PPV) spectral observations. A previous method calibrated with simulation data exists to recover the 3D turbulent velocity dispersion from PPV data. However, that method relies on optically-thin conditions, ignoring any radiative transfer (RT) and chemical effects. In the present study we determine how opacity, RT, and chemical effects influence turbulence measurements with CO lines. We post-process a chemo-dynamical simulation of a turbulent collapsing cloud with a non-local thermodynamic equilibrium line RT code to generate PPV spectral cubes of the CO (1-0) and CO (2-1) lines, and obtain moment maps. We isolate the turbulence in the first-moment maps by using a Gaussian smoothing approach. We compare the CO results with the optically-thin scenario to explore how line excitation and RT impact the turbulence measurements. We find that the turbulent velocity dispersion (sigma_v) measured via CO requires a correction by a factor R_CO, with R_CO,1-0 = 0.88 (+0.09, -0.08) for the CO (1-0) line and R_CO,2-1 = 0.88 (+0.10, -0.08) for the CO (2-1) line. As a consequence, previous measurements of sigma_v were overestimated by about 10-15% on average, with potential overestimates as high as 40%, taking the 1-sigma uncertainty into account.

Figures

Figures reproduced from arXiv: 2509.04818 by the authors.

Figure 1
Figure 1. Zeroth-moment maps (first row), first-moment maps (second row), and second-moment maps (third row) for the LOS defined via Eq. 2 and for t = tff. The left column shows the Ideal (left) case, and the middle and right columns present the CO (J = 1 → 0) and (J = 2 → 1) transitions, respectively. The zeroth-moment maps (first row) are normalised by their mean values (⟨I⟩, listed in Tab. B1 of Appendix B) to enable direc… view at source ↗
Figure 2
Figure 2. The top panels are the same as the middle row of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. PDFs of the first-moment maps shown in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

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Reference graph

Works this paper leans on

55 extracted references · 8 canonical work pages · cited by 2 Pith papers

  1. [1]

    L., 1976, , https://ui.adsabs.harvard.edu/abs/1976A&A....50..327B 50, 327

    Baker P. L., 1976, , https://ui.adsabs.harvard.edu/abs/1976A&A....50..327B 50, 327

    work page 1976

  2. [2]

    A., Tafalla M., 2007, @doi [ ] 10.1146/annurev.astro.45.071206.100404 , https://ui.adsabs.harvard.edu/abs/2007ARA&A..45..339B 45, 339

    Bergin E. A., Tafalla M., 2007, @doi [ ] 10.1146/annurev.astro.45.071206.100404 , https://ui.adsabs.harvard.edu/abs/2007ARA&A..45..339B 45, 339

    arXiv 2007

  3. [3]

    Bialy S., Sternberg A., 2015, @doi [ ] 10.1093/mnras/stv851 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.450.4424B 450, 4424

    doi:10.1093/mnras/stv851 2015

  4. [4]

    G., Tan J

    Bisbas T. G., Tan J. C., Tanaka K. E. I., 2021, @doi [ ] 10.1093/mnras/stab121 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.2701B 502, 2701

    doi:10.1093/mnras/stab121 2021

  5. [5]

    G., et al., 2024, @doi [ ] 10.1093/mnras/stad3782 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.527.8886B 527, 8886

    Bisbas T. G., et al., 2024, @doi [ ] 10.1093/mnras/stad3782 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.527.8886B 527, 8886

    work page doi:10.1093/mnras/stad3782 2024

  6. [6]

    M., 2010, @doi [ ] 10.1051/0004-6361/200913506 , 513, A67

    Brunt C. M., 2010, @doi [ ] 10.1051/0004-6361/200913506 , 513, A67

    doi:10.1051/0004-6361/200913506 2010

  7. [7]

    C., Glover S

    Clark P. C., Glover S. C. O., 2015, @doi [ ] 10.1093/mnras/stv1369 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.452.2057C 452, 2057

    doi:10.1093/mnras/stv1369 2015

  8. [8]

    C., Glover S

    Clark P. C., Glover S. C. O., Ragan S. E., Duarte-Cabral A., 2019, @doi [ ] 10.1093/mnras/stz1119 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.486.4622C 486, 4622

    doi:10.1093/mnras/stz1119 2019

Show all 55 references
  1. [9]

    V., Audit E., Zank G

    Dubey A., et al., 2008, in Pogorelov N. V., Audit E., Zank G. P., eds, Astronomical Society of the Pacific Conference Series Vol. 385, Numerical Modeling of Space Plasma Flows. p. 145

    2008

  2. [10]

    L., 1995, , https://ui.adsabs.harvard.edu/abs/1995A&A...293..840F 293, 840

    Falgarone E., Puget J. L., 1995, , https://ui.adsabs.harvard.edu/abs/1995A&A...293..840F 293, 840

    1995

  3. [11]

    Federrath C., 2013, @doi [ ] 10.1093/mnras/stt1644 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.436.1245F 436, 1245

    2013 doi

  4. [12]

    Federrath C., 2015, @doi [ ] 10.1093/mnras/stv941 , http://adsabs.harvard.edu/abs/2015MNRAS.450.4035F 450, 4035

    2015 doi

  5. [13]

    S., 2012, @doi [ ] 10.1088/0004-637X/761/2/156 , http://adsabs.harvard.edu/abs/2012ApJ...761..156F 761, 156

    Federrath C., Klessen R. S., 2012, @doi [ ] 10.1088/0004-637X/761/2/156 , http://adsabs.harvard.edu/abs/2012ApJ...761..156F 761, 156

    2012 doi

  6. [14]

    S., Schmidt W., Mac Low M

    Federrath C., Roman-Duval J., Klessen R. S., Schmidt W., Mac Low M. M., 2010, @doi [ ] 10.1051/0004-6361/200912437 , https://ui.adsabs.harvard.edu/abs/2010A&A...512A..81F 512, A81

    2010 doi

  7. [15]

    Federrath C., et al., 2016, @doi [ ] 10.3847/0004-637X/832/2/143 , https://ui.adsabs.harvard.edu/abs/2016ApJ...832..143F 832, 143

    2016 doi

  8. [16]

    S., Schmidt W., Mac Low M

    Federrath C., Roman-Duval J., Klessen R. S., Schmidt W., Mac Low M. M., 2022, TG: Turbulence Generator , Astrophysics Source Code Library, record ascl:2204.001 ( @eprint ascl 2204.001 )

    2022

  9. [17]

    Fryxell B., et al., 2000, @doi [ ] 10.1086/317361 , https://ui.adsabs.harvard.edu/abs/2000ApJS..131..273F 131, 273

    2000 doi

  10. [18]

    A., et al., 2023, @doi [ ] 10.1093/mnras/stad2718 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.526..982G 526, 982

    Gerrard I. A., et al., 2023, @doi [ ] 10.1093/mnras/stad2718 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.526..982G 526, 982

    2023 doi

  11. [19]

    A., Noon K

    Gerrard I. A., Noon K. A., Federrath C., Di Teodoro E. M., Marchal A., McClure-Griffiths N. M., 2024, @doi [ ] 10.1093/mnras/stae1144 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.530.4317G 530, 4317

    2024 doi

  12. [20]

    Ginsburg A., Federrath C., Darling J., 2013, @doi [ ] 10.1088/0004-637X/779/1/50 , http://adsabs.harvard.edu/abs/2013ApJ...779...50G 779, 50

    2013 doi

  13. [21]

    Glover S. C. O., Clark P. C., 2012, @doi [ ] 10.1111/j.1365-2966.2011.20260.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.421..116G 421, 116

    2012

  14. [22]

    C., Kim C.-G., Kim J.-G., 2020, @doi [ ] 10.3847/1538-4357/abbdab , https://ui.adsabs.harvard.edu/abs/2020ApJ...903..142G 903, 142

    Gong M., Ostriker E. C., Kim C.-G., Kim J.-G., 2020, @doi [ ] 10.3847/1538-4357/abbdab , https://ui.adsabs.harvard.edu/abs/2020ApJ...903..142G 903, 142

    2020 doi

  15. [23]

    I., Herbst E., Leung C

    Hasegawa T. I., Herbst E., Leung C. M., 1992, @doi [ ] 10.1086/191713 , https://ui.adsabs.harvard.edu/abs/1992ApJS...82..167H 82, 167

    1992 doi

  16. [24]

    Hennebelle P., Chabrier G., 2008, @doi [ ] 10.1086/589916 , http://cdsads.u-strasbg.fr/abs/2008ApJ...684..395H 684, 395

    2008 doi

  17. [25]

    Hennebelle P., Chabrier G., 2011, @doi [ ] 10.1088/2041-8205/743/2/L29 , http://adsabs.harvard.edu/abs/2011ApJ...743L..29H 743, L29

    2011 doi

  18. [26]

    Hily-Blant P., Falgarone E., Pety J., 2008, @doi [ ] 10.1051/0004-6361:20078423 , https://ui.adsabs.harvard.edu/abs/2008A&A...481..367H 481, 367

    2008 doi

  19. [27]

    F., 2012, @doi [Monthly Notices of the Royal Astronomical Society] 10.1111/j.1365-2966.2012.20730.x , 423, 2016

    Hopkins P. F., 2012, @doi [Monthly Notices of the Royal Astronomical Society] 10.1111/j.1365-2966.2012.20730.x , 423, 2016

    2012

  20. [28]

    F., 2021, @doi [ ] 10.3847/1538-4357/ac0dbd , https://ui.adsabs.harvard.edu/abs/2021ApJ...920...44H 920, 44

    Hu C.-Y., Sternberg A., van Dishoeck E. F., 2021, @doi [ ] 10.3847/1538-4357/ac0dbd , https://ui.adsabs.harvard.edu/abs/2021ApJ...920...44H 920, 44

    2021 doi

  21. [29]

    F., 2022, @doi [ ] 10.3847/1538-4357/ac65fd , https://ui.adsabs.harvard.edu/abs/2022ApJ...931...28H 931, 28

    Hu C.-Y., Schruba A., Sternberg A., van Dishoeck E. F., 2022, @doi [ ] 10.3847/1538-4357/ac65fd , https://ui.adsabs.harvard.edu/abs/2022ApJ...931...28H 931, 28

    2022 doi

  22. [30]

    C., 2013, @doi [ ] 10.1051/0004-6361/201219526 , http://adsabs.harvard.edu/abs/2013A

    Kainulainen J., Tan J. C., 2013, @doi [ ] 10.1051/0004-6361/201219526 , http://adsabs.harvard.edu/abs/2013A

    2013 doi

  23. [31]

    R., McKee C

    Krumholz M. R., McKee C. F., 2005, @doi [ ] 10.1086/431734 , http://cdsads.u-strasbg.fr/abs/2005ApJ...630..250K 630, 250

    2005 doi

  24. [32]

    B., 1981, @doi [ ] 10.1093/mnras/194.4.809 , https://ui.adsabs.harvard.edu/abs/1981MNRAS.194..809L 194, 809

    Larson R. B., 1981, @doi [ ] 10.1093/mnras/194.4.809 , https://ui.adsabs.harvard.edu/abs/1981MNRAS.194..809L 194, 809

    1981 doi

  25. [33]

    S., 2004, @doi [Reviews of Modern Physics] 10.1103/RevModPhys.76.125 , https://ui.adsabs.harvard.edu/abs/2004RvMP...76..125M 76, 125

    Mac Low M.-M., Klessen R. S., 2004, @doi [Reviews of Modern Physics] 10.1103/RevModPhys.76.125 , https://ui.adsabs.harvard.edu/abs/2004RvMP...76..125M 76, 125

    2004 doi

  26. [34]

    S., Federrath C., Seta A., 2023, @doi [ ] 10.1093/mnras/stac3415 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.518.5190M 518, 5190

    Mathew S. S., Federrath C., Seta A., 2023, @doi [ ] 10.1093/mnras/stac3415 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.518.5190M 518, 5190

    2023 doi

  27. [35]

    F., Ostriker E

    McKee C. F., Ostriker E. C., 2007, @doi [Annual Review of Astronomy and Astrophysics] https://doi.org/10.1146/annurev.astro.45.051806.110602 , 45, 565

    2007 arXiv

  28. [36]

    H., Federrath C., Klaassen P., Kuiper R., Reiter M., 2021, @doi [ ] 10.1093/mnras/staa3271 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.500.1721M 500, 1721

    Menon S. H., Federrath C., Klaassen P., Kuiper R., Reiter M., 2021, @doi [ ] 10.1093/mnras/staa3271 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.500.1721M 500, 1721

    2021 doi

  29. [37]

    G., Federrath C., Krumholz M

    Nam D. G., Federrath C., Krumholz M. R., 2021, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stab505 , 503, 1138

    2021 doi

  30. [38]

    C., Stone J

    Ostriker E. C., Stone J. M., Gammie C. F., 2001, @doi [ ] 10.1086/318290 , https://ui.adsabs.harvard.edu/abs/2001ApJ...546..980O 546, 980

    2001 doi

  31. [39]

    Padoan P., Nordlund ., 2002, @doi [ ] 10.1086/341790 , 576, 870

    2002 doi

  32. [40]

    Padoan P., Nordlund A ., 2011, @doi [ ] 10.1088/0004-637X/730/1/40 , https://ui.adsabs.harvard.edu/abs/2011ApJ...730...40P 730, 40

    2011 doi

  33. [41]

    Padoan P., Jones B. J. T., Nordlund A . P., 1997, @doi [ ] 10.1086/303482 , https://ui.adsabs.harvard.edu/abs/1997ApJ...474..730P 474, 730

    1997 doi

  34. [42]

    J., Johnstone D., J rgensen J

    Padoan P., Federrath C., Chabrier G., Evans II N. J., Johnstone D., J rgensen J. K., McKee C. F., Nordlund ., 2014, in Beuther H., Klessen R. S., Dullemond C. P., Henning T., eds, Protostars and Planets VI. University of Arizona Press, pp 77--100 ( @eprint arXiv 1312.5365 ), @...

    2014 arXiv

  35. [43]

    L., Goldsmith P

    Pineda J. L., Goldsmith P. F., Chapman N., Snell R. L., Li D., Cambr \'e sy L., Brunt C., 2010, @doi [ ] 10.1088/0004-637X/721/1/686 , https://ui.adsabs.harvard.edu/abs/2010ApJ...721..686P 721, 686

    2010 doi

  36. [44]

    L., van der Tak F

    Sch \"o ier F. L., van der Tak F. F. S., van Dishoeck E. F., Black J. H., 2005, @doi [ ] 10.1051/0004-6361:20041729 , https://ui.adsabs.harvard.edu/abs/2005A&A...432..369S 432, 369

    2005 doi

  37. [45]

    M., Dye S., 2018, @doi [ ] 10.1093/mnras/sty886 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.4380S 477, 4380

    Sharda P., Federrath C., da Cunha E., Swinbank A. M., Dye S., 2018, @doi [ ] 10.1093/mnras/sty886 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.477.4380S 477, 4380

    2018 doi

  38. [46]

    Sharda P., et al., 2019, @doi [ ] 10.1093/mnras/stz1543 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4305S 487, 4305

    2019 doi

  39. [47]

    Sharda P., et al., 2022, @doi [ ] 10.1093/mnras/stab3048 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.509.2180S 509, 2180

    2022 doi

  40. [48]

    L., 2015, @doi [Publications of the Astronomical Society of the Pacific] 10.1086/680342 , 127, 299

    Shirley Y. L., 2015, @doi [Publications of the Astronomical Society of the Pacific] 10.1086/680342 , 127, 299

    2015 doi

  41. [50]

    Stewart M., Federrath C., 2022b, @doi [ ] 10.1093/mnras/stab3313 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.509.5237S 509, 5237

    doi

  42. [51]

    W., Turner N

    Tassis K., Willacy K., Yorke H. W., Turner N. J., 2012, @doi [ ] 10.1088/0004-637X/753/1/29 , https://ui.adsabs.harvard.edu/abs/2012ApJ...753...29T 753, 29

    2012 doi

  43. [52]

    Tritsis A., Kylafis N., 2024, @doi [ ] 10.1051/0004-6361/202347791 , https://ui.adsabs.harvard.edu/abs/2024A&A...692A..75T 692, A75

    2024 doi

  44. [53]

    Tritsis A., Tassis K., Willacy K., 2016, @doi [ ] 10.1093/mnras/stw329 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.458..789T 458, 789

    2016 doi

  45. [54]

    Tritsis A., Yorke H., Tassis K., 2018, @doi [ ] 10.1093/mnras/sty1152 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.478.2056T 478, 2056

    2018 doi

  46. [55]

    Tritsis A., Federrath C., Willacy K., Tassis K., 2022, @doi [ ] 10.1093/mnras/stab3740 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.510.4420T 510, 4420

    2022 doi

  47. [57]

    Tritsis A., Basu S., Federrath C., 2025b, @doi [ ] 10.1051/0004-6361/202452013 , https://ui.adsabs.harvard.edu/abs/2025A&A...695A..18T 695, A18

    doi

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.