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arxiv: 2512.11309 · v2 · pith:YAVBSKWHnew · submitted 2025-12-12 · 🌌 astro-ph.GA

Kennicutt-Schmidt relation of galaxies over 13 billion years in the COLIBRE hydrodynamical simulations

Claudia del P. Lagos (1 , 2) , Joop Schaye , Matthieu Schaller , Danail Obreschkow , Yannick M. Bahe , Alejandro Benitez-Llambay , Evgenii Chaikin
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Camila Correa Timothy A. Davis Carlos S. Frenk Filip Husko Melanie Kaasinen Robert J. McGibbon Kyle Oman Sylvia Ploeckinger Alexander J. Richings James W. Trayford Jing Wang Ruby J. Wright ((1) International Centre for Radio Astronomy Research (ICRAR) M468 University of Western Australia Crawley WA Australia (2) Cosmic Dawn Center (DAWN) Denmark)
This is my paper

Pith reviewed 2026-05-21 18:22 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords Kennicutt-Schmidt relationmolecular gas depletion timehydrodynamical simulationsgalaxy star formationredshift evolutionspecific star formation rateatomic and molecular hydrogen
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The pith

The COLIBRE simulations predict that the H2 depletion time decreases by a factor of 20 from the present to z=8, matching observations up to z=5.

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

The paper examines the Kennicutt-Schmidt relation between star formation rate surface density and gas surface density using COLIBRE hydrodynamical simulations from redshift 0 to 8 for galaxies above 10^9 solar masses. These simulations track atomic and molecular gas through non-equilibrium chemistry and dust evolution. The results show the molecular depletion time shortens by a factor of about 20 at high redshift due to lower metallicity, causing more atomic gas and less molecular gas for the same star formation rate. The predictions for how depletion time changes and correlates with specific star formation rate align well with data from z=0 to z=5. This would matter if true because it confirms that the simulations capture the evolving link between gas and stars in galaxies over most of cosmic history.

Core claim

In the COLIBRE simulations the H2 KS relation shifts to higher normalization in galaxies with higher sSFR while the HI KS relation steepens for lower-mass galaxies. The H2 depletion time decreases by a factor of approximately 20 from z = 0 to z = 8 primarily due to the decreasing gas-phase metallicity. This leads to less H2 and more HI being associated with a given SFR at higher redshift. Galaxies with higher sSFRs have a larger molecular gas content and higher star formation efficiency per unit gas mass on kpc scales. The predicted evolution of the H2 depletion time and its correlation with a galaxy's sSFR agree remarkably well with observations in a wide redshift range, 0≤z≤5.

What carries the argument

On-the-fly non-equilibrium chemistry coupled to dust grain evolution and radiative cooling, enabling direct predictions of atomic HI and molecular H2 Kennicutt-Schmidt relations.

If this is right

  • The H2 depletion time shortens with increasing redshift due to lower metallicity reducing the molecular gas fraction.
  • Galaxies with elevated specific star formation rates exhibit higher molecular gas content and star formation efficiency on kiloparsec scales.
  • The scatter in the KS relations correlates with stellar surface density, local specific SFR, and gas metallicity.
  • At high redshifts a fixed star formation rate corresponds to higher atomic gas and lower molecular gas surface densities.

Where Pith is reading between the lines

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

  • If the trend continues, depletion times at z greater than 5 should be even shorter than at z=5.
  • This agreement suggests the subgrid models can be used to predict other gas-related properties in high-redshift galaxies.
  • Observations targeting the HI to H2 ratio at fixed SFR in distant galaxies could provide a direct test.
  • Similar simulations without non-equilibrium chemistry might not reproduce the same redshift evolution.

Load-bearing premise

The subgrid models for star formation, stellar feedback, and non-equilibrium chemistry accurately capture unresolved physical processes across the full range of galaxy masses and redshifts studied.

What would settle it

Direct observations of molecular gas depletion times in galaxies at redshifts between 0 and 5 that fail to show a decrease by a factor of roughly 20 or lack the predicted correlation with specific star formation rate.

Figures

Figures reproduced from arXiv: 2512.11309 by 2), (2) Cosmic Dawn Center (DAWN), Alejandro Benitez-Llambay, Alexander J. Richings, Australia, Camila Correa, Carlos S. Frenk, Claudia del P. Lagos (1, Crawley, Danail Obreschkow, Denmark), Evgenii Chaikin, Filip Husko, James W. Trayford, Jing Wang, Joop Schaye, Kyle Oman, M468, Matthieu Schaller, Melanie Kaasinen, Robert J. McGibbon, Ruby J. Wright ((1) International Centre for Radio Astronomy Research (ICRAR), Sylvia Ploeckinger, Timothy A. Davis, University of Western Australia, WA, Yannick M. Bahe.

Figure 1
Figure 1. Figure 1: Three example galaxies at 𝑧 = 0 in the L025m6 COLIBRE simulation used in this work. The top and middle panels show face-on and edge-on views of the gas and stellar disk, which were produced using R-package swift. The gas is coloured by the ionisation fraction, with blue indicating neutral gas (H i + H2), and red ionised gas (primarily HII regions when the red compact regions are in the disk). The stellar c… view at source ↗
Figure 2
Figure 2. Figure 2: KS relation for H i (left panels), H2 (middle panels) and total neutral hydrogen (H i+H2) (right panels) for galaxies at 𝑧 = 0 in the COLIBRE simulation L200m6 (see [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Probability density function of the gas density of gas particles in the CNM, weighted by the H2, H i mass or the SFR, as labelled. This is shown for 𝑧 = 0 for gas particles in the L200 m6 (thick lines) and L025m5 (thin lines) simulations, that are in the CNM of galaxies at 𝑧 = 0 with 𝑀★ ≥ 109 M⊙ and SFR> 0. colder due to the difficulty in forming H2 in the absence of dust. This is in qualitative agreement … view at source ↗
Figure 3
Figure 3. Figure 3: The distribution of all gas particles within 50 pkpc of the centre of mass of galaxies at 𝑧 = 0 with 𝑀★ > 109 M⊙ and SFR > 0 in the temperature-density plane. Contours enclose the regions where 99%, 95%, 68% and 50% of the particles are. The coloured hexbins show the H i (top), H2 (middle) and SFR (bottom) contribution from each bin to the total HI, H2 and SFR, respectively. The totals are obtained by summ… view at source ↗
Figure 5
Figure 5. Figure 5: As [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The fraction of the CNM in the form of H i (orange solid line) and H2 (orange dotted line), and the SFR-weighted gas density (blue line with shaded region), as a function of gas metallicity. This is constructed with all the gas particles that are within 50 pkpc from the centres of galaxies with 𝑀★ ≥ 109 M⊙ and SFR > 0 at 𝑧 = 0 in the L200m6 (thick lines) and L025m5 (thin lines) simulations. The H i fractio… view at source ↗
Figure 7
Figure 7. Figure 7: The correlation between the H2 (top) and H i (bottom) depletion times, defined as Σgas/ΣSFR, with gas being either H2 or HI, and the stellar surface density, cold gas metallicity, surface density of dust, local sSFR and cool gas velocity dispersion (as defined in Eq. 2), as labelled. Lines and shaded regions show medians and 16th − 84th percentile ranges, respectively. To plot all the latter properties on … view at source ↗
Figure 9
Figure 9. Figure 9: The dependence of the (resolved) H i depletion time, 𝜏HI on the local stellar surface density, Σ★, for COLIBRE galaxies at 𝑧 = 0 with 𝑀★ > 109 M⊙ compared with the FEASTS (Wang et al. 2024) and PHANGS (Sun et al. 2022) surveys. The lines and symbols show the median of COLIBRE and the observations, respectively, while the shaded region and error bars show the 16th − 84th percentile ranges. This threshold ma… view at source ↗
Figure 8
Figure 8. Figure 8: The H2 KS relation at 𝑧 = 0 for galaxies selected based on their sSFR (top panels) and stellar mass (bottom panel). The median and 16th −84th percentiles are shown with solid lines and shaded regions, respectively. All galaxies included here have 𝑀★ > 109 M⊙ and SFR > 0. L025m6 simulation (see Table A1), there is an offset in normalisa￾tion. This is not surprising given that the stellar mass-gas metallicit… view at source ↗
Figure 10
Figure 10. Figure 10: Top panel: Deviations from the median molecular gas KS relation (log10 (ΣSFR) − ⟨log10 (ΣSFR) ⟩) at 𝑧 = 0 as a function of H2 surface density, separating regions by their local sSFR (sΣSFR ≡ ΣSFR/Σ★, for observations (symbols) and COLIBRE (lines). Symbols and lines show medians, while error bars and shaded regions show the 16th − 84th percentile ranges. For ALMaQUEST (Lin et al. 2019), we include all gala… view at source ↗
Figure 12
Figure 12. Figure 12: As the top panel of [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The slope (top) and zero-point (bottom) of the KS relation fits for individual 𝑧 = 0 galaxies as a function of stellar mass in COLIBRE. We show results for the L200m6 (solid lines) and L025m5 (dotted lines) simulations, as labelled in the bottom panel. The equation being fitted is Eq. 3. We show the slope and zero-point of the fits for the case of fitting only H i (blue) and H2 (red). Lines with shaded re… view at source ↗
Figure 14
Figure 14. Figure 14: As [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Top panel: The fraction of the CNM in H i (solid lines) and H2 (dotted lines) as a function of gas metallicity, from 𝑧 = 0 to 𝑧 = 5. We apply the same stellar and SFR selection of [PITH_FULL_IMAGE:figures/full_fig_p016_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: The evolution of the H2 depletion time compared with the com￾pilation of observations presented in Tacconi et al. (2020). Small circles correspond to individual galaxies, while the stars correspond to the medians computed from the observations. The thick and thin solid lines correspond to the median and 16th −84th percentile ranges of all galaxies in COLIBRE with 𝑀★ ≤ 109 M⊙ and SFR > 0. To compute 𝜏H2 , … view at source ↗
Figure 18
Figure 18. Figure 18: The H2 depletion time as a function of sSFR at different redshift bins from 𝑧 ≈ 0.5 to 𝑧 ≈ 5, compared with a compilation of observations presented in Tacconi et al. (2020). The solid and dashed lines in each panel show the median and 16th −84th percentile ranges, respectively, for galaxies in COLIBRE. Symbols are as in [PITH_FULL_IMAGE:figures/full_fig_p017_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Evolution of some of the strongest resolved relations found in COLIBRE, between local galaxy properties and the kpc-scale H2 (left) and H i (right) depletion timescales. For H2, we show the evolution of the relation between the resolved 𝜏H2 and the local gas metallicity (top-left panel) and sSFR surface density (bottom-left panel), between 𝑧 = 0 and 8. Solid lines with shaded regions represent the medians… view at source ↗
read the original abstract

We investigate the correlation between star formation rate (SFR) surface density and gas surface density (known as the Kennicutt-Schmidt, KS, relation) at kiloparsec (kpc) scales across cosmic time ($0\le z \le 8$) for galaxies with stellar masses $>10^9\,\rm M_{\odot}$, using the COLIBRE state-of-the-art cosmological hydrodynamical simulations. These simulations feature on-the-fly non-equilibrium chemistry coupled to dust grain evolution and detailed radiative cooling down to $\approx 10$~K, enabling direct predictions for the atomic (HI) and molecular (H$_2$) KS relations. At $z\approx 0$, COLIBRE reproduces the observed (spatially-resolved) KS relations for HI and H$_2$, including the associated scatter, which we predict to be significantly correlated with stellar surface density, local specific SFR (sSFR), and gas metallicity. We show that the HI KS relation steepens for lower-mass galaxies, while the H$_2$ KS relation shifts to higher normalisation in galaxies with higher sSFRs. The H$_2$ depletion time decreases by a factor of $\approx 20$ from $z = 0$ to $z = 8$, primarily due to the decreasing gas-phase metallicity. This results in less H$_2$ and more HI being associated with a given SFR at higher redshift. We also find that galaxies with higher sSFRs have a larger molecular gas content and higher star formation efficiency per unit gas mass on kpc scales. The predicted evolution of the H$_2$ depletion time and its correlation with a galaxy's sSFR agree remarkably well with observations in a wide redshift range, $0\le z\le 5$.

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

3 major / 2 minor

Summary. The paper uses the COLIBRE cosmological hydrodynamical simulations, which include on-the-fly non-equilibrium chemistry and dust evolution, to examine the Kennicutt-Schmidt (KS) relations for HI and H2 at kpc scales in galaxies with M* > 10^9 Msun from z=0 to z=8. It reports reproduction of observed low-z KS relations including scatter correlated with stellar surface density, local sSFR, and metallicity; the HI KS relation steepens in lower-mass galaxies while the H2 KS shifts with sSFR. The central result is that the H2 depletion time drops by a factor of ~20 from z=0 to z=8, driven primarily by lower gas-phase metallicity yielding less H2 for a given SFR, with galaxies of higher sSFR showing larger molecular fractions and higher star-formation efficiency per unit gas mass. The predicted depletion-time evolution and sSFR correlation are claimed to match observations from z=0 to z=5.

Significance. If the subgrid models prove robust, the work supplies a valuable forward-model prediction for the redshift evolution of molecular-gas depletion times and KS relations, directly linking low- and high-redshift observations through physics-based hydrodynamics rather than post-processed fits. The on-the-fly non-equilibrium chemistry coupled to dust grain evolution is a clear technical strength that enables self-consistent HI/H2 predictions without additional assumptions.

major comments (3)
  1. [Results on high-redshift trends] The attribution of the factor-of-20 drop in H2 depletion time primarily to decreasing metallicity (abstract and high-z results) is load-bearing for the evolutionary claim, yet the manuscript provides no quantitative decomposition isolating the metallicity effect from concurrent changes in gas density, radiation field, or dynamical state across the z>2 regime.
  2. [Simulation methods and validation] No resolution-convergence tests or subgrid-parameter variation suite is described for z>2, where galaxies are more metal-poor and dynamically hotter; this directly affects the reliability of the metallicity-dependent H2 formation and local SF efficiency in the non-equilibrium chemistry module that underpins the depletion-time evolution.
  3. [Comparison with observations] The reported agreement with observations up to z=5 for depletion time and sSFR correlation (abstract) rests on the subgrid star-formation efficiency and feedback parameters that were calibrated at z~0; without explicit tests showing that the same parameters remain unbiased at lower metallicities, the high-z extrapolation carries an unquantified systematic risk.
minor comments (2)
  1. [Figures] Figure captions and axis labels should explicitly state the surface-density units (e.g., M⊙ yr⁻¹ kpc⁻²) and the exact aperture or smoothing scale used for all KS measurements.
  2. [Methods] The definition of 'local sSFR' used for the scatter correlations should be given with a precise radial or mass-weighted averaging prescription to allow direct comparison with observational selections.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed report. We address each major comment below and have revised the manuscript accordingly to improve the robustness and clarity of our results.

read point-by-point responses

  1. Referee: [Results on high-redshift trends] The attribution of the factor-of-20 drop in H2 depletion time primarily to decreasing metallicity (abstract and high-z results) is load-bearing for the evolutionary claim, yet the manuscript provides no quantitative decomposition isolating the metallicity effect from concurrent changes in gas density, radiation field, or dynamical state across the z>2 regime.

    Authors: We appreciate this observation. Our attribution follows from the strong dependence of H2 formation on dust abundance (hence metallicity) in the non-equilibrium chemistry module, combined with the fact that average gas surface densities do not rise sufficiently with redshift to offset the metallicity decline. To make this more quantitative, we have added a new subsection and figure that holds gas surface density and local radiation field fixed while varying metallicity and redshift; this decomposition shows that metallicity accounts for the large majority of the depletion-time evolution, with density and dynamical effects contributing at the ~20% level or less. revision: yes

  2. Referee: [Simulation methods and validation] No resolution-convergence tests or subgrid-parameter variation suite is described for z>2, where galaxies are more metal-poor and dynamically hotter; this directly affects the reliability of the metallicity-dependent H2 formation and local SF efficiency in the non-equilibrium chemistry module that underpins the depletion-time evolution.

    Authors: The referee is correct that dedicated high-redshift convergence tests were not presented. The COLIBRE runs exist at two resolutions, and internal checks confirm that the H2 depletion-time trend is consistent between them at z>2. In the revised manuscript we have added an appendix with explicit resolution-convergence plots for the KS relations and depletion times focused on the z=2–8 range, together with a brief discussion of how the non-equilibrium chemistry behaves under the higher dynamical temperatures encountered at early times. revision: yes

  3. Referee: [Comparison with observations] The reported agreement with observations up to z=5 for depletion time and sSFR correlation (abstract) rests on the subgrid star-formation efficiency and feedback parameters that were calibrated at z~0; without explicit tests showing that the same parameters remain unbiased at lower metallicities, the high-z extrapolation carries an unquantified systematic risk.

    Authors: We agree that the subgrid star-formation and feedback parameters were calibrated at z≈0 and that this introduces a potential systematic when extrapolating to lower metallicities. The non-equilibrium chemistry itself is physically motivated and independent of the SF-efficiency calibration, and the model reproduces the observed depletion-time evolution without retuning. In the revised version we have expanded the discussion to quantify this uncertainty, added a short parameter-variation test at high redshift (varying the H2 formation rate coefficient within plausible bounds), and explicitly flagged the calibration limitation in the conclusions. revision: partial

Circularity Check

0 steps flagged

No significant circularity: forward-model outputs from calibrated hydro simulations

full rationale

The paper reports direct outputs from the COLIBRE cosmological hydrodynamical simulations, including on-the-fly non-equilibrium chemistry and dust evolution, to predict the evolution of the HI and H2 Kennicutt-Schmidt relations from z=0 to z=8. These are not derived by fitting parameters to the high-redshift data being reported, nor do any equations reduce the claimed depletion-time evolution or sSFR correlations to the low-redshift calibration inputs by construction. Subgrid calibration to z≈0 observations is standard practice for such simulations and does not force the redshift evolution results; the high-z predictions remain independent tests against external observations. No self-citation chains, self-definitional steps, or ansatzes smuggled via prior work are load-bearing in the derivation chain described.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Central claims rest on the fidelity of subgrid star-formation and feedback prescriptions plus the accuracy of the non-equilibrium chemistry network; these are not derived from first principles within the paper.

free parameters (1)
  • subgrid star formation efficiency and feedback parameters
    Parameters controlling unresolved star formation and supernova feedback are calibrated to reproduce galaxy properties at low redshift.
axioms (2)
  • standard math Lambda-CDM cosmology and standard hydrodynamical equations govern large-scale structure and gas dynamics
    Invoked as the background framework for the cosmological simulation volume.
  • domain assumption Non-equilibrium chemistry network and dust model accurately track HI/H2 transitions down to 10 K
    Central to the direct prediction of atomic versus molecular KS relations.

pith-pipeline@v0.9.0 · 6002 in / 1347 out tokens · 62190 ms · 2026-05-21T18:22:47.833257+00:00 · methodology

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Forward citations

Cited by 3 Pith papers

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

  1. The galaxy ultraviolet luminosity function from $z=7$ to $15$ in the COLIBRE simulations

    astro-ph.GA 2026-05 unverdicted novelty 5.0

    COLIBRE simulations underpredict bright-end UV galaxy luminosities by 1 to 2.5 magnitudes at z=7-15 compared with observations, with the discrepancy persisting after dust attenuation and uncertainty accounting.

  2. Galaxy luminosity functions from far-UV to submillimetre at $z=0$ in the COLIBRE simulations

    astro-ph.GA 2026-05 conditional novelty 5.0

    COLIBRE simulations with SKIRT post-processing match observed galaxy luminosity functions from FUV to submm at z=0, except underpredicting bright mid-IR galaxies.

  3. The morphologies of present-day galaxies in the COLIBRE simulations

    astro-ph.GA 2026-04 unverdicted novelty 5.0

    COLIBRE simulations find kinematic galaxy morphology peaks in rotational support at stellar masses of 1-2 x 10^10 solar masses and correlates more with internal properties like gas richness than with host halo properties.

Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages · cited by 3 Pith papers

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    Abbott T. M. C., Aguena M., Alarcon A., Allam S., Alves O., Amon A., Andrade-Oliveira F., Annis J. et al, 2022, Phys. Rev. D, 105, 023520 Agertz O., Kravtsov A. V., Leitner S. N., Gnedin N. Y., 2013, ApJ, 770, 25 Agertz O., Renaud F., Feltzing S., Read J. I., Ryde N., Andersson E. P., Rey M. P., Bensby T. et al, 2021, MNRAS, 503, 5826 Ali-Haïmoud Y., Bird...

    work page arXiv 2022

  2. [2]

    Below that surface density, m5 displays the steepest relationship (at 0≲log 10 (ΣHI/M⊙ pc−2)≲1)

    At𝑧=2, there are differences between the three resolutions at low surface densities of HI,log10 (ΣHI/M⊙ pc−2)≲1. Below that surface density, m5 displays the steepest relationship (at 0≲log 10 (ΣHI/M⊙ pc−2)≲1). In that regime, it follows the same slope as predicted for higher surface densities. For H2, we see good convergence at high surface densities. At ...

    work page 2025

  3. [3]

    2 but for the simulations L025m5, L025m6 and L025m7, as labelled, at𝑧=0(top) and𝑧=2(middle)

    6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5 T otal 0.1Gyr 1Gyr 10Gyr Bigiel+08 Bigiel+10 Figure A1.As Fig. 2 but for the simulations L025m5, L025m6 and L025m7, as labelled, at𝑧=0(top) and𝑧=2(middle). The bottom panel shows the𝑧=0 KS relation again, but for the runs L050m6 Thermal and Hybrid, as labelled. Table 1 summarises the runs used in thi...

    work page 2025

  4. [4]

    A3 shows an overall good convergence between the three resolutions

    In the case of𝜏HI, Fig. A3 shows an overall good convergence between the three resolutions. ThisagreeswiththeconvergenceseenintheaverageHiKSrelation in Fig. A1. The convergence is particularly good for the properties that are most strongly correlated with𝜏HI, i.e.Σ★ andΣ dust. For𝜏 H2 we see that the m5 and m6 resolutions produce very similar correlations...

    work page 2025

  5. [5]

    Annulionface-ongalaxy

    10 1 100 H2/Gyr 1 Figure A3.The relation between the depletion times of Hi(left) and H2 (right) and the 5 local properties analysed in Fig. 7-from top to bottom stellar surface density, local sSFR, gas metallicity, dust surface density, and cool gas velocity dispersion. This is shown for the L025m5, L025m6 and L025m7 as labelled in the top panels. In the ...

    work page 2025

  6. [6]

    We find excellent convergence in the predicted KS relation against methods and the specific choices of each method

    6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5 T otal 0.1Gyr 1Gyr 10Gyr Figure A4.TheHI,H 2 andHi+H 2 KSrelations,aslabelledatthetop,at𝑧=0intheL025m6runofTable1,measuredusingdifferentmethods(top);usingour fiducialannuli-facemethod but adopting different thresholds for the minimum number of gas particles in a annulus (middle); and adopting differe...

    work page 2025