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

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 ($0\le z \le 8$) 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, $0\le z\le 5$.

💡 Research Summary

This paper presents a comprehensive investigation of the Kennicutt‑Schmidt (KS) relation – the correlation between star‑formation rate surface density (Σ_SFR) and gas surface density (Σ_gas) – using the state‑of‑the‑art COLIBRE cosmological hydrodynamical simulation suite. COLIBRE distinguishes itself by incorporating on‑the‑fly non‑equilibrium chemistry for hydrogen and helium, a live dust evolution model with multiple grain species, and radiative cooling that reaches temperatures as low as ~10 K. Because the simulation directly tracks the formation, growth, and destruction of atomic (HI) and molecular (H₂) hydrogen, the HI and H₂ surface densities are genuine predictions rather than post‑processed estimates.

The authors analyse the KS relation on kiloparsec scales across the full redshift range 0 ≤ z ≤ 8. At z≈0 the simulated galaxies reproduce the observed spatially‑resolved HI and H₂ KS relations, including the measured slopes (≈1.5 for HI, ≈1.0 for H₂) and normalisations. Importantly, the scatter around both relations is found to correlate strongly with three secondary parameters: stellar surface density (Σ_*), local specific star‑formation rate (sSFR), and gas‑phase metallicity (Z_gas). This confirms observational suggestions that these quantities act as “second parameters” governing the efficiency of gas‑to‑star conversion.

A key result is the mass‑dependence of the HI KS relation: low‑mass galaxies (M_* ≲ 10⁹ M_⊙) exhibit a markedly steeper HI slope, indicating that atomic gas dominates the star‑forming reservoir in dwarf systems. Conversely, galaxies with high sSFR show an upward shift in the H₂ KS normalisation, meaning that for a given molecular gas surface density they form stars more rapidly. This behaviour aligns with the notion that elevated sSFR reflects a larger molecular gas fraction and a higher star‑formation efficiency on kpc scales.

The redshift evolution of the molecular KS relation is dramatic. The H₂ depletion time (t_dep = M_H₂/Ṁ_*) declines by roughly a factor of 20 from ~2 Gyr at z = 0 to ~0.1 Gyr at z = 8. The authors attribute this primarily to the systematic drop in gas‑phase metallicity at early times, which suppresses H₂ formation. Consequently, a given Σ_SFR at high redshift is associated with more HI and less H₂ than at low redshift. The simulated evolution of t_dep and its anti‑correlation with sSFR matches a wide range of observational data up to z ≈ 5, providing strong validation of the model.

The paper also explores how Σ_* and Z_gas modulate the KS scatter. High Σ_* enhances gravitational stability, reducing the star‑formation efficiency at fixed gas surface density, while high metallicity promotes H₂ formation and boosts Σ_SFR. These competing effects generate the observed multi‑dimensional trends in the KS plane. The authors perform extensive resolution‑convergence tests, demonstrating that the KS relations converge for spatial resolutions better than 1 kpc, even across simulations with gas particle masses spanning two orders of magnitude.

In summary, the COLIBRE simulations, with their sophisticated treatment of ISM physics, successfully reproduce the observed atomic and molecular KS relations, their scatter, and their evolution over 13 billion years. The work highlights the pivotal roles of sSFR, stellar surface density, and metallicity in shaping the KS law, and provides a robust theoretical framework for interpreting forthcoming high‑redshift observations from facilities such as JWST, ALMA, and next‑generation 30‑meter class telescopes.