---
title: COLIBRE Galaxy Formation Model
url: https://www.emergentmind.com/topics/colibre-galaxy-formation-model
type: topic
---

# COLIBRE Galaxy Formation Model

The COLIBRE Galaxy Formation Model is a state-of-the-art, physically motivated, and extensively calibrated suite of cosmological hydrodynamical simulations designed to model galaxy formation and evolution across a broad range of mass scales and redshifts. It explicitly resolves the multiphase interstellar medium (ISM), captures non-equilibrium chemistry, incorporates detailed dust evolution, and provides self-consistent stellar and AGN feedback recipes, representing a significant advancement over previous models. The model is calibrated to reproduce observed galaxy stellar mass functions, size-mass relations, and black hole mass scaling at low redshift, and achieves very good numerical convergence and excellent agreement with diverse observational data [2508.21126].

## 1. Multiphase ISM, Non-Equilibrium Chemistry, and Radiative Cooling

COLIBRE directly models the cold (down to $\sim$10 K), warm ($\sim$10$^4$ K), and hot ISM phases without imposing an artificial pressure floor, unlike many older large-volume simulations. Hydrogen and helium abundances are evolved in non-equilibrium, crucial for accurately determining the free electron density that controls metal-line cooling rates. Metal cooling is treated using equilibrium tables, but with a correction factor based on the non-equilibrium electron density:
$$
\Lambda_{\rm metal} = \Lambda_{\rm metal}(\rho, T, Z) \times \left(\frac{n_e^{\rm NE}}{n_e^{\rm eq}}\right)
$$
Cooling rates account for both a redshift-dependent metagalactic UV background and a local ISRF, as well as self-shielding by gas and dust (typically estimated locally using the Jeans length) [2508.21126].

The chemical network, based on "hybrid-chimes," tracks approximately 157 ions and molecules, ensures non-equilibrium treatment for H and He, and includes molecule formation on grain surfaces (e.g., H$_2$, CO). Dust is critical for accurately modeling the ISM and molecular cloud physics, modulating cooling, shielding, and chemical pathways.

## 2. Dust Evolution and Chemical Coupling

Dust grain evolution is explicitly followed, with three species (carbonaceous/graphite and two silicates—olivine forms forsterite, fayalite) and two size bins (small, $r_{\rm s} \approx 0.01\ \mu$m; large, $r_{\rm l} \approx 0.1\ \mu$m). Formation occurs via gas-phase accretion and grain coagulation, enhanced by a subgrid clumping factor for unresolved molecular clouds:
$$
\tau_{\rm acc} \propto \left( \frac{r_{\rm g}}{0.1\,\mu{\rm m}} \right) \left( \frac{n_{\rm H}'}{10\,{\rm cm}^{-3}} \right)^{-1}
\left( \frac{T}{10\,{\rm K}} \right)^{-1/2}
$$
Destruction processes include sputtering in hot gas and astration (removal by star formation). The dust model directly couples to the chemical network and cooling, controlling formation rates of molecules like H$_2$ and CO [2508.21126].

## 3. Star Formation, Early Feedback, and Turbulent Diffusion

Star formation is stochastic; gas is eligible if locally gravitationally unstable as determined by a dimensionless stability parameter:
$$
\alpha \equiv \frac{ \sigma_{\rm th}^2 + \sigma_{\rm turb}^2 }
   { G\, \langle N_{\rm ngb}\rangle^{2/3}\,m_{\rm g}^{2/3}\,\rho_{\rm g}^{1/3} } < \alpha_{\rm crit}
$$
with $\alpha_{\rm crit}=1$. SFR density follows a Schmidt law:
$$
\dot{\rho}_\star = \varepsilon\, \frac{\rho_{\rm g}}{ t_{\rm ff} } = \varepsilon \left( \frac{32 G}{3\pi} \right)^{1/2} \rho_{\rm g}^{3/2}
$$
where $\varepsilon\sim0.01$ (per free-fall time). At higher resolution, star formation naturally proceeds in denser and colder gas [2508.21126].

Early feedback from massive stars includes mechanical winds, radiative pressure, and ionization producing H II regions. Local attenuation by dust/gas is modeled, and gas in H II regions is kept at $>$10$^4$ K and excluded from star formation, dispersing natal clouds prior to supernova onset.

Turbulent mixing is implemented as explicit diffusion between SPH particles:
$$
\frac{dX}{dt} = \nabla\cdot(D\,\nabla X)
$$
where $D$ is proportional to the local velocity shear. This is essential to distribute metals and dust, mitigating inhomogeneities arising from discrete enrichment events.

## 4. Stellar Mass Loss, Supernova Feedback, and Outflows

Stellar mass loss and metal enrichment use updated yields for AGB stars, core-collapse SN, Type Ia SN, and r-process sources. Feedback energy from CCSNe is parameterized:
$$
\Delta E_{\rm CCSN} = 10^{51}\,{\rm erg} \; f_E \, m_* \int_{m_{\rm d}(t+\Delta t)}^{m_{\rm d}(t)} \Phi(m)\;dm
$$
with $f_E$ possibly dependent on local birth pressure $P_{\rm birth}$. SN energy injects both stochastic thermal (target $\Delta T_{\rm SN}$, density-dependent) and kinetic (10% of energy, driving turbulence, $\sim$50 km/s) channels. Energy accumulates until adequate for the target temperature jump, reducing over-cooling in dense gas [2508.21126].

A distinctive feature is the parameterized variation of SN feedback strength with ambient conditions:
$$
f_E(P_{\rm birth}) = f_{E,\mathrm{min}} + \frac{ f_{E,\mathrm{max}} - f_{E,\mathrm{min}} }
   {1+\exp\left[ -\frac{ \log_{10}P_{\rm birth} - \log_{10}P_{E,\mathrm{pivot}} }{ \sigma_P } \right] }
$$

## 5. BH Growth, AGN Spin-Dependent Feedback, and Subgrid Calibration

Supermassive black holes are seeded in halos above a defined mass threshold. Accretion follows a modified Bondi-Hoyle-Lyttleton rate:
$$
\dot{m}_{\rm BHL} = 4\pi G^2 \frac{ \rho_{\rm g} }{ (c_s^2 + v^2)^{3/2} } m_{\rm BH}^2
$$
with modifications for turbulence ($f_{\rm turb}$) and vorticity ($f_{\rm ang}$). The Eddington limit is not strictly enforced (up to 100x the classic Eddington rate is allowed).

Fiducial AGN feedback is purely thermal: energy accumulates and is injected stochastically once enough is stored to heat nearby gas by $\Delta T_{\rm AGN}$, with sampling adjusted for BH mass.

A subset of simulations uses a hybrid jet/thermal AGN model with spin-dependent jet formation (Blandford-Znajek-like mechanism). BH spin evolves with gas accretion, mergers, and torques. Depending on the accretion-disc state (thin, slim, thick), the feedback splits into bipolar kinetic jets ($v_{\rm jet} \propto m_{\rm BH}^{1/2}$) and thermal energy:
$$
\dot{m}_{\rm BH} = (1-\epsilon_r-\epsilon_{\rm jet}-\epsilon_{\rm wind})\epsilon_{\rm accr}\dot{m}_{\rm accr}
$$
This adds a physically motivated channel for regulating massive galaxy and BH growth [2508.21126].

Subgrid feedback parameters are calibrated via machine-learning emulators trained on moderate-volume runs ($\sim$50 cMpc, $m_7$), targeting agreement with $z\sim0$ scaling relations (stellar mass function, galaxy size-mass, BH–stellar mass relation).

## 6. Simulation Suite, Convergence, and Observational Comparisons

The COLIBRE suite spans three resolutions: particle masses of $\sim10^5$, $10^6$, $10^7\,M_\odot$, in volumes of up to 50, 200, and 400 cMpc. The largest runs contain 136 billion ($5\times3008^3$) particles. Dark matter is supersampled by a factor of 4, ensuring nearly equal baryonic and dark matter particle masses, suppressing spurious energy transfer.

The subgrid model is calibrated to reproduce observed low-redshift galaxy properties:
- Stellar mass function
- Galaxy size-mass relation
- Black hole mass in massive galaxies

A broad array of other observables are matched, including quenched fractions, specific SFRs, gas fractions of H I and H$_2$, dust masses, metallicities, and circumgalactic X-ray luminosity. Numerical convergence is very good over the observed range. Agreement with data is described as "excellent" for these diagnostics [2508.21126].

## 7. Limitations and Prospects

While COLIBRE represents significant progress, limitations are acknowledged:
- Inability to resolve internal molecular cloud structure directly; subgrid clumping factors are required for dust and molecule growth rates.
- AGN feedback efficiency remains sensitive to numerical resolution because of injection in unresolved inner regions.
- Physical parameters (feedback strength, energy coupling efficiency, etc.) must be empirically calibrated, limiting strict ab initio predictive power.
- Physics such as magnetic fields, fully-coupled radiation transport, and cosmic ray pressure are omitted.

A plausible implication is that further increases in resolution and expansion of physical ingredients (e.g., full radiation hydrodynamics) may further improve model fidelity and predictive power.

## Concluding Perspective

The COLIBRE galaxy formation model synthesizes advanced physical prescriptions for an explicitly multiphase ISM, live dust chemistry, and sophisticated feedback with a rigorous calibration methodology. Its ability to capture chemical, thermal, and dynamical evolutionary pathways—validated against a wide span of observational data—marks it as a reference hydrodynamical model for galaxy formation applications at low redshift and sets a robust platform for further testing and development in cosmological simulations [2508.21126].

Source: https://www.emergentmind.com/topics/colibre-galaxy-formation-model