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arxiv: 2606.10026 · v1 · pith:KEKQIDE5new · submitted 2026-06-08 · 🌌 astro-ph.GA · astro-ph.CO

Pressure-regulated feedback-modulated star formation as a subgrid model for galaxy formation simulations

Sarah M. R. Jeffreson , Eve C. Ostriker , Chang-Goo Kim , Jan Burger This is my paper

Pith reviewed 2026-06-27 15:48 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords star formationsubgrid modelgalaxy formation simulationsinterstellar mediumstellar feedbackgas depletion time
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The pith

PRFM subgrid model ties star formation rate to the local balance between gravity and stellar feedback in galaxy disks.

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

The paper introduces two versions of a subgrid prescription for star formation in cosmological galaxy simulations, both derived from the pressure-regulated feedback-modulated theory. Instead of using fixed efficiency parameters, the model sets the star formation rate from the equilibrium between gravitational collapse and the momentum injected by stellar feedback. Calibrated directly on parsec-scale TIGRESS simulations, the prescriptions are tested in isolated Milky Way-like disks at resolutions from 10^5 to 10^7 solar masses. Both the volumetric and integrated implementations produce shorter gas depletion times than the IllustrisTNG approach, especially at high pressure and density, while the integrated version remains stable when the disk scale height is unresolved.

Core claim

The PRFM theory supplies a subgrid star formation model in which the local star formation rate is determined by the dynamic balance between gravity and the momentum supplied by stellar feedback; the two numerical implementations (volumetric when scale height is resolved, integrated when it is not) reproduce the star formation rates of resolved TIGRESS simulations more closely than empirical prescriptions and remain consistent across a wide range of mass resolutions.

What carries the argument

Pressure-regulated, feedback-modulated (PRFM) theory, which equates the star formation rate to the rate needed to maintain vertical equilibrium between gravitational weight and feedback momentum injection.

If this is right

  • Gas depletion times become shorter than in current empirical models, particularly inside dense, high-pressure regions.
  • At the highest tested resolution the two PRFM implementations agree with each other and with the underlying TIGRESS simulation for the global star formation rate.
  • The integrated formulation remains numerically stable and produces consistent results even when the gas disk scale height is not resolved.
  • Both versions supply a physically motivated effective equation of state that can be used directly in larger-volume cosmological simulations.

Where Pith is reading between the lines

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

  • Adoption of PRFM would likely reduce the need for separate tunable parameters that currently control star formation efficiency in cosmological codes.
  • Because the model predicts an explicit dependence of star formation on local pressure, it could alter the predicted distribution of star-forming gas across different galactic environments.
  • The robustness of the integrated version at low resolution suggests it could be applied immediately to existing large-volume runs without requiring changes to the numerical resolution.

Load-bearing premise

The calibration of PRFM on parsec-scale simulations can be applied unchanged as a subgrid rule at the much coarser resolutions used in cosmological galaxy formation runs.

What would settle it

A direct comparison, at the same mass resolution, of the star formation rate surface density versus mid-plane pressure relation in a full cosmological run using the PRFM subgrid model versus one using the IllustrisTNG prescription, checked against observed Kennicutt-Schmidt relations in nearby galaxies.

Figures

Figures reproduced from arXiv: 2606.10026 by Chang-Goo Kim, Eve C. Ostriker, Jan Burger, Sarah M. R. Jeffreson.

Figure 1
Figure 1. Figure 1: Equation of state comparison. Distribution of the gas effective pressure Peff (left and right) or weight W (center) as a function of the measured gas hydrogen number density nH,meas (left and right) or computed equilibrium density nH (center), in pixels of scale 1 × 1 kpc2 , and averaged over all simulation time-stamps with an interval of 10 Myr between 50 Myr and 600 Myr, inclusive. All results are from s… view at source ↗
Figure 2
Figure 2. Figure 2: Upper row: Effective gas velocity dispersion (σeff , orange, computed from the effective EoS), and measured stellar velocity dispersion (σ∗,z, blue) in the vertical direction as a function of galactocentric radius R from simulations adopting the PRFM-int implementation, at resolutions of 105 , 106 and 107 M⊙. Lower row: Ratio of these two velocity dispersions (blue lines), in comparison to the measured rat… view at source ↗
Figure 3
Figure 3. Figure 3: Ratio of dynamical time to depletion time, i.e. the star formation efficiency per dynamical time εdyn = tdyn/tdep (see Equation 1), as a function of gas pressure or weight. We show the distribution of gas cells in the plane spanned by the measured mid-plane effective pressure Peff (left and right columns) or computed weight W (center column) and the ratio of the dynamical time to depletion time tdyn/tdep. … view at source ↗
Figure 4
Figure 4. Figure 4: Depletion time as a function of gas density, from simulations with mass resolution 105 M⊙, at a simulation time of 50 Myr. The gas cell depletion time is tdep = Mg/M˙ ∗, and density is measured in the simulation as nH,meas (left and right) or computed as an equilibrium value nH (center). The black lines represent the least-squares best fit (log tdep ≈ −0.96 log nH −0.46) to the PRFM-vol simulation, includi… view at source ↗
Figure 5
Figure 5. Figure 5: Depletion and dynamical time as a function of gas pressure, from simulations with mass resolution 105 M⊙ at time 50 Myr. We show the distribution of gas cells in the plane spanned by the gas cell measured effective pressure Peff (left and right columns) or computed weight W (center column) and the gas cell depletion time tdep ≡ Mg/M˙ ∗ (top row) or the gas cell dynamical time tdyn (bottom row). For PRFM-vo… view at source ↗
Figure 6
Figure 6. Figure 6: Time evolution of the total galactic SFR in each set of simulations (PRFM-vol, PRFM-int, and TNG-model implementations) at each of the three resolutions tested (105 M⊙ in blue, 106 M⊙ in orange, and 107 M⊙ in green). The transparent blue line in the center panel is a copy of the 105 M⊙ evolution from the PRFM-vol case (blue line, left panel). SFRs obtained at high pressure (and density), relative to the im… view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of SFR surface densities ΣSFR as a function of the mid-plane effective gas pressure Peff (left and right), or computed weight W (center), measured in projected pixels of scale 1 × 1 kpc2 , and averaged over all simulation time-stamps between 50 Myr and 600 Myr, inclusive. All three simulation resolutions of 105 M⊙ (top row), 106 M⊙ (center row) and 107 M⊙ (bottom row) are shown. The thick blac… view at source ↗
Figure 8
Figure 8. Figure 8: Distribution of gas cells in the plane spanned by the gas cell dynamical time tdyn and the gas cell depletion time tdep = Mg/M˙ ∗, at a simulation time of 50 Myr, at the three simulation resolutions of 105 M⊙ (top row), 106 M⊙ (center row) and 107 M⊙ (bottom row). Computation of timescales is described in [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Maps of the gas surface density Σg (upper row), the stellar surface density Σ∗ (center row) and the SFR surface density ΣSFR (lower row) for simulations adopting the PRFM-vol implementation. Results are shown from simulations at three different mass resolutions (and corresponding typical cell size): 105 M⊙ (80 pc), 106 M⊙ (190 pc), 107 M⊙ (370 pc), at a simulation time of 50 Myr. In the top two rows, the m… view at source ↗
Figure 10
Figure 10. Figure 10: Upper panels: Histograms of the gas surface density Σg and the SFR surface density ΣSFR, summed over columns at a scale of 1 kpc. Results are from simulations adopting the PRFM-vol implementation at resolutions of 105 M⊙ (blue), 106 M⊙ (orange) and 107 M⊙ (green), at a time of 50 Myr. Lower panels: Histograms of the depletion time tdep computed from individual cells within the PRFM model for each simulati… view at source ↗
Figure 11
Figure 11. Figure 11: Histograms of the measured pressure (left), measured volume density (center), and measured scale-height (right) of star-forming gas from simulations adopting the PRFM-vol implementation at resolutions of 105 M⊙ (blue), 106 M⊙ (orange) and 107 M⊙ (green). All values are those obtained directly from the simulation in post-processing. −1 0 log (Peff/W) 0 1 2 3 PDF 105M 106M 107M −2 −1 0 1 log (nH,meas/nH) −1… view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of measured values for ISM properties and equilibrium predictions from simulations using the PRFM￾vol implementation at a resolution of 105 M⊙ (blue), 106 M⊙ (orange) and 107 M⊙ (green). Left: Ratios of the effective pressure Peff at the midplane, computed via the EoS (Equation 15) from the measured gas density, to the dynamical equilibrium pressure computed via the ISM weight W (using Equation… view at source ↗
Figure 13
Figure 13. Figure 13: Maps of Σg, Σ∗, and ΣSFR as in [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Histograms of Σg, ΣSFR, and tdep as in [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Histograms of the computed ISM weight W from Equation 31 (left), computed equilibrium mid-plane volume density nH from Equation 29 (center), and computed equilibrium scale-height Hg from Equation 28 (right) for the PRFM-int implementation at resolutions of 105 M⊙ (blue), 106 M⊙ (orange) and 107 M⊙ (green) [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Radial profiles of the gas surface densities Σg (top) and volume densities n (bottom) in the PRFM-vol (left) and PRFM-int (right) simulations at all numerical resolutions (see key). In the lower panels, solid lines show measured volume densities nH,meas, while the dotted lines in the lower right show calculated volume densities nH. The dashed horizontal black lines in lower panels indicate the star format… view at source ↗
read the original abstract

We present a new subgrid model for interstellar gas evolution in cosmological simulations of galaxy formation, based on the pressure-regulated, feedback-modulated (PRFM) theory of star formation. In contrast to the empirically pegged star formation prescriptions employed in current cosmological simulations, the PRFM model links the local star formation rate to the dynamic balance achieved in galactic interstellar gas between gravity and stellar feedback effects. With this formulation, both the star formation efficiency and the effective equation of state may be directly calibrated using numerical simulations, such as TIGRESS, which resolve physics of the interstellar medium and star formation at parsec scales. We develop, and implement in the Arepo moving-mesh code, two complementary classes of the subgrid model: a volumetric version (PRFM-vol) applicable when the gas disk scale height of a galaxy is numerically resolved in a simulation, and an integrated version (PRFM-int) that reconstructs the mid-plane density and pressure from vertical equilibrium considerations when the true gas scale height cannot be numerically resolved. Using isolated Milky-Way-like disk simulations across mass resolutions $10^5$-$10^7~{\rm M}_\odot$, we show that both implementations yield shorter gas depletion times than the IllustrisTNG prescription, especially in regions where pressure and density are large. At high resolution, PRFM-vol and PRFM-int agree closely with each other and with TIGRESS for the star formation rate; PRFM-int remains robust at all resolutions tested. These results demonstrate that PRFM-derived subgrid prescriptions provide a physically grounded and numerically stable framework for star formation across the dynamic range of galaxy formation simulations, paving the way for future cosmological applications.

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 / 1 minor

Summary. The paper presents a pressure-regulated, feedback-modulated (PRFM) subgrid model for interstellar gas and star formation in galaxy simulations. It develops two implementations in Arepo (PRFM-vol for resolved scale heights and PRFM-int for unresolved cases), calibrates star formation efficiency and effective EOS directly from TIGRESS parsec-scale simulations, and tests both on isolated Milky Way-like disk runs at mass resolutions 10^5–10^7 M_⊙. Results show shorter gas depletion times than the IllustrisTNG prescription (especially at high pressure/density), close agreement with TIGRESS at high resolution, and robustness of PRFM-int across resolutions. The work frames these as a physically grounded framework paving the way for cosmological applications.

Significance. If the direct transfer of the TIGRESS calibration holds without additional scale-dependent corrections, the model supplies a physically motivated alternative to empirical prescriptions, with explicit strengths in the TIGRESS-based calibration of both efficiency and EOS plus the dual volumetric/integrated implementations that address numerical resolution limits. The isolated-disk tests credibly demonstrate shorter depletion times and resolution robustness relative to TNG. However, because all quantitative results (depletion times, SFR agreement, convergence) are confined to isolated disks, the significance for cosmological runs with accretion and mergers remains prospective rather than demonstrated.

major comments (2)
  1. [Abstract] Abstract: The claim that PRFM-int 'remains robust at all resolutions tested' and that the prescriptions 'provide a physically grounded and numerically stable framework for star formation across the dynamic range of galaxy formation simulations' is load-bearing for the central contribution, yet rests exclusively on isolated MW-like disk simulations; no cosmological runs incorporating accretion, mergers, or varying environments are shown, leaving the assumption of direct transfer without scale-dependent corrections untested.
  2. [Abstract] Abstract: The statement that 'both the star formation efficiency and the effective equation of state may be directly calibrated using numerical simulations, such as TIGRESS' provides no quantitative error bars, exact fitting procedure, or data exclusion criteria for the TIGRESS-derived constants; this directly affects assessment of the reported agreement with TIGRESS SFRs and the shorter depletion times versus TNG.
minor comments (1)
  1. [Abstract] Abstract: Quantitative metrics for 'shorter gas depletion times' and 'agree closely' (e.g., specific depletion time ratios or SFR values with uncertainties) are not supplied, limiting evaluation of the strength of the comparison to TIGRESS and TNG.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and constructive comments. We address each major comment below, agreeing where revisions are warranted to better reflect the scope of our tests and the calibration details.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that PRFM-int 'remains robust at all resolutions tested' and that the prescriptions 'provide a physically grounded and numerically stable framework for star formation across the dynamic range of galaxy formation simulations' is load-bearing for the central contribution, yet rests exclusively on isolated MW-like disk simulations; no cosmological runs incorporating accretion, mergers, or varying environments are shown, leaving the assumption of direct transfer without scale-dependent corrections untested.

    Authors: We agree that all quantitative results, including resolution robustness and depletion times, are demonstrated exclusively in isolated Milky Way-like disk simulations. The manuscript presents the PRFM model as a framework that paves the way for cosmological applications rather than claiming validation in those regimes. We will revise the abstract to explicitly state that the current tests are limited to isolated disks, that robustness is shown with respect to numerical resolution in these setups, and that cosmological runs with accretion and mergers are left for future work. This removes any implication that direct transfer without scale-dependent corrections has been tested in complex environments. revision: yes

  2. Referee: [Abstract] Abstract: The statement that 'both the star formation efficiency and the effective equation of state may be directly calibrated using numerical simulations, such as TIGRESS' provides no quantitative error bars, exact fitting procedure, or data exclusion criteria for the TIGRESS-derived constants; this directly affects assessment of the reported agreement with TIGRESS SFRs and the shorter depletion times versus TNG.

    Authors: The calibration of the star formation efficiency and effective equation of state from TIGRESS, including the fitting procedure and associated constants, is described in detail in Section 3 of the manuscript. To improve clarity in the abstract, we will add a concise reference to the calibration method and note that quantitative uncertainties and fitting details are provided in the main text. This will allow readers to assess the agreement with TIGRESS and comparisons to TNG more directly from the abstract. revision: yes

Circularity Check

1 steps flagged

PRFM calibration from TIGRESS makes reported agreement with TIGRESS a fitted result by construction

specific steps
  1. fitted input called prediction [Abstract]
    "With this formulation, both the star formation efficiency and the effective equation of state may be directly calibrated using numerical simulations, such as TIGRESS, which resolve physics of the interstellar medium and star formation at parsec scales. [...] At high resolution, PRFM-vol and PRFM-int agree closely with each other and with TIGRESS for the star formation rate"

    The efficiency and EOS parameters are fitted/calibrated from TIGRESS; therefore the reported close agreement with TIGRESS SFRs at high resolution in the Arepo runs is a direct consequence of that calibration rather than an independent prediction.

full rationale

The paper explicitly states that star formation efficiency and effective EOS are calibrated directly from TIGRESS simulations. It then presents close agreement between the Arepo implementations and TIGRESS SFRs at high resolution as a validation result. This agreement is forced by the calibration step rather than an independent test. The comparison to IllustrisTNG and resolution robustness tests retain independent content, and no load-bearing self-citation chain or definitional reduction appears in the derivation of the PRFM framework itself. The assumption of direct transfer to cosmological runs without scale corrections is noted as future work rather than a derived claim.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Central claim rests on transferability of TIGRESS-calibrated PRFM relations to unresolved scales and on the validity of vertical-equilibrium reconstruction for the integrated version; no new entities postulated.

free parameters (1)
  • PRFM calibration constants from TIGRESS
    Star formation efficiency and effective EOS stated to be directly calibrated from TIGRESS; these act as fitted inputs to the subgrid model.
axioms (1)
  • domain assumption Vertical hydrostatic equilibrium allows reconstruction of mid-plane density and pressure when scale height is unresolved
    Invoked for PRFM-int version in the abstract description of the integrated model.

pith-pipeline@v0.9.1-grok · 5851 in / 1408 out tokens · 22104 ms · 2026-06-27T15:48:58.791990+00:00 · methodology

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