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arxiv: 2509.04067 · v2 · submitted 2025-09-04 · 🌌 astro-ph.GA

COLIBRE: calibrating subgrid feedback in cosmological simulations that include a cold gas phase

Evgenii Chaikin , Joop Schaye , Matthieu Schaller , Sylvia Ploeckinger , Yannick M. Bah\'e , Alejandro Ben\'itez-Llambay , Camila Correa , Victor J. Forouhar Moreno
show 12 more authors
Carlos S. Frenk Filip Hu\v{s}ko Roi Kugel Robert McGibbon Alexander J. Richings James W. Trayford Josh Borrow Robert A. Crain John C. Helly Cedric G. Lacey Aaron Ludlow Folkert S. J. Nobels
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Pith reviewed 2026-05-18 19:32 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords COLIBREgalaxy formationsubgrid feedbackcosmological simulationsstellar mass functiongalaxy sizessupernova feedbackAGN feedback
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The pith

Calibrating up to four subgrid feedback parameters lets COLIBRE match both the galaxy stellar mass function and size-stellar mass relation at z=0.

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

The paper calibrates stellar and AGN feedback in the COLIBRE hydrodynamical simulations, which directly model the multi-phase interstellar medium and dust evolution. It runs Latin hypercubes of about 200 simulations in (50 cMpc)^3 volumes, varying up to four subgrid parameters, then trains Gaussian process emulators to predict the z=0 galaxy stellar mass function and size-stellar mass relation. These emulators are used to find parameter values that fit observations, and the resulting model is shown to reproduce the targets plus additional galaxy properties. The same parameters are applied to higher-resolution runs with only slight manual adjustments. A sympathetic reader would care because the approach demonstrates how to tune complex simulations efficiently while achieving agreement across multiple observables.

Core claim

The calibrated m7 COLIBRE model reproduces the z=0 galaxy stellar mass function and size-stellar mass relation after fitting subgrid supernova and AGN feedback parameters with Gaussian process emulators trained on Latin hypercube samples. While each observable can be matched individually with a relatively simple supernova feedback model, reproducing both simultaneously requires a more sophisticated prescription. The trained emulators also reveal how different aspects of the feedback affect predictions. The calibrated model matches various other galaxy properties to which it was not tuned, and the m7 parameters transfer to m6 and m5 resolutions after minor adjustments.

What carries the argument

Gaussian process emulators trained on Latin hypercube samples of simulations that predict the galaxy stellar mass function and size-stellar mass relation as functions of up to four subgrid feedback parameters.

If this is right

  • Matching both the galaxy stellar mass function and size-stellar mass relation at once requires a more sophisticated supernova feedback prescription than matching either target individually.
  • The calibrated m7 parameters can be transferred to m6 and m5 resolutions with only slight manual adjustments while retaining similar agreement with observations.
  • The model reproduces additional galaxy properties beyond the two calibration targets.
  • The emulators allow investigation of how specific choices in supernova and AGN feedback prescriptions affect the predicted galaxy properties.

Where Pith is reading between the lines

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

  • The emulator-based approach could be reused to explore additional observables or parameters without running thousands of full simulations.
  • Success across three resolutions suggests the subgrid model captures effects that are largely independent of numerical resolution once parameters are retuned.
  • The finding that both mass and size relations need sophisticated feedback together implies that galaxy size is sensitive to the detailed implementation of supernova-driven outflows.

Load-bearing premise

That varying only up to four subgrid feedback parameters and using Gaussian process emulators on Latin hypercube samples is sufficient to capture the dominant effects needed to match both the galaxy stellar mass function and size-stellar mass relation simultaneously.

What would settle it

Running a new set of COLIBRE simulations with the emulator-derived best-fit parameters and finding that the resulting z=0 galaxy stellar mass function or size-stellar mass relation deviates significantly from the observational data used for calibration.

Figures

Figures reproduced from arXiv: 2509.04067 by Aaron Ludlow, Alejandro Ben\'itez-Llambay, Alexander J. Richings, Camila Correa, Carlos S. Frenk, Cedric G. Lacey, Evgenii Chaikin, Filip Hu\v{s}ko, Folkert S. J. Nobels, James W. Trayford, John C. Helly, Joop Schaye, Josh Borrow, Matthieu Schaller, Robert A. Crain, Robert McGibbon, Roi Kugel, Sylvia Ploeckinger, Victor J. Forouhar Moreno, Yannick M. Bah\'e.

Figure 1
Figure 1. Figure 1: The Latin hypercube for the ThermalKinetic_var∆TSNvarfE model. The axes of the panels correspond to different parameters of the model: 𝑚BH,seed, 𝑓kin, 𝑛H,pivot, and 𝑃E,pivot (see §4.2 for details). The grey (black) hatched rectangle marks level 1 (level 2) of the hypercube’s domain, while light-blue triangles (circles) indicate the sampling for level 1 (level 2), consisting of 40 (8) individual simulations… view at source ↗
Figure 2
Figure 2. Figure 2: The galaxy stellar mass function (GSMF; left) and the median size – stellar mass relation (SSMR; right) at 𝑧 = 0, for the Basic (green) and ThermalKinetic (yellow) models fit to the observed GSMF and SSMR. The dashed and solid curves indicate, respectively, the best-fitting predictions of the emulator and the corresponding simulations with the best-fitting parameters from [PITH_FULL_IMAGE:figures/full_fig… view at source ↗
Figure 3
Figure 3. Figure 3: Posterior distribution of the parameters for the Basic (green) and ThermalKinetic (yellow) models fit to the observed 𝑧 = 0 GSMF and SSMR. The 𝜒 2 𝜈 values of the fits are shown in the legend. The three contours of each colour indicate 34, 68, and 95 per cent credibility levels. The vertical and horizontal dotted lines indicate the best-fitting values of the model parameters, corresponding to the maximum o… view at source ↗
Figure 4
Figure 4. Figure 4: The stellar to halo mass relation (SHMR) at 𝑧 = 0 predicted by the trained emulators. The results are shown for the ThermalKinetic model fit to the observed GSMF and SSMR. The individual panels show how the emulated SHMR varies with the BH seed mass (𝑚BH,seed; left), the energy in SN feedback in units of 1051 erg ( 𝑓E; middle), and the fraction of SN energy injected in kinetic form ( 𝑓kin; right). Differen… view at source ↗
Figure 5
Figure 5. Figure 5: Predictions of the best-fitting ThermalKinetic model fit to the observed galaxy stellar mass function (GSMF, purple), galaxy size – stellar mass relation (SSMR, brown), or to both the GSMF and SSMR (yellow). We show the 𝑧 = 0 GSMF (left), the 𝑧 = 0 SSMR (middle), and the 𝑧 = 0 stellar to halo mass relation (SHMR; right). The emulator predictions are shown as dashed curves, and the results from simulations … view at source ↗
Figure 6
Figure 6. Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: As [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Posterior distributions of the parameters of the ThermalKinetic_var∆TSN model (navy-blue) and the ThermalKinetic_var∆TSNvarfE model (light-blue), obtained by fitting the emulator to the observed 𝑧 = 0 GSMF and SSMR. The contours of the same colour indicate the 34, 68, and 95 per cent credibility regions of the posterior distributions. Vertical and horizontal dotted lines mark the best-fitting parameter val… view at source ↗
Figure 9
Figure 9. Figure 9: The median specific star formation rate (sSFR) of active galaxies (sSFR > 10−2 Gyr−1 ) versus stellar mass (left), the fraction of quenched galaxies versus stellar mass (middle), and the median mass of supermassive black holes versus stellar mass (right), all shown at 𝑧 = 0. Differently coloured solid curves show the results from the simulations with the best-fitting parameter values for the Basic (green),… view at source ↗
Figure 10
Figure 10. Figure 10: Cosmic star formation rate density (SFRD) versus redshift from the simulations with the best-fitting models to the 𝑧 = 0 GSMF and SSMR: Basic, ThermalKinetic, ThermalKinetic_var∆TSN, and ThermalKine￾tic_var∆TSNvarfE (differently coloured solid curves). For comparison, the black points show a compilation of observational data from Driver et al. (2012); Novak et al. (2017); Gruppioni et al. (2020); Khusanov… view at source ↗
Figure 11
Figure 11. Figure 11: The 𝑧 = 2 galaxy stellar mass function (GSMF; left) and the 𝑧 = 2 median specific star formation rate of all galaxies (i.e. both star-forming and quenched; right) as a function of stellar mass. The solid curves show results from simulations using the best-fitting parameters for the Basic, ThermalKinetic, ThermalKinetic_var∆TSN, and ThermalKinetic_var∆TSNvarfE models. For comparison, we include the observe… view at source ↗
Figure 12
Figure 12. Figure 12: As in [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: As [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The galaxy stellar mass function (GSMF; left), the median size – stellar mass relation (SSMR; middle), and the median black hole mass – stellar mass relation (BSMR; right), all shown at 𝑧 = 0. The light-blue and dark-red solid curves are simulation predictions with the best-fitting ThermalKine￾tic_var∆TSNvarfE model (using Δ𝑇AGN = 109 K) and its modified version with the variable Δ𝑇AGN (i.e. the fiducial … view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of the simulation predictions from the best-fitting ThermalKinetic_var∆TSNvarfE model (with Δ𝑇AGN = 109 K; light-blue) and its modified version with the variable Δ𝑇AGN (i.e. the fiducial colibre model; dark-red) for various relations that were not used to calibrate the models. Both simulations were run in a (50 cMpc)3 volume at m7 resolution. The panels, from left to right, top to bottom, displ… view at source ↗
Figure 16
Figure 16. Figure 16: The 𝑧 = 0 galaxy stellar mass function (GSMF; left), the 𝑧 = 0 median size – stellar mass relation (SSMR; middle) and the 𝑧 = 0 median black hole mass – stellar mass relation (BSMR; right) in the simulations with the fiducial colibre models (i.e. the best-fitting colibre models with variable Δ𝑇AGN) at m7, m6, and m5 resolutions. All simulations were run in a (25 cMpc)3 cosmological volume. The GSMF and SS… view at source ↗
Figure 17
Figure 17. Figure 17: The galaxy stellar mass function (GSMF) at redshift 𝑧 = 0. Different panels show the effect of varying different SN and AGN feedback-related subgrid parameters of the colibre fiducial model at m7 resolution. For each variation, we run a separate (50 cMpc) 3 volume simulation. Only one parameter is varied per panel, while the others are held fixed to their best-fitting values. Starting from the top-left pa… view at source ↗
Figure 18
Figure 18. Figure 18: As [PITH_FULL_IMAGE:figures/full_fig_p034_18.png] view at source ↗
read the original abstract

We present the calibration of stellar and active galactic nucleus (AGN) feedback in the subgrid model for the new COLIBRE hydrodynamical simulations of galaxy formation. COLIBRE directly simulates the multi-phase interstellar medium and the evolution of dust grains, which is coupled to the chemistry. COLIBRE is calibrated at three resolutions: particle masses of $m_{\rm gas} \approx m_{\rm dm} \sim 10^7$ (m7), $10^6$ (m6), and $10^5~\mathrm{M_\odot}$ (m5). To calibrate the COLIBRE feedback at m7 resolution, we run Latin hypercubes of $\approx 200$ simulations that vary up to four subgrid parameters in cosmological volumes of ($50~\mathrm{cMpc}$)$^{3}$. We train Gaussian process emulators on these simulations to predict the $z=0$ galaxy stellar mass function (GSMF) and size - stellar mass relation (SSMR) as functions of the model parameters, which we then fit to observations. The trained emulators not only provide the best-fitting parameter values but also enable us to investigate how different aspects of the prescriptions for supernova and AGN feedback affect the predictions. In particular, we demonstrate that while the observed $z=0$ GSMF and SSMR can be matched individually with a relatively simple supernova feedback model, simultaneously reproducing both necessitates a more sophisticated prescription. We show that the calibrated m7 COLIBRE model not only reproduces the calibration target observables, but also matches various other galaxy properties to which the model was not calibrated. Finally, we apply the calibrated m7 model to the m6 and m5 resolutions and, after slight manual adjustments of the subgrid parameters, achieve a similar level of agreement with the observed $z=0$ GSMF and SSMR.

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 / 3 minor

Summary. The manuscript presents the calibration of subgrid stellar and AGN feedback in the COLIBRE cosmological hydrodynamical simulations, which include a multi-phase ISM and dust evolution. Using Latin hypercube sampling of up to four feedback parameters in (50 cMpc)^3 volumes at m7 resolution, Gaussian process emulators are trained to fit the z=0 galaxy stellar mass function (GSMF) and size-stellar mass relation (SSMR) to observations. The paper demonstrates that matching both observables simultaneously requires a more complex supernova feedback prescription than matching either individually, and shows that the calibrated model reproduces additional uncalibrated galaxy properties. The calibration is then extended to higher resolutions (m6 and m5) with minor parameter adjustments.

Significance. If the calibration is robust, this work provides a valuable calibrated model for galaxy formation simulations that directly resolve the cold gas phase, with the emulator-based approach enabling efficient parameter exploration and insights into feedback mechanisms. A key strength is the explicit demonstration that the model matches several properties beyond the calibration targets, supporting its predictive capability. The use of machine-learned emulators and the investigation of how different feedback aspects affect predictions are notable methodological contributions.

major comments (2)
  1. [Section 3] In the simulation suite description (Section 3), the Latin hypercube runs use (50 cMpc)^3 volumes. The high-mass end of the GSMF (M_* ≳ 10^11 M_⊙) is then dominated by Poisson noise and cosmic variance given the small number of such galaxies. The manuscript does not indicate that sample variance is folded into the emulator likelihood or that the fit is restricted to the well-sampled mass range; if the best-fit parameters are influenced by noisy high-mass bins, this would undermine the reliability of the generalization to uncalibrated properties reported in Section 4.
  2. [Section 4.2] Section 4.2 states that a sophisticated supernova feedback prescription is required to match both the GSMF and SSMR simultaneously. However, the quantitative comparison of emulator accuracy (e.g., cross-validation errors or posterior widths) for the four-parameter space is not shown; without this, it is difficult to assess whether the claimed necessity of the more complex model is robust to emulator uncertainty.
minor comments (3)
  1. [Figure 3] Figure 3: the panels comparing emulator predictions to the training simulations would benefit from explicit uncertainty bands from the Gaussian process to illustrate emulator fidelity.
  2. [Abstract] The abstract refers to 'various other galaxy properties' without naming them; adding a short list (e.g., specific star-formation rates, gas fractions) would improve readability.
  3. [Section 5] Section 5: the manual adjustments for m6 and m5 resolutions are described only qualitatively; a table listing the adjusted parameter values and the resulting χ² or residual statistics relative to observations would clarify the procedure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major comment in turn below, indicating the revisions we will make.

read point-by-point responses

  1. Referee: [Section 3] In the simulation suite description (Section 3), the Latin hypercube runs use (50 cMpc)^3 volumes. The high-mass end of the GSMF (M_* ≳ 10^11 M_⊙) is then dominated by Poisson noise and cosmic variance given the small number of such galaxies. The manuscript does not indicate that sample variance is folded into the emulator likelihood or that the fit is restricted to the well-sampled mass range; if the best-fit parameters are influenced by noisy high-mass bins, this would undermine the reliability of the generalization to uncalibrated properties reported in Section 4.

    Authors: We thank the referee for raising this point. The (50 cMpc)^3 volume indeed limits the sampling of the highest-mass galaxies, and we acknowledge that the manuscript does not explicitly describe how this is handled in the fitting procedure. In the revised manuscript we will restrict the GSMF fitting range to M_* < 10^{11} M_⊙ (where the number of galaxies per bin is sufficient to keep Poisson and cosmic-variance errors sub-dominant) and will add a clear statement to Section 3 explaining this choice. We will also include a brief test showing that the best-fit parameters are insensitive to modest extensions of the mass range. These changes improve the robustness of the calibration without altering the main conclusions. revision: yes

  2. Referee: [Section 4.2] Section 4.2 states that a sophisticated supernova feedback prescription is required to match both the GSMF and SSMR simultaneously. However, the quantitative comparison of emulator accuracy (e.g., cross-validation errors or posterior widths) for the four-parameter space is not shown; without this, it is difficult to assess whether the claimed necessity of the more complex model is robust to emulator uncertainty.

    Authors: We agree that quantitative metrics of emulator performance would strengthen the argument. In the revised manuscript we will add, in Section 4.2, a direct comparison of cross-validation errors and posterior widths obtained for the simpler versus the more sophisticated supernova feedback models within the four-parameter space. This will demonstrate that the necessity of the complex prescription is not driven by differences in emulator fidelity. The additional material will be presented as a short table or supplementary figure. revision: yes

Circularity Check

0 steps flagged

No significant circularity: explicit calibration targets distinguished from uncalibrated validation

full rationale

The paper runs Latin hypercube simulations, trains Gaussian process emulators, and fits up to four subgrid parameters to match the observed z=0 GSMF and SSMR. It then reports that the resulting model also reproduces additional galaxy properties to which it was not calibrated. Because the fitting procedure is confined to the two named calibration observables and the paper explicitly separates those from the uncalibrated diagnostics, no step reduces by construction to its own inputs. The derivation chain is therefore self-contained against external observational benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the adequacy of a small number of tunable subgrid parameters to represent unresolved supernova and AGN feedback across resolutions, plus the assumption that the emulator accurately interpolates simulation outcomes within the sampled parameter volume.

free parameters (1)
  • subgrid feedback parameters
    Up to four parameters controlling supernova and AGN feedback efficiency and coupling are varied in the Latin hypercube and fitted to observations.
axioms (1)
  • domain assumption A small set of subgrid parameters can adequately capture the net effect of unresolved stellar and AGN feedback on galaxy properties when tuned to z=0 observations.
    This is the foundational premise of subgrid modeling in cosmological hydrodynamical simulations.

pith-pipeline@v0.9.0 · 5985 in / 1477 out tokens · 53295 ms · 2026-05-18T19:32:06.208524+00:00 · methodology

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Forward citations

Cited by 7 Pith papers

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

  1. Ripples in the baryon to dark matter ratio in $\Lambda$CDM: implications for galaxy formation

    astro-ph.GA 2025-12 unverdicted novelty 7.0

    Baryon-CDM isocurvature perturbations reduce mean baryon fractions by 5% and star formation rates by 12% in resolved halos at z=8, with effects fading to 0.1% and 1% by z=0.

  2. pop-cosmos: Star formation over 12 Gyr from generative modelling of a deep infrared-selected galaxy catalogue

    astro-ph.GA 2025-09 unverdicted novelty 7.0

    A score-based diffusion generative model on deep infrared galaxy photometry yields a star formation rate density peaking at z=1.3 and shows distinct non-parametric star formation histories plus AGN activity peaking du...

  3. 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.

  4. 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.

  5. The evolution of the galaxy stellar mass function and star formation rates in the COLIBRE simulations from redshift 17 to 0

    astro-ph.GA 2025-09 accept novelty 5.0

    COLIBRE simulations match observed galaxy stellar mass functions, star formation rates, and quenched fractions from z=17 to z=0, including JWST massive quiescent galaxies at high redshift.

  6. The FLAMINGO simulations data release

    astro-ph.CO 2026-04 accept novelty 4.0

    FLAMINGO releases >2.3 PB of hydrodynamical and gravity-only cosmological simulation data products including snapshots, halo/galaxy catalogues, HEALPix lightcones, and power spectra across multiple resolutions, cosmol...

  7. Forged by Feedback: Stellar Properties of Brightest Group Galaxies in Cosmological Simulations

    astro-ph.GA 2026-02 unverdicted novelty 4.0

    The OBSIDIAN simulation with its three-regime AGN feedback best reproduces the observed stellar masses, star formation rates, and ages of brightest group galaxies, unlike the other simulations which show mismatches in...

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