[Paper Review] Tests of subgrid models for star formation using simulations of isolated disk galaxies

Folkert S J Nobels, Joop Schaye+4 more|arXiv (Cornell University)|Sep 24, 2023

Astrophysics and Star Formation Studies4 citations

TL;DR

This study tests subgrid star formation models in smoothed-particle hydrodynamics simulations of isolated Milky Way-mass galaxies, finding that a fiducial model combining a Schmidt law with a gravitational instability criterion and 1% star formation efficiency per free-fall time best reproduces observed Kennicutt-Schmidt relations. The model shows good numerical convergence across four orders of magnitude in mass resolution and outperforms density thresholds and temperature ceilings, especially in low-metallicity regimes.

ABSTRACT

We use smoothed-particle hydrodynamics simulations of isolated Milky Way-mass disk galaxies that include cold, interstellar gas to test subgrid prescriptions for star formation (SF). Our fiducial model combines a Schmidt law with a gravitational instability criterion, but we also test density thresholds and temperature ceilings. While SF histories are insensitive to the prescription for SF, the Kennicutt-Schmidt (KS) relations between SF rate and gas surface density can discriminate between models. We show that our fiducial model, with an SF efficiency per free-fall time of 1 per cent, agrees with spatially-resolved and azimuthally-averaged observed KS relations for neutral, atomic and molecular gas. Density thresholds do not perform as well. While temperature ceilings selecting cold, molecular gas can match the data for galaxies with solar metallicity, they are unsuitable for very low-metallicity gas and hence for cosmological simulations. We argue that SF criteria should be applied at the resolution limit rather than at a fixed physical scale, which means that we should aim for numerical convergence of observables rather than of the properties of gas labelled as star-forming. Our fiducial model yields good convergence when the mass resolution is varied by nearly 4 orders of magnitude, with the exception of the spatially-resolved molecular KS relation at low surface densities. For the gravitational instability criterion, we quantify the impact on the KS relations of gravitational softening, the SF efficiency, and the strength of supernova feedback, as well as of observable parameters such as the inclusion of ionized gas, the averaging scale, and the metallicity.

Motivation & Objective

• To evaluate the performance of various subgrid star formation prescriptions in isolated disk galaxy simulations.
• To determine which star formation criteria—density thresholds, temperature ceilings, or gravitational instability—best reproduce observed Kennicutt-Schmidt (KS) relations.
• To assess numerical convergence of star formation observables under varying mass resolution and physical parameters.
• To establish whether star formation criteria should be applied at the resolution limit rather than at fixed physical scales.

Proposed method

• Simulates isolated Milky Way-mass disk galaxies using smoothed-particle hydrodynamics (SPH) with cold interstellar gas and a fiducial subgrid model combining a Schmidt law with a gravitational instability criterion.
• Tests alternative prescriptions: density thresholds (n_H,crit), temperature ceilings (T_crit), and gravitational instability using the criterion α_crit = 1.5 × (1 + 0.5 × (T/T_cold)²) × (n_H / n_crit)⁻¹.
• Varying the star formation efficiency per free-fall time (ε) from 0.1% to 1000% to assess its impact on SFR and KS relations.
• Adjusts supernova feedback strength by a factor of 32 to evaluate its influence on SF history and KS normalization.
• Varies gravitational softening length between 50 and 800 pc and mass resolution by a factor of 4096 to test numerical convergence.
• Compares simulated KS relations (for neutral, atomic, and molecular gas) with spatially resolved and azimuthally averaged observational data.

Figure 1: The gravitational instability criterion in temperature-density space for different velocity dispersions (solid lines, different colours; gas at higher densities or lower temperatures is unstable) and different resolutions and/or normalisations (two sets of lines labelled with different val

Experimental results

Research questions

• RQ1 Which subgrid star formation criterion—density threshold, temperature ceiling, or gravitational instability—best reproduces observed Kennicutt-Schmidt relations in isolated disk galaxies?
• RQ2 How does the star formation efficiency per free-fall time affect the normalization and break in the Kennicutt-Schmidt relation?
• RQ3 To what extent is the star formation history and KS relation numerically converged under varying mass resolution and gravitational softening?
• RQ4 Does applying the star formation criterion at the resolution limit yield better convergence than scaling it with resolution?
• RQ5 How do feedback strength and metallicity influence the robustness of different subgrid models in cosmological contexts?

Key findings

• The fiducial model—combining a Schmidt law with a gravitational instability criterion and 1% star formation efficiency per free-fall time—best matches observed spatially-resolved and azimuthally-averaged Kennicutt-Schmidt relations for neutral, atomic, and molecular gas.
• Density thresholds and temperature ceilings fail to reproduce the observed KS relations, especially at low metallicities, where cold, nearly metal-free gas remains unresolved and cannot form stars.
• The gravitational instability criterion shows good numerical convergence across four orders of magnitude in mass resolution, with the exception of the molecular KS relation at low surface densities.
• Varying the gravitational softening length from 50 to 800 pc has minimal impact on the KS relations, though it slightly increases gas consumption times at high surface densities.
• A fixed α_crit value yields better convergence in KS relations than a resolution-scaled α_crit, supporting the use of resolution-limited criteria.
• The star formation efficiency per free-fall time is constrained to ~1% by comparison with observations, as higher or lower values disrupt the normalization and break in the KS relation.

Figure 2: The fiducial simulation with $Z=Z_{\odot}$ at $t=1~{}\rm Gyr$ . Top two rows: Edge-on and face-on gas surface density for the total gas (left column), atomic hydrogen (middle column) and molecular hydrogen (right column). Third row: Face-on view of the mass-weighted temperature (left), mas