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arxiv: 2606.10022 · v1 · pith:GDIYDTYFnew · submitted 2026-06-08 · 🌌 astro-ph.GA

Learning the Universe with PRFM-vol: Introducing a new subgrid model for star formation in cosmological simulations

Jan D. Burger , Volker Springel , Eve C. Ostriker , Chang-Goo Kim , Ulrich Steinwandel , Matthew C. Smith , Lars Hernquist , Greg L. Bryan
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Rachel S. Somerville Alon Gurman
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Pith reviewed 2026-06-27 15:51 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords star formationcosmological simulationssubgrid modelsPRFMgalaxy morphologyeffective equation of stateTIGRESS scaling relations
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The pith

PRFM-vol introduces a subgrid star formation model for cosmological simulations that uses pressure-regulated feedback-modulated relations.

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

The paper introduces PRFM-vol, a subgrid model for star formation in cosmological simulations based on the pressure-regulated feedback-modulated (PRFM) theory. The model uses a modified effective equation of state and calculates star formation rates from ambient densities, and tests show it reproduces PRFM predictions and TIGRESS relations in isolated galaxies at high resolution. In cosmological simulations, it produces larger stellar scale heights, slightly higher stellar masses, and morphology changes due to Toomre instabilities that depend on the effective pressure. This matters because it offers a way to bridge small-scale ISM physics with large-volume simulations while retaining key physical predictions.

Core claim

PRFM-vol deploys a modified effective equation of state and a density-dependent star formation rate prescription based on PRFM theory. This allows the model to match the scaling relations from TIGRESS in isolated galaxy tests, including the effect of the stellar potential on the star formation rate. In cosmological multizoom simulations, PRFM-vol results in increased stellar scale heights and slight stellar mass increase, and shows that the effective equation of state controls whether Toomre instabilities produce stellar clumps in galaxy morphologies.

What carries the argument

The PRFM-vol model that uses a modified effective equation of state and a density-dependent star formation rate based on PRFM theory.

Load-bearing premise

The PRFM scaling relations and TIGRESS results obtained in focused ISM simulations can be directly transplanted into cosmological volumes through a single modified effective equation of state and a density-dependent SFR prescription without additional resolution-dependent corrections.

What would settle it

If PRFM-vol simulations do not produce the expected increase in stellar scale heights or the morphology variations with effective pressure, the direct transplantation of the model would be called into question.

Figures

Figures reproduced from arXiv: 2606.10022 by Alon Gurman, Chang-Goo Kim, Eve C. Ostriker, Greg L. Bryan, Jan D. Burger, Lars Hernquist, Matthew C. Smith, Rachel S. Somerville, Ulrich Steinwandel, Volker Springel.

Figure 1
Figure 1. Figure 1: Comparison of the effective equations of state used in PRFM-vol (black lines), TNG (blue lines) and TIGRESS/Schmidt (green lines). In the upper panel, we show pressure as a function of hydrogen number density, while the logarithmic slope of the relations is displayed in the middle panel, and the resulting isothermal sound speeds are shown in the bottom panel. In both the upper and the bottom panel, we addi… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the pressure vs. star formation rate surface density scaling relation in different model realizations. In the top row, we show results obtained using the TIGRESS/Schmidt model – PRFM-vol results are displayed in the bottom row. The gray shaded line is the original TIGRESS scaling relation, while coloured circles show the simulation results obtained after 75 Myr of simulation time. Different c… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the P−ΣSFR relation measured in the full PRFM￾vol model (top panel) to the relation obtained when not including the renor￾malization factor (bottom panel). As expected, we find overall lower star formation rates in the non-renormalized theory. Although the differences are not excessive overall, there is a significant improvement when comparing the less massive disks, in particular model D1. t… view at source ↗
Figure 4
Figure 4. Figure 4: Scale heights of gas (filled points), star forming gas (squares), and stars (stars), for the TIGRESS/Schmidt model (blue) as well as for two ver￾sions of PRFM-vol: the full PRFM-vol implementation (red), and a version in which no velocity kicks are added to newly born stars (green). Both pan￾els show results obtained after 400 Myr of simulation time. In the top and bottom panels, we show results of the D1 … view at source ↗
Figure 5
Figure 5. Figure 5: Scale height ratio as a function of cylindrical radius for two of our isolated setups. In the left (right) panel we show our D3 (D1) setup with an initial old star disk fraction of 50% (90%). For both of them, we show one measurement and two estimates of the scale height ratio, all calculated in 15 radial bins. For the measurement, we show the ratio of the half mass heights as black dots. Our two estimator… view at source ↗
Figure 6
Figure 6. Figure 6: Galaxy stellar light projections for different star formation models. We show 10 side-by-side comparisons for galaxies in matched host haloes from cosmological multizoom simulations using the TNG, TIGRESS/Schmidt, and the PRFM-vol models. The images are created by mapping luminosities in the K-, B-, and U-bands to RGB colour space. For each galaxy, we show face-on and edge-on projections with a panel side-… view at source ↗
Figure 7
Figure 7. Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Cumulative star-forming gas mass as a function of hydrogen num￾ber density, shown for the PRFM-vol (black lines) and PRFM-vol 2 (red lines) simulations, at redshifts z = 0 (solid), 0.5 (dotted), and 1.2 (dashed). Star-forming gas cells are identified within a 30 kpc sphere around the host galaxy’s centre of potential, and with instantaneous star formation rate larger than zero. In the small bottom panel, w… view at source ↗
Figure 9
Figure 9. Figure 9: Cumulative stellar mass as a function of birth density – here defined as the physical density of the parent gas cell at the time the star was formed. We show the cumulative mass of all stars formed until redshift z = 0, stacked over the twenty simulated high-resolution galaxies, for the multizoom sim￾ulations with log(Mvir/M⊙) = 12 and zoom factor 4, using the TNG (blue line), TIGRESS/Schmidt (green line),… view at source ↗
Figure 10
Figure 10. Figure 10: From top to bottom, we show maps of Toomre Q, gas density, isothermal sound speed, and star formation rate surface density in a single galaxy picked from [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Cumulative distribution of stellar mass as a function of ambient stellar density for the fourth galaxy in the right column of Figs 6 and 7. In both panels, we compare between the distributions measured in the TNG (blue), TIGRESS/Schmidt (green), PRFM-vol (black), and PRFM-vol 2 (red) models. The left panel shows the cumulative distribution inferred from all stars in the galaxies, while in the right panel,… view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of the final stellar masses of the 20 simulated zoom galaxies with log(Mvir/M⊙) = 12 and zoom factor 4 for four different models, TNG (blue open circles), TIGRESS/Schmidt (green open circles), PRFM-vol (black open circles) and PRFM-vol 2 (red closed circles). Stellar masses are shown as a function of halo mass, and galaxies corresponding to the same halo are matched as indicated by the connecti… view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of the stellar masses in TNG (blue open circles) and PRFM-vol-2 (red closed circles) as a function of halo mass at redshiftz = 1.2. Galaxies are matched as in [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Star formation histories of two selected cosmological multizoom galaxies. We show star formation rate as a function of lookback time (and redshift) for the TNG (blue), TIGRESS/Schmidt (green), PRFM-vol (black) and PRFM-vol-2 (red) models. In most galaxies, differences between the star formation histories are fairly noisy. However, we find that in a few of them, the TIGRESS/Schmidt rate systematically drop… view at source ↗
Figure 16
Figure 16. Figure 16: Half-mass radii of the simulated galaxies as a function of halo virial mass. We show a comparison between the TNG (blue open circles), TIGRESS/Schmidt (green open circles), PRFM-vol (black open circles), and PRFM-vol-2 (red closed circles) models. Horizontal dashed lines show av￾erages over the 20 multizoom galaxies simulated for each model. Galaxies with corresponding host haloes are matched and connecte… view at source ↗
Figure 17
Figure 17. Figure 17: Comparison of the stellar scale heights of our 20 multizoom galaxies simulated using the TNG (blue open circles), TIGRESS/Schmidt (green open circles), PRFM-vol (black open circles), and PRFM-vol 2 (red filled circles) models. Scale heights are shown as a function of halo virial mass, and galaxies are matched as in previous figures, with vertical dashed lines showing averages over the 20 galaxies, and lin… view at source ↗
read the original abstract

We introduce PRFM-vol, a new subgrid model for star formation in cosmological simulations that aims to increase the physical realism of cosmological simulations by leveraging results obtained with focused ISM simulations. We deploy a modified effective equation of state and calculate the star formation rate for each gas cell as a function of the ambient densities of gas, dark matter, and stars, based on the pressure-regulated feedback-modulated (PRFM) theory of star formation. Test simulations of our model in isolated galaxies show that we match PRFM predictions and TIGRESS scaling relations remarkably well, provided sufficiently high resolution is available. In particular, we are able to clearly demonstrate the impact of the stellar potential on the star formation rate, thereby retaining an important prediction of PRFM. We then apply our new model to cosmological multizoom simulations and find, compared to our previous TIGRESS/Schmidt model, a significant increase in the stellar scale heights and a slight increase in stellar mass. We demonstrate that modifying the effective equation of state significantly affects the morphology of simulated galaxies. Pronounced stellar clumps appear if the effective pressure at low hydrogen number densities is low, and disappear for higher pressure. We show that the formation of clumps is a result of Toomre instabilities, and conclude that simulated galaxy morphologies can be used to constrain effective equation of state models. Overall, our results establish PRFM-vol as a new self-consistent, physics-motivated subgrid model for star formation in high-resolution cosmological simulations.

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 / 1 minor

Summary. The paper introduces PRFM-vol, a subgrid star formation model for cosmological simulations that combines a modified effective equation of state with a density-dependent SFR prescription derived from PRFM theory (using gas, dark matter, and stellar densities). Isolated galaxy tests are reported to match PRFM predictions and TIGRESS scaling relations at sufficiently high resolution, including the effect of stellar potential; cosmological multizoom runs then show increased stellar scale heights, slightly higher stellar mass, and morphology changes (clump formation via Toomre instabilities) that depend on the low-density EOS pressure. The authors conclude that PRFM-vol is a self-consistent, physics-motivated model and that galaxy morphologies can constrain effective EOS choices.

Significance. If the transplantation of PRFM/TIGRESS relations to cosmological volumes holds without additional resolution-dependent corrections, the model would offer a more physically grounded alternative to standard subgrid prescriptions, with the potential to link ISM-scale theory directly to galaxy-scale outcomes and use morphology as an EOS diagnostic. The use of independent TIGRESS results and absence of new free parameters are strengths. However, the current lack of quantitative validation in the cosmological regime limits the immediate impact.

major comments (3)
  1. [Abstract] Abstract (final paragraph) and § on cosmological runs: The central claim that PRFM-vol is self-consistent in cosmological multizoom simulations rests on the unverified assumption that the isolated-galaxy 'sufficiently high resolution' threshold is met and that PRFM scaling relations hold without further corrections; no resolution values, convergence tests, or direct SFR-density comparisons are reported for the cosmological runs, so the reported scale-height and morphology changes may not reflect the intended PRFM physics.
  2. [Abstract] Abstract: The reported 'significant increase in the stellar scale heights and a slight increase in stellar mass' relative to the TIGRESS/Schmidt model are presented without error bars, sample statistics, or quantitative measures of difference, weakening the ability to judge whether these outcomes are robust or resolution-dependent.
  3. [Abstract] Abstract (morphology discussion): The demonstration that clump formation is controlled by the low-density effective pressure and arises from Toomre instabilities is interesting, but the EOS modification itself is described as an exploratory choice rather than derived from PRFM; this makes it unclear whether the morphology-EOS link is a genuine prediction or a consequence of the ad-hoc adjustment.
minor comments (1)
  1. [Abstract] The abstract states that the model 'retain[s] an important prediction of PRFM' regarding stellar potential, but no explicit comparison metric or figure reference is given to quantify how well this is recovered.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which help clarify the presentation of our results. We respond to each major comment below and indicate where revisions will be made to the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract (final paragraph) and § on cosmological runs: The central claim that PRFM-vol is self-consistent in cosmological multizoom simulations rests on the unverified assumption that the isolated-galaxy 'sufficiently high resolution' threshold is met and that PRFM scaling relations hold without further corrections; no resolution values, convergence tests, or direct SFR-density comparisons are reported for the cosmological runs, so the reported scale-height and morphology changes may not reflect the intended PRFM physics.

    Authors: We agree that the cosmological multizoom section would benefit from explicit resolution information. In the revised manuscript we will report the spatial resolution achieved in the cosmological runs, confirm that it meets or exceeds the threshold validated in the isolated-galaxy tests, and add a brief discussion of why direct cell-by-cell SFR-density comparisons are not straightforward in the full cosmological volume. We will also note any available convergence information from the simulation suite. These additions will make the self-consistency argument more transparent without altering the underlying results. revision: yes

  2. Referee: [Abstract] Abstract: The reported 'significant increase in the stellar scale heights and a slight increase in stellar mass' relative to the TIGRESS/Schmidt model are presented without error bars, sample statistics, or quantitative measures of difference, weakening the ability to judge whether these outcomes are robust or resolution-dependent.

    Authors: We acknowledge that the abstract would be strengthened by quantitative context. In revision we will replace the qualitative descriptors with approximate numerical differences (e.g., fractional change in scale height and stellar mass) drawn from the simulation outputs and will clarify the number of galaxies and resolution regime involved. Because the runs are single realizations, formal error bars are not available, but we will add a short statement on robustness based on the controlled comparison between the two models. revision: yes

  3. Referee: [Abstract] Abstract (morphology discussion): The demonstration that clump formation is controlled by the low-density effective pressure and arises from Toomre instabilities is interesting, but the EOS modification itself is described as an exploratory choice rather than derived from PRFM; this makes it unclear whether the morphology-EOS link is a genuine prediction or a consequence of the ad-hoc adjustment.

    Authors: We agree that the distinction should be stated more clearly. The PRFM-vol model derives the SFR from PRFM theory; the low-density EOS is varied in an exploratory manner precisely to test its influence on morphology. In the revised abstract and discussion we will explicitly separate the PRFM-based SFR prescription from the exploratory EOS choice, while retaining the demonstration that Toomre instabilities drive the clumps when the low-density pressure is reduced. This framing presents the morphology-EOS sensitivity as a model outcome rather than a direct PRFM prediction, consistent with the manuscript's intent to show that galaxy morphologies can constrain effective EOS prescriptions. revision: partial

Circularity Check

0 steps flagged

No significant circularity; model implements independent prior theory

full rationale

The derivation adopts PRFM theory and TIGRESS scaling relations from prior focused ISM simulations as the foundation for the subgrid prescription (modified EOS plus density-dependent SFR). Isolated-galaxy tests verify faithful reproduction of those relations at high resolution, which constitutes an implementation check rather than a prediction that reduces to the input by construction. Cosmological multizoom applications then explore morphological consequences of the chosen EOS, without any load-bearing step that equates the central claim to a self-citation chain, fitted parameter renamed as prediction, or self-definitional loop. The paper remains self-contained against external benchmarks from the cited prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on the transferability of PRFM theory and TIGRESS scaling relations to cosmological volumes via a modified effective equation of state; no explicit free parameters, axioms, or invented entities are enumerated in the provided text.

pith-pipeline@v0.9.1-grok · 5843 in / 1248 out tokens · 19493 ms · 2026-06-27T15:51:38.681064+00:00 · methodology

discussion (0)

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