Galaxy Evolution and Assembly (GAEA)

Updated 18 November 2025

GAEA is a semi-analytic framework that simulates galaxy formation from reionization to the present by integrating dark matter merger trees with detailed baryonic physics.
It calibrates key processes such as star formation, feedback, and chemical enrichment against observables like the stellar mass function and mass–metallicity relations.
The model incorporates environmental effects and AGN feedback to explore galaxy quenching, structural evolution, and high-redshift predictions.

The Galaxy Evolution and Assembly (GAEA) semi-analytic model is a state-of-the-art framework for modeling galaxy formation and evolution across cosmic time. Built on N-body merger trees (Millennium, Millennium-II, Planck-Millennium), GAEA integrates modular baryonic physics—including cooling, star formation, feedback, chemical enrichment, and black-hole growth—to reproduce observed galaxy properties from the epoch of reionization (z~13) to the present. The model calibrates its free parameters against key observables such as the stellar mass function (GSMF), mass–metallicity relations, and star-formation rates, and incorporates physically motivated improvements as new data and simulation results become available.

1. Physical Foundations and Model Architecture

GAEA adopts a modular semi-analytic approach wherein the baryonic evolution is solved within dark-matter merger-tree branches (Hirschmann et al., 2015, Cantarella et al., 5 Nov 2025). Each tree node tracks baryonic reservoirs: hot gas, cold gas (ISM), molecular (H₂) and atomic (H I) gas phases (Zoldan et al., 2019, Zakharova et al., 30 Aug 2024), stars, an ejected gas reservoir (beyond the halo), and a central black hole mass. Key physical prescriptions include:

Gas cooling: Metallicity-dependent radiative cooling from the hot halo onto the galaxy disk, using the cooling-radius formalism (Lucia et al., 2016).
Star formation: Molecular-gas-based Schmidt–Kennicutt law, with atomic–molecular partitioning determined by mid-plane pressure or metallicity (Zoldan et al., 2019, Cantarella et al., 5 Nov 2025).
Feedback: Ejective outflows (mass loading scaling as function of V_c and redshift) following FIRE-calibrated parametrizations (Fontanot et al., 2017, Hirschmann et al., 2015), and delayed reincorporation timescales.
Chemical enrichment: Explicit, finite-lifetime yields from SN II, SN Ia, and AGB stars; tracked element-by-element (Hirschmann et al., 2015, Lucia et al., 2016).
SMBH growth and AGN feedback: Distinction between radio-mode (hot gas, maintenance) and quasar-mode (cold gas, merger/instability triggered) accretion and outflow, with prescriptions for reservoir physics and Eddington-limited accretion (Fontanot et al., 2020, Lucia et al., 11 Jan 2024).
Environmental physics: Gradual stripping of satellite hot/cold gas, ram-pressure and tidal effects, explicitly partitioning stripping timescales (Lucia et al., 11 Jan 2024, Xie et al., 2020, Zakharova et al., 30 Aug 2024).

In recent model versions, feedback and stripping are implemented as continuous processes, molecular cloud-scale physics is explicitly resolved, and quasar-driven winds are coupled to AGN luminosity via physically motivated mass-loading factors.

2. Star Formation Laws, Feedback, and Gas Reservoir Cycling

GAEA’s star-formation law is rooted in molecular gas physics: SFR $=\alpha_{\rm SF} \cdot M_{\rm H_2} / \tau_{\rm dyn, disk}$ (Zoldan et al., 2019, Lucia et al., 11 Jan 2024, Cantarella et al., 5 Nov 2025). The partitioning between atomic and molecular gas is given by a pressure law $R_{\rm mol} = (P_{\rm ext}/P_0)^\alpha$ , with $P_{\rm ext}$ set by the gas and stellar disk surface densities. Only gas above a threshold surface density is eligible for SF, suppressing spurious starbursts in massive galaxies (Lucia et al., 11 Jan 2024).

Stellar feedback follows mass-loading scalings of the form

$\dot M_{\rm reheat} = \epsilon_{\rm reheat} (1+z)^{1.25} \left( \frac{V_{\rm max}}{60\,{\rm km/s}} \right)^{-\alpha} \dot M_\star$

with $\alpha \simeq 3.2$ and $\epsilon_{\rm reheat}$ calibrated to match the GSMF (Hirschmann et al., 2015, Cantarella et al., 5 Nov 2025). Ejective feedback expels gas to a reservoir with reincorporation timescales decreasing for higher mass halos, establishing a baryon cycle that regulates SF and chemical enrichment (Fontanot et al., 2017). Preventive feedback—suppression of gas infall—is an alternative mechanism that has also been tested (Hirschmann et al., 2015).

For satellites, gradual stripping is implemented:

$\frac{dM_{\rm hot}}{dt}= -\frac{M_{\rm hot}}{\tau_{\rm strip}};\quad \frac{dM_{\rm cold}}{dt}= -\frac{M_{\rm cold}}{\tau_{\rm cold}}$

where stripping timescales $\tau_{\rm strip}$ and $\tau_{\rm cold}$ are functions of halo dynamical time and calibration coefficients (Lucia et al., 11 Jan 2024, Xie et al., 2020).

3. Chemical Evolution, Mass–Metallicity Relations, and IMF Variations

GAEA implements an explicit non-instantaneous chemical enrichment module, tracking H, He, C, N, O, Mg, Si, S, Fe yields from SN II, SN Ia, and AGB stars (Portinari, Karakas, Thielemann yields) (Hirschmann et al., 2015, Fontanot, 2019, Fontanot et al., 2021). The cold gas metallicity evolves as (Fontanot et al., 2021):

$\frac{d(M_{Z,\rm cold})}{dt} = Z_{\rm hot}\dot M_{\rm cool} - Z_{\rm cold}\dot M_{\rm reheat} + Z_{\rm eject}\dot M_{\rm reinc} - Z_{\rm cold}\psi + y_{\rm eff}\psi$

The model reproduces the observed gas-phase MZR up to $z\sim3.5$ ; $12+\log({\rm O}/H) \simeq 8.76 - 0.12z + 0.30\log(M_\star/10^{10}M_\odot)$ (Fontanot et al., 2021). At high redshift ( $z \gtrsim 3.5$ ), GAEA overpredicts stellar metallicity, indicating unresolved tensions possibly related to systematic uncertainties or missing physical mechanisms (e.g., variable IMF, metal-rich outflows).

GAEA supports variable IMF scenarios, including the Integrated Galaxy-Wide IMF (IGIMF), cosmic-ray regulated IMF, or SFR-dependent prescriptions (Fontanot et al., 2016, Fontanot, 2019). SFR-flattened IMFs increase [α/Fe] at high mass and high redshift, resolving the classic $\alpha$ -enhancement vs mass tension in hierarchical models (Lucia et al., 2016). Intrinsic stellar masses and mass-to-light ratios computed under variable IMFs can differ by 0.2–0.5 dex for massive galaxies compared to photometric estimates, with implications for mass-function and SFR history reconstructions.

4. AGN Physics and Impact on Galaxy Quenching

GAEA’s AGN module distinguishes “radio-mode” maintenance feedback (suppression of cooling in massive halos) and “quasar-mode” outflows (mechanical feedback during cold-gas accretion events) (Fontanot et al., 2020, Lucia et al., 11 Jan 2024). Cold accretion onto the SMBH proceeds from a low-J reservoir:

$\dot M_{\rm lowJ} = f_{\rm lowJ} \mathrm{SFR};\quad \dot M_{\rm BH} = \frac{f_{\rm BH} M_{\rm res}}{t_{\rm visc}}$

Quasar-mode winds eject mass at a rate

$\dot M_{\rm out} = \frac{2\epsilon_{\rm qw}L_{\rm AGN}}{V_{\rm vir}^2}$

with mass-loading $\eta_w \sim (2\epsilon_{\rm qw}\eta c^2)/V_{\rm vir}^2$ (Lucia et al., 11 Jan 2024).

Quasar winds efficiently suppress residual star formation in massive ( $M_\star > 10^{10} M_\odot$ ) galaxies, producing agreement with observed quenched fractions and specific SFR distributions up to $z\sim4$ (Lucia et al., 11 Jan 2024, Fontanot et al., 2020). For satellites, the adoption of non-instantaneous stripping reduces the excess passive population at low masses (Lucia et al., 11 Jan 2024, Xie et al., 2020).

The model tracks AGN statistics such as the bolometric luminosity function, Eddington ratios, and AGN downsizing trend, confirming that only SMBHs above $10^8 M_\odot$ are predominantly self-regulated.

5. Galaxy Structural Properties: Sizes, Angular Momentum, and Assembly

GAEA has explicit bookkeeping for angular momentum exchanges among DM halos, hot gas, cold disk gas, and stellar disks (Zoldan et al., 2019). This ensures that the scale radius $R_x$ of disks (gas or stars) scales as

$R_x = \frac{j_x}{2V_{\rm max}}$

and for idealized disks,

$R_d = \frac{1}{\sqrt{2}} f_j \lambda R_{200}$

where $f_j$ is the retention factor and $\lambda$ the halo spin. Bulge sizes are set by energy conservation and dissipative corrections in gas-rich mergers.

GAEA reproduces observed size–mass and size–halo relations for late-type galaxies to $z\sim2$ , but tends to underpredict bulge sizes for massive quiescent galaxies—a discrepancy associated with excess central gas and insufficient mechanical AGN feedback (Zoldan et al., 2019). Compact quiescent galaxies at high z form preferentially in low angular momentum halos; most merge away before $z=0$ (Zoldan et al., 2019).

6. Environmental Effects: Quenching and Gas Content Across Cosmic Structures

GAEA incorporates environmental quenching mechanisms, including ram-pressure stripping (cold and hot phases), tidal interactions, and gradual gas depletion (Zakharova et al., 30 Aug 2024, Lucia et al., 11 Jan 2024). Cold gas partitioning allows differentiated stripping efficiencies: H I is preferentially depleted over H₂, reflecting the spatial distributions within disks.

Analysis of filament, cluster, and field environments reveals that HI deficiency in clusters and filaments is more pronounced at low stellar masses ( $M_* < 10^{10} M_\odot$ ) and that filaments provide intermediate depletion, mainly due to the presence of group satellites, not a direct filament-specific effect (Zakharova et al., 30 Aug 2024). H₂ depletion is generally milder. The model matches observational HI and H₂ deficiency statistics after bias corrections, and galaxy populations in filaments split into group satellites (depleted) and “pure-field” type galaxies (Zakharova et al., 30 Aug 2024).

7. High-Redshift Predictions, JWST Era, and Outstanding Challenges

GAEA runs on Planck-Millennium merger trees reproduce the GSMF up to $z\sim13$ and UV luminosity functions up to $z\sim10$ , including the contribution from AGN at the bright end (Cantarella et al., 5 Nov 2025). At $z>10$ , observed galaxy abundances exceed fiducial model predictions by up to an order of magnitude. Physically-motivated variants—such as feedback-free starbursts in dense clouds or saturated feedback—raise the high-z GSMF and UVLF to match JWST data but increase the high-z mass-metallicity normalization, exacerbating tensions with available ISM metallicity measurements (Cantarella et al., 5 Nov 2025). These scenarios predict distinct main-sequence (SFR– $M_*$ ) slopes and metallicity relations, providing prospective observational tests.

GAEA maintains consistency with hierarchical galaxy formation, demonstrating that physically motivated feedback, chemical enrichment, and AGN prescriptions together reproduce most observed galaxy demographic trends, with remaining tensions (quenching thresholds, metallicity normalization, massive galaxy sizes) identifying directions for future refinement.

Key References:

(Hirschmann et al., 2015, Lucia et al., 2016, Zoldan et al., 2019, Fontanot et al., 2017, Fontanot, 2019, Lucia et al., 11 Jan 2024, Fontanot et al., 2021, Fontanot et al., 2020, Zakharova et al., 30 Aug 2024, Cantarella et al., 5 Nov 2025, Fontanot et al., 2016, Xie et al., 2020)