Pith. sign in

REVIEW 3 major objections 3 minor 1 cited by

Precipitation plausible: magnetized thermal instability in the intracluster medium

T0 review · 3 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Magnetic fields allow thermally unstable gas in galaxy-cluster cores to condense into cold clouds at cooling-to-freefall ratios of 10–20, where unmagnetized gas stays single-phase, which would explain the observed threshold.

desk verdict A credible, well-scoped numerical result that magnetized atmospheres precipitate at higher tc/tff, though the quantitative boundary needs sensitivity tests on the thermostat and exclusion zone. read the letter →

arxiv 2506.10277 v1 pith:N3CVQ4MI submitted 2025-06-12 astro-ph.GA

Benjamin D. Wibking , G. Mark Voit , Brian W. O'Shea This is my paper · ORCID
classification astro-ph.GA
keywords intraclustermediumthermalinstabilitymagneticfieldscoldgasprecipitationAGNfeedbackplasmabetacooling-to-freefalltimemagnetohydrodynamicsimulations
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

Observations of galaxy-cluster cores show that cold gas and AGN activity appear when the ratio of cooling time to freefall time, $t_{\rm c}/t_{\rm ff}$, is near 10–30, that the ratio is rarely observed below 10, and that multiphase gas is rare above roughly 30. This paper argues that the physical mechanism behind that threshold is magnetized thermal instability: the purely hydrodynamic instability stops precipitating once $t_{\rm c}/t_{\rm ff}$ exceeds about 5, but the magnetohydrodynamic simulations here accumulate cold gas at $t_{\rm c}/t_{\rm ff}\approx10$ whenever the plasma $\beta$ $\beta$ (gas pressure divided by magnetic pressure) is below about 100, and at $t_{\rm c}/t_{\rm ff}\approx20$ whenever $\beta$ is below about 10. If the simulations capture real cluster cores, magnetic fields would explain both why multiphase gas and AGN feedback cluster in the observed range and why $t_{\rm c}/t_{\rm ff}$ seldom falls below 10.

What carries the argument

The central mechanism is magnetothermal instability, the magnetic-field-mediated version of thermal instability in which a weak field deforms with the flow and opposes the buoyancy that otherwise damps growing density perturbations, an effect the paper traces to the idea of magnetic pinning. Its control parameter is the plasma $\beta$, $\beta\equiv P_{\rm gas}/P_{\rm mag}$: lower $\beta$ means a stronger field and a higher ceiling on $t_{\rm c}/t_{\rm ff}$. The simulations are held in thermal balance by a volume-averaged thermostat heating term that drives the mean temperature at each height back to the initial profile, so that local cooling can still grow into cold clouds while the background does not collapse.

What would settle it

A decisive test would be to rerun the simulations with a physically motivated AGN heating term in place of the volume-averaged thermostat and with heating and cooling enabled in the midplane, or observationally to map $\beta$ in cluster cores at $t_{\rm c}/t_{\rm ff}\approx15$–20 and check whether multiphase gas appears only where $\beta\lesssim10$.

Watch

Extended reading notes

Core claim

This paper's central claim is that a magnetic field, even one whose pressure is small compared with the thermal pressure, changes thermal instability in a stratified atmosphere from a damped process into one that reaches nonlinear amplitudes and makes cold gas. It reports 100 magnetohydrodynamic simulations with initially horizontal magnetic fields and a volume-averaged heating term that keeps each altitude in thermal balance, then maps whether cold gas ($T<2\times10^6$ K) accumulates near the midplane. The results define a boundary in the ($\beta$, $t_{\rm c}/t_{\rm ff}$) plane: multiphase gas appears for $\beta\lesssim100$ at $t_{\rm c}/t_{\rm ff}\approx10$, and for $\beta\lesssim10$ at $t_{\rm c}/t_{\rm ff}\approx20$, with an approximate dividing line $\log_{10}(t_{\rm c}/t_{\rm ff})=-0.3\log_{10}\beta+1.5$ for $10\lesssim\beta\lesssim1000$. Because Faraday-rotation observations suggest cluster cores have $\beta\sim10$–$100$, the paper concludes that magnetically assisted precipitation is a plausible explanation for the observed multiphase threshold at $10\lesssim t_{\rm c}/t_{\rm ff}\lesssim30$ and for the observational floor near $t_{\rm c}/t_{\rm ff}\approx10$, where AGN feedback triggered by cold gas would push the ratio back up.

Load-bearing premise

The result stands or falls on whether the artificial volume-averaged heating used to hold the atmosphere in thermal balance truly mimics AGN feedback, and on whether disabling heating and cooling just above the midplane manufactures the very cold gas that the paper counts as precipitation.

Editorial extensions

If this is right

  • Cluster cores with $t_{\rm c}/t_{\rm ff}\approx10$ should become multiphase whenever the local plasma beta is below about 100, even with no externally driven turbulence.
  • At $t_{\rm c}/t_{\rm ff}\approx20$, multiphase gas requires $\beta\lesssim10$, so the simulation boundary predicts where cold clouds and the associated AGN fuel should and should not appear.
  • The observed floor at $t_{\rm c}/t_{\rm ff}\approx10$ would be a feedback equilibrium: precipitation fuels the AGN, the AGN heats the atmosphere, and $t_{\rm c}/t_{\rm ff}$ is pushed back above the precipitation threshold.
  • The magnetic field strengths inferred from Faraday rotation and depolarization, corresponding to $\beta\sim10$–$100$, place real cluster cores inside the regime where magnetized thermal instability accelerates precipitation.

Reading between the lines

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

  • Editorial inference: the boundary's location is anchored by the thermostat heating prescription, so a physically motivated AGN heating model could shift the threshold even if the qualitative magnetic effect remains.
  • Editorial inference: combining magnetic fields with the external turbulent driving the paper sets aside for future work may push precipitation to $t_{\rm c}/t_{\rm ff}$ values above 20, sharpening the model against the observed cut-off near $t_{\rm c}/t_{\rm ff}\approx30$.
  • Editorial inference: a direct observational test would be to measure whether cluster cores with $t_{\rm c}/t_{\rm ff}\approx15$–20 are multiphase only when their magnetic fields are strong enough that $\beta\lesssim10$.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. This paper uses 100 idealized AthenaPK MHD simulations of stratified, thermally balanced galactic atmospheres with a uniform horizontal magnetic field to argue that magnetized thermal instability can produce cold gas ('precipitation') at cooling-to-freefall ratios tc/tff up to ~20 for plasma beta below ~10, and up to tc/tff ~ 10 for beta up to ~100. The simulations use a height-dependent volume-averaged thermostat (Eq. 6) to maintain thermal balance, an exclusion zone near the midplane where heating/cooling are disabled, and a cold-gas mass fraction threshold f_cold > 0.1 to classify multiphase behavior. The authors fit a linear SVM in log(beta)-log(tc/tff) space (Eq. 7) to separate single-phase from multiphase outcomes and compare that boundary with observed cluster-core thresholds, concluding that magnetically assisted precipitation could plausibly explain the observed 10 < tc/tff < 30 window for multiphase gas.

Significance. If the central claim holds, it is an important step toward connecting idealized precipitation simulations with cluster-core observations: prior hydrodynamic simulations by the same group (Paper I) found no precipitation for tc/tff > 5 even with turbulent driving, whereas the present runs find cold-gas accumulation up to tc/tff ~ 20 in magnetized atmospheres, extending the earlier Ji et al. (2018) simulations into the observationally relevant regime. The paper is also valuable for isolating the role of magnetic tension in suppressing buoyancy damping, for closely documenting the numerical setup, and for making a falsifiable prediction (Eq. 7) about the multiphase boundary. The main caveats are that the thermostat and exclusion-zone prescriptions are not sensitivity-tested, the cold-gas threshold and SVM boundary are not quantified with uncertainties, and each parameter point has only one realization. These issues are load-bearing for the quantitative threshold claim but appear addressable with additional runs and analysis.

major comments (3)
  1. [§2.2, Eq. (6)] The thermostat gain K_p is not stated anywhere in the paper, and no sensitivity tests are presented for K_p or for the size of the |z| < 5 kpc exclusion zone where heating and cooling are disabled. Since the cold-gas fraction f_cold used to classify multiphase outcomes is measured in |z| < 10 kpc, a region that overlaps the exclusion zone, the dividing line in Fig. 1 could in principle be controlled by these numerical prescriptions rather than by magnetized thermal instability. Please report K_p and demonstrate that the tc/tff threshold is stable to, for example, a factor-of-two change in K_p and to exclusion-zone half-widths of 3 and 7 kpc.
  2. [§3, Fig. 1] The multiphase classification uses a single simulation per parameter point and an arbitrary threshold f_cold > 0.1, with no uncertainty estimates. The SVM boundary in Eq. (7) is therefore fit to a binary outcome that may depend on the initial perturbation seed and on the threshold choice. Please quantify this robustness, for instance by rerunning several representative points with different random seeds and by recomputing the boundary for f_cold thresholds of 0.05 and 0.2.
  3. [§3, Eq. (7), and §4.1] The power-law dividing line in Eq. (7) is derived from the same simulation outcomes used to draw it and is presented without classification accuracy, margin width, or confidence intervals. The text also notes that for beta < 10 the boundary may instead be a horizontal line near tc/tff ~ 20, so the quoted power law should not be extrapolated to the observationally relevant beta ~ 50 range without a quantified uncertainty. Please provide the SVM fit parameters with errors and a simple measure of separator robustness, such as cross-validated classification accuracy.
minor comments (3)
  1. [§2.2, Eq. (6)] In the sentence defining <Delta T>_z, the text reads '<Delta T>_z = <T>_z - T0 is the is volume-averaged mean difference'; the word 'the is' should be removed.
  2. [Appendix A] In Eq. (A1) the classification y_i is described as a 2-dimensional vector, but in a two-class SVM it is a scalar sign label (+1/-1); please correct the wording.
  3. [Fig. 1 caption] The middle panel is described as using 'the mean beta at the moment of maximum cold-gas accumulation', but the text in §3 says the mean beta at 10 kpc does not significantly evolve; a sentence explaining why the two panels are not identical would help the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the multiphase boundary is a post-hoc fit to simulation outcomes, not used to construct them.

full rationale

The paper's central claim is an empirical result from new MHD simulations: cold gas accumulates in magnetized stratified atmospheres at higher tc/tff than in pure hydrodynamics. The dividing line in Eq. (7) is obtained by fitting an SVM to the simulated cold-gas classifications after the simulations were run; it is a summary of outcomes, not an input to the simulation setup. No fitted parameter is renamed as a prediction, and the abstract's statements about beta and tc/tff are direct descriptions of the plotted simulation results, not predictions derived from Eq. (7). The thermostat of Eq. (6) and the midplane exclusion zone are numerical prescriptions described in Section 2.2; they are not tuned to reproduce the claimed threshold, and their possible role in setting the boundary is a modeling/sensitivity concern rather than a logical circularity. Self-citations to Paper I (Wibking et al. 2025) provide the hydrodynamical baseline and numerical methods; Paper I is an independent simulation study that did not include magnetic fields and did not assume the magnetized result, so using it as a comparison is legitimate external evidence. The acknowledged limitations (no thermal conduction, fixed field geometry, no external turbulence, and restricted beta/tc-tff sampling) make the conclusion conditional but do not make the derivation equivalent to its inputs. Overall, the paper is self-contained in its simulation evidence and shows no step where an output is defined in terms of itself or where a fitted value is presented as an independent prediction.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No new particles, forces, or dimensions are introduced. The paper's central claim rests on parameters fitted to simulation outcomes (the SVM boundary and the cold-gas threshold) and on modeling assumptions about the feedback prescription, conduction suppression, and magnetic field geometry.

free parameters (4)
  • SVM dividing-line slope = -0.3 in log10(tc/tff) vs log10(beta) space
    Fitted to the multiphase/single-phase classification of the 100 simulations; used in Eq. (7) as the boundary summarizing the central claim.
  • SVM dividing-line intercept = 1.5
    Fitted intercept of the same dividing line in Eq. (7).
  • Cold-gas mass fraction threshold f_cold = 0.1
    Hand-selected threshold for classifying a simulation as multiphase; directly controls the position of the fitted boundary.
  • Thermostat gain K_p = not stated in text (inherited from Paper I)
    Dimensionless gain in Eq. (6) that sets how strongly the volume-averaged temperature is forced back to the initial profile; could affect whether thermal instability reaches nonlinear amplitudes.
assumptions (4)
  • domain assumption The ICM is described by single-fluid inviscid ideal MHD with a temperature-independent cooling function C = rho^2 Lambda.
    Used in Section 2.1-2.2; ignores conduction, viscosity, cosmic rays, and the temperature dependence of cooling, which could change thermal instability saturation.
  • ad hoc to paper Volume-averaged thermostat heating (Eq. 6) is a suitable proxy for the heating that maintains approximate thermal balance in cluster cores.
    Controls the background entropy profile; results may depend on this prescription, but no sensitivity tests are shown.
  • domain assumption Thermal conduction is suppressed by at least a factor of about 100 relative to Spitzer in the cluster core, so the Field length is reduced below the scales relevant for thermal instability growth.
    Invoked in Section 4.3 to argue that neglecting conduction does not invalidate the results; based on Meinecke et al. (2022).
  • domain assumption The initial horizontal, uniform, net-flux magnetic field is representative of cluster magnetic fields; vertical fields give a similar saturation density contrast (Ji et al. 2018).
    Used in Section 2.3 and 4.4; fields with zero net flux or tangled geometry may behave differently.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Precipitation plausible: magnetized thermal instability in the intracluster medium." pith.science (2026). https://pith.science/paper/N3CVQ4MI

@misc{pith2026250610277,
  author       = {Pith},
  title        = {Pith review of: Precipitation plausible: magnetized thermal instability in the intracluster medium},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N3CVQ4MI}},
  note         = {Machine review of arXiv:2506.10277}
}
abstract

Observations of galaxy-cluster cores reveal that AGN feedback is strongly associated with both a short central cooling time ($t_{\rm c} \lesssim 10^9 \, {\rm yr}$) and accumulations of cold gas ($\lesssim 10^4 \, {\rm K}$). Also, the central ratio of cooling time to freefall time is rarely observed to drop below $t_{\rm c}/t_{\rm ff} \approx 10$, and large accumulations of cold gas are rarely observed in environments with $t_{\rm c} / t_{\rm ff} \gtrsim 30$. Here we show that the critical range -- $10 \lesssim t_{\rm c}/t_{\rm ff} \lesssim 30$ -- plausibly results from magnetized thermal instability. We present numerical simulations of magnetized stratified atmospheres with an initially uniform magnetic field. Thermal instability in an otherwise static atmosphere with $t_{\rm c}/t_{\rm ff} \approx 10$ progresses to nonlinear amplitudes, causing cooler gas to accumulate, as long as the background ratio of thermal pressure to magnetic pressure is $\beta \lesssim 100$. And in atmospheres with $t_{\rm c}/t_{\rm ff} \approx 20$, cooler gas accumulates for $\beta \lesssim 10$. Magnetized atmospheres are therefore much more likely to precipitate than unmagnetized atmospheres with otherwise identical properties. We hypothesize that AGN feedback triggered by accumulations of cold gas prevents $t_{\rm c}/t_{\rm ff}$ from dropping much below 10, because cold gas inevitably precipitates out of magnetized galactic atmospheres with lower ratios, causing $t_{\rm c}/t_{\rm ff}$ to rise.

Figures

Figures reproduced from arXiv: 2506.10277 by the authors.

Figure 1
Figure 1. Dependence of cold gas accumulation on the mean value of 𝛽 at 10 kpc and the approximate 𝑡c/𝑡ff ratio in the 5 kpc to 50 kpc altitude range. The left panel shows the initial 𝛽 and the central panel shows the mean 𝛽 at the moment of maximum cold-gas accumulation. The corresponding hydrodynamic simulations without magnetic fields (𝛽 = ∞, right panel) are shown as points in a nearly vertical line (with horizontal jitte… view at source ↗
Figure 2
Figure 2. Mass-weighted probability distribution functions (PDFs) for tem￾perature at the moment of maximum cold-gas accumulation. Simulation A (solid line, 𝛽 ≈ 10, 𝑡c/𝑡ff ≈ 3) has the broadest PDF and the greatest accu￾mulation of cold gas. Simulation B (dashed line, 𝛽 ≈ 10, 𝑡c/𝑡ff ≈ 15) has a narrower PDF but still produces cold gas. Simulation C (dot-dashed line, 𝛽 ≈ 100, 𝑡c/𝑡ff ≈ 15) has the narrowest PDF and essentially … view at source ↗
Figure 3
Figure 3. Volume renderings of simulations B and C (first row) and A and D (second row). The colorbar associated with the magnetic field lines indicates the magnetic field amplification with respect to the initial conditions. The color-coded surfaces indicate contours of constant density contrast with respect to the local mean density at a given height. Each simulation volume is 100 kpc in width and extends vertically 100 kpc… view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. $\textit{Eppur Si Muove}$: Self-Sustained Streaming Motions in Multi-Phase MHD

    astro-ph.GA 2025-06 conditional novelty 7.0 of 10

    In MHD, radiatively cooling gas forms self-sustained, field-aligned streaming flows, with adjacent flux tubes counter-streaming, driven by anisotropic magnetic pressure support.

Reference graph

Works this paper leans on

63 extracted references · 7 canonical work pages · cited by 1 Pith paper

  1. [1]

    S., et al., 2024, @doi [ ] 10.1093/mnras/stae1954 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.533.4068A 533, 4068

    Anderson C. S., et al., 2024, @doi [ ] 10.1093/mnras/stae1954 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.533.4068A 533, 4068

    doi:10.1093/mnras/stae1954 2024

  2. [2]

    A., 1991, @doi [ ] 10.1086/169951 , https://ui.adsabs.harvard.edu/abs/1991ApJ...372...25B 372, 25

    Balbus S. A., 1991, @doi [ ] 10.1086/169951 , https://ui.adsabs.harvard.edu/abs/1991ApJ...372...25B 372, 25

    doi:10.1086/169951 1991

  3. [3]

    Berblinger M., Schlier C., 1991, @doi [Computer Physics Communications] https://doi.org/10.1016/0010-4655(91)90064-R , 66, 157

    work page doi:10.1016/0010-4655(91)90064-r 1991

  4. [4]

    Binney J., Tabor G., 1995, @doi [ ] 10.1093/mnras/276.2.663 , https://ui.adsabs.harvard.edu/abs/1995MNRAS.276..663B 276, 663

    doi:10.1093/mnras/276.2.663 1995

  5. [5]

    pp 108--122

    Buitinck L., et al., 2013, in ECML PKDD Workshop: Languages for Data Mining and Machine Learning. pp 108--122

    work page 2013

  6. [6]

    L., Taylor G

    Carilli C. L., Taylor G. B., 2002, @doi [ ] 10.1146/annurev.astro.40.060401.093852 , https://ui.adsabs.harvard.edu/abs/2002ARA&A..40..319C 40, 319

    arXiv 2002

  7. [7]

    W., Donahue M., Voit G

    Cavagnolo K. W., Donahue M., Voit G. M., Sun M., 2008, @doi [ ] 10.1086/591665 , https://ui.adsabs.harvard.edu/abs/2008ApJ...683L.107C 683, L107

    doi:10.1086/591665 2008

  8. [8]

    W., Donahue M., Voit G

    Cavagnolo K. W., Donahue M., Voit G. M., Sun M., 2009, @doi [ ] 10.1088/0067-0049/182/1/12 , https://ui.adsabs.harvard.edu/abs/2009ApJS..182...12C 182, 12

    doi:10.1088/0067-0049/182/1/12 2009

Show all 63 references
  1. [9]

    pp 357--372, @doi 10.1201/b12985

    Childs H., et al., 2012, in , High Performance Visualization--Enabling Extreme-Scale Scientific Insight. pp 357--372, @doi 10.1201/b12985

    2012 doi

  2. [10]

    u ggen M., Kaiser C. R., B \

    Churazov E., Br \"u ggen M., Kaiser C. R., B \"o hringer H., Forman W., 2001, @doi [ ] 10.1086/321357 , https://ui.adsabs.harvard.edu/abs/2001ApJ...554..261C 554, 261

    2001 doi

  3. [11]

    D., Schnitzer T., Wesenberg M., 2002, @doi [Journal of Computational Physics] 10.1006/jcph.2001.6961 , https://ui.adsabs.harvard.edu/abs/2002JCoPh.175..645D 175, 645

    Dedner A., Kemm F., Kr \"o ner D., Munz C. D., Schnitzer T., Wesenberg M., 2002, @doi [Journal of Computational Physics] 10.1006/jcph.2001.6961 , https://ui.adsabs.harvard.edu/abs/2002JCoPh.175..645D 175, 645

    2002

  4. [12]

    M., 2022, @doi [ ] 10.1016/j.physrep.2022.04.005 , https://ui.adsabs.harvard.edu/abs/2022PhR...973....1D 973, 1

    Donahue M., Voit G. M., 2022, @doi [ ] 10.1016/j.physrep.2022.04.005 , https://ui.adsabs.harvard.edu/abs/2022PhR...973....1D 973, 1

    2022 doi

  5. [13]

    J., Cavagnolo K

    Donahue M., Horner D. J., Cavagnolo K. W., Voit G. M., 2006, @doi [ ] 10.1086/503270 , https://ui.adsabs.harvard.edu/abs/2006ApJ...643..730D 643, 730

    2006 doi

  6. [14]

    C., Nulsen P

    Fabian A. C., Nulsen P. E. J., Canizares C. R., 1984, @doi [ ] 10.1038/310733a0 , https://ui.adsabs.harvard.edu/abs/1984Natur.310..733F 310, 733

    1984 doi

  7. [15]

    C., Nulsen P

    Fabian A. C., Nulsen P. E. J., Canizares C. R., 1991, @doi [ ] 10.1007/BF00872767 , https://ui.adsabs.harvard.edu/abs/1991A&ARv...2..191F 2, 191

    1991 doi

  8. [16]

    P., 2015, @doi [Journal of Computational Science] https://doi.org/10.1016/j.jocs.2015.08.008 , 11, 46

    Feinberg J., Langtangen H. P., 2015, @doi [Journal of Computational Science] https://doi.org/10.1016/j.jocs.2015.08.008 , 11, 46

    2015 doi

  9. [17]

    Gaspari M., Ruszkowski M., Sharma P., 2012, @doi [ ] 10.1088/0004-637X/746/1/94 , https://ui.adsabs.harvard.edu/abs/2012ApJ...746...94G 746, 94

    2012 doi

  10. [18]

    P., 2013, @doi [ ] 10.1093/mnras/stt692 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.432.3401G 432, 3401

    Gaspari M., Ruszkowski M., Oh S. P., 2013, @doi [ ] 10.1093/mnras/stt692 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.432.3401G 432, 3401

    2013 doi

  11. [19]

    Gommers R., et al., 2025, scipy/scipy: SciPy 1.16.0rc1, @doi 10.5281/zenodo.15484555 , https://doi.org/10.5281/zenodo.15484555

    2025 doi

  12. [20]

    arXiv:2202.12309

    Grete P., et al., 2022, @doi [arXiv e-prints] 10.48550/arXiv.2202.12309 , https://ui.adsabs.harvard.edu/abs/2022arXiv220212309G p. arXiv:2202.12309

    2022 doi arXiv

  13. [21]

    H., 1960, @doi [Numerische Mathematik] 10.1007/BF01386213 , 2, 84

    Halton J. H., 1960, @doi [Numerische Mathematik] 10.1007/BF01386213 , 2, 84

    1960 doi

  14. [22]

    R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , 585, 357

    Harris C. R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , 585, 357

    2020 doi

  15. [23]

    T., et al., 2017, @doi [ ] 10.3847/1538-4357/aa9af3 , https://ui.adsabs.harvard.edu/abs/2017ApJ...851...66H 851, 66

    Hogan M. T., et al., 2017, @doi [ ] 10.3847/1538-4357/aa9af3 , https://ui.adsabs.harvard.edu/abs/2017ApJ...851...66H 851, 66

    2017 doi

  16. [24]

    D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    Hunter J. D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    2007 doi

  17. [25]

    Jaccard P., 1912, @doi [New Phytologist] 10.1111/j.1469-8137.1912.tb05611.x , https://ui.adsabs.harvard.edu/abs/1912NewPh..11...37J 11, 37

    1912

  18. [26]

    P., McCourt M., 2018, @doi [ ] 10.1093/mnras/sty293 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.476..852J 476, 852

    Ji S., Oh S. P., McCourt M., 2018, @doi [ ] 10.1093/mnras/sty293 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.476..852J 476, 852

    2018 doi

  19. [27]

    R., Rudnick L., Jones T

    Johnson A. R., Rudnick L., Jones T. W., Mendygral P. J., Dolag K., 2020, @doi [ ] 10.3847/1538-4357/ab5d30 , https://ui.adsabs.harvard.edu/abs/2020ApJ...888..101J 888, 101

    2020 doi

  20. [28]

    K \"a ppeli R., Mishra S., 2014, @doi [Journal of Computational Physics] 10.1016/j.jcp.2013.11.028 , https://ui.adsabs.harvard.edu/abs/2014JCoPh.259..199K 259, 199

    2014 doi

  21. [29]

    pp 87 -- 90

    Kluyver T., et al., 2016, in Loizides F., Schmidt B., eds, Positioning and Power in Academic Publishing: Players, Agents and Agendas. pp 87 -- 90

    2016

  22. [30]

    L., Ruszkowski M., Voit G

    Li Y., Bryan G. L., Ruszkowski M., Voit G. M., O'Shea B. W., Donahue M., 2015, @doi [ ] 10.1088/0004-637X/811/2/73 , https://ui.adsabs.harvard.edu/abs/2015ApJ...811...73L 811, 73

    2015 doi

  23. [31]

    Loewenstein M., 1990, @doi [ ] 10.1086/168331 , https://ui.adsabs.harvard.edu/abs/1990ApJ...349..471L 349, 471

    1990 doi

  24. [33]

    R., Tremblay G

    McDonald M., Gaspari M., McNamara B. R., Tremblay G. R., 2018, @doi [ ] 10.3847/1538-4357/aabace , https://ui.adsabs.harvard.edu/abs/2018ApJ...858...45M 858, 45

    2018 doi

  25. [34]

    F., Cowie L

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

    1977 doi

  26. [35]

    R., Nulsen P

    McNamara B. R., Nulsen P. E. J., 2007, @doi [ ] 10.1146/annurev.astro.45.051806.110625 , https://ui.adsabs.harvard.edu/abs/2007ARA&A..45..117M 45, 117

    2007 arXiv

  27. [36]

    R., Nulsen P

    McNamara B. R., Nulsen P. E. J., 2012, @doi [New Journal of Physics] 10.1088/1367-2630/14/5/055023 , https://ui.adsabs.harvard.edu/abs/2012NJPh...14e5023M 14, 055023

    2012 doi

  28. [37]

    R., Russell H

    McNamara B. R., Russell H. R., Nulsen P. E. J., Hogan M. T., Fabian A. C., Pulido F., Edge A. C., 2016, @doi [ ] 10.3847/0004-637X/830/2/79 , https://ui.adsabs.harvard.edu/abs/2016ApJ...830...79M 830, 79

    2016 doi

  29. [38]

    R., O'Shea B

    Meece G. R., O'Shea B. W., Voit G. M., 2015, @doi [ ] 10.1088/0004-637X/808/1/43 , https://ui.adsabs.harvard.edu/abs/2015ApJ...808...43M 808, 43

    2015 doi

  30. [39]

    Meinecke J., et al., 2022, @doi [Science Advances] 10.1126/sciadv.abj6799 , https://ui.adsabs.harvard.edu/abs/2022SciA....8J6799M 8, eabj6799

    2022 doi

  31. [40]

    Mignone A., Tzeferacos P., Bodo G., 2010, @doi [Journal of Computational Physics] 10.1016/j.jcp.2010.04.013 , https://ui.adsabs.harvard.edu/abs/2010JCoPh.229.5896M 229, 5896

    2010 doi

  32. [41]

    Minoshima T., Miyoshi T., 2021, @doi [Journal of Computational Physics] 10.1016/j.jcp.2021.110639 , https://ui.adsabs.harvard.edu/abs/2021JCoPh.44610639M 446, 110639

    2021

  33. [42]

    Miyoshi T., Kusano K., 2005, @doi [Journal of Computational Physics] 10.1016/j.jcp.2005.02.017 , https://ui.adsabs.harvard.edu/abs/2005JCoPh.208..315M 208, 315

    2005 doi

  34. [43]

    Nobels F. S. J., Schaye J., Schaller M., Bah \'e Y. M., Chaikin E., 2022, @doi [ ] 10.1093/mnras/stac2061 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.515.4838N 515, 4838

    2022 doi

  35. [44]

    Nulsen P. E. J., 1986, @doi [ ] 10.1093/mnras/221.2.377 , https://ui.adsabs.harvard.edu/abs/1986MNRAS.221..377N 221, 377

    1986 doi

  36. [45]

    Osinga E., et al., 2022, @doi [ ] 10.1051/0004-6361/202243526 , https://ui.adsabs.harvard.edu/abs/2022A&A...665A..71O 665, A71

    2022 doi

  37. [46]

    Osinga E., et al., 2025, @doi [ ] 10.1051/0004-6361/202451885 , https://ui.adsabs.harvard.edu/abs/2025A&A...694A..44O 694, A44

    2025 doi

  38. [47]

    Pedregosa F., et al., 2011, Journal of Machine Learning Research, 12, 2825

    2011

  39. [48]

    E., 2007, @doi [Computing in Science and Engineering] 10.1109/MCSE.2007.53 , https://ui.adsabs.harvard.edu/abs/2007CSE.....9c..21P 9, 21

    Perez F., Granger B. E., 2007, @doi [Computing in Science and Engineering] 10.1109/MCSE.2007.53 , https://ui.adsabs.harvard.edu/abs/2007CSE.....9c..21P 9, 21

    2007 doi

  40. [49]

    Pizzolato F., Soker N., 2005, @doi [ ] 10.1086/444344 , https://ui.adsabs.harvard.edu/abs/2005ApJ...632..821P 632, 821

    2005 doi

  41. [50]

    Prasad D., Sharma P., Babul A., 2015, @doi [ ] 10.1088/0004-637X/811/2/108 , https://ui.adsabs.harvard.edu/abs/2015ApJ...811..108P 811, 108

    2015 doi

  42. [51]

    A., et al., 2018, @doi [ ] 10.3847/1538-4357/aaa54b , https://ui.adsabs.harvard.edu/abs/2018ApJ...853..177P 853, 177

    Pulido F. A., et al., 2018, @doi [ ] 10.3847/1538-4357/aaa54b , https://ui.adsabs.harvard.edu/abs/2018ApJ...853..177P 853, 177

    2018 doi

  43. [52]

    J., 2012, @doi [ ] 10.1111/j.1365-2966.2011.20246.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.420.3174S 420, 3174

    Sharma P., McCourt M., Quataert E., Parrish I. J., 2012, @doi [ ] 10.1111/j.1365-2966.2011.20246.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.420.3174S 420, 3174

    2012

  44. [53]

    Tremmel M., et al., 2019, @doi [ ] 10.1093/mnras/sty3336 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.483.3336T 483, 3336

    2019 doi

  45. [54]

    J., Smith B

    Turk M. J., Smith B. D., Oishi J. S., Skory S., Skillman S. W., Abel T., Norman M. L., 2011, @doi [ ] 10.1088/0067-0049/192/1/9 , https://ui.adsabs.harvard.edu/abs/2011ApJS..192....9T 192, 9

    2011 doi

  46. [55]

    Virtanen P., et al., 2020, @doi [Nature Methods] 10.1038/s41592-019-0686-2 , https://rdcu.be/b08Wh 17, 261

    2020 doi

  47. [56]

    M., 2018, @doi [ ] 10.3847/1538-4357/aae8e2 , https://ui.adsabs.harvard.edu/abs/2018ApJ...868..102V 868, 102

    Voit G. M., 2018, @doi [ ] 10.3847/1538-4357/aae8e2 , https://ui.adsabs.harvard.edu/abs/2018ApJ...868..102V 868, 102

    2018 doi

  48. [57]

    M., 2021, @doi [ ] 10.3847/2041-8213/abe11f , https://ui.adsabs.harvard.edu/abs/2021ApJ...908L..16V 908, L16

    Voit G. M., 2021, @doi [ ] 10.3847/2041-8213/abe11f , https://ui.adsabs.harvard.edu/abs/2021ApJ...908L..16V 908, L16

    2021 doi

  49. [58]

    M., Donahue M., Bryan G

    Voit G. M., Donahue M., Bryan G. L., McDonald M., 2015, @doi [ ] 10.1038/nature14167 , https://ui.adsabs.harvard.edu/abs/2015Natur.519..203V 519, 203

    2015 doi

  50. [59]

    M., Meece G., Li Y., O'Shea B

    Voit G. M., Meece G., Li Y., O'Shea B. W., Bryan G. L., Donahue M., 2017, @doi [ ] 10.3847/1538-4357/aa7d04 , https://ui.adsabs.harvard.edu/abs/2017ApJ...845...80V 845, 80

    2017 doi

  51. [60]

    S., 2024, arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2024arXiv240604405W p

    Wagg T., Broekgaarden F. S., 2024, arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2024arXiv240604405W p. arXiv:2406.04405

    2024

  52. [61]

    Wagg T., Broekgaarden F., Gültekin K., 2024, TomWagg/software-citation-station: v1.2, @doi 10.5281/zenodo.13225824 , https://doi.org/10.5281/zenodo.13225824

    2024 doi

  53. [62]

    D., Voit G

    Wibking B. D., Voit G. M., O'Shea B. W., 2025, @doi [ ] 10.1093/mnras/staf092 , https://ui.adsabs.harvard.edu/abs/2025MNRAS.537..739W 537, 739

    2025 doi

  54. [63]

    da Costa-Luis C., et al., 2024, tqdm: A fast, Extensible Progress Bar for Python and CLI, @doi 10.5281/zenodo.14231923 , https://doi.org/10.5281/zenodo.14231923

    2024 doi

  55. [64]

    scikit-learn developers T., 2025, scikit-learn, @doi 10.5281/zenodo.14627164 , https://doi.org/10.5281/zenodo.14627164

    2025 doi

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.