L-Galaxies SAM Model for Galaxy Formation

• L-Galaxies is a semi-analytical model that evolves baryonic components in dark matter haloes using merger trees and calibrated physical prescriptions.
• It integrates modules for star formation, chemical enrichment, dust evolution, and AGN feedback, matching key observables like stellar mass functions and scaling relations.
• Recent enhancements include radially resolved discs and refined environmental treatments, addressing challenges in orphan galaxy modeling and high-redshift quenched populations.

L-Galaxies is the Munich semi-analytic model (SAM) of galaxy formation and evolution, designed to evolve the baryonic components that reside in and between dark matter haloes along merger trees derived from cosmological $N$-body simulations. Across its major implementations, it tracks hot halo gas, cold interstellar gas, stars, black holes, and ejected material, and couples radiative cooling, star formation, chemical enrichment, feedback, mergers, environmental stripping, and structural evolution through calibrated prescriptions. Over time it has developed from a single-zone galaxy model into a radially resolved, lightcone-native framework with dedicated modules for dust, hot X-ray haloes, and other observables (Guo et al., 2010, Henriques et al., 2020, Barrera et al., 2022).

1. Historical development and model families

L-Galaxies belongs to the Munich lineage of semi-analytic galaxy formation models associated with Springel et al., Croton et al., De Lucia & Blaizot, Guo et al., Henriques et al., and later extensions. An important milestone was the application of updated L-Galaxies physics simultaneously to the Millennium and Millennium-II simulations, which differ by a factor of $125$ in mass resolution and enabled explicit resolution tests for galaxy abundances, clustering, satellite populations, and orphan treatments (Guo et al., 2010). Subsequent branches incorporated Planck cosmology, MCMC-based calibration, radially resolved discs, local environmental stripping, and continuous past-lightcone outputs (Vani et al., 2024, Barrera et al., 2022).

Three recent calibrated “flavours” organize much of the contemporary literature:

Flavour	Distinguishing ingredients	Calibration targets
Henriques2015	Planck-1 cosmology; revised gas reincorporation; virial-mass threshold for ram-pressure stripping	SMF and quenched fractions at $z=0,1,2,3$
Henriques2020	12 disc rings; H$_2$-based star formation; delayed chemical enrichment	SMF and quenched fractions at $z=0,2$; HI mass function at $z=0$
Ayromlou2021	Local background environment ram-pressure stripping for all satellites and centrals, within and beyond virial radii	SMF and quenched fractions at $z=0,1,2$

This progression did not replace the underlying semi-analytic logic; it refined its spatial resolution, feedback couplings, and environmental realism. The 2025 analysis of galaxy scaling relations from $z=0$ to $z\simeq 10$ explicitly treats Henriques2015, Henriques2020, and Ayromlou2021 as the three latest calibrated L-Galaxies variants, emphasizing continuity of lineage alongside changes in physical prescriptions (Vani et al., 2024).

2. Core architecture and baryon cycle

At its core, L-Galaxies evolves baryons on top of dark-matter merger trees extracted from simulations such as Millennium, Millennium-II, eagleDMO, and MillenniumTNG. In the model, baryons are distributed among several reservoirs: hot halo gas, cold interstellar gas, stars, supermassive black holes, and an ejected reservoir beyond the halo. For some branches, baryons are also tracked in halo stars or intracluster light, and in recent resolved implementations the cold disc is subdivided into multiple annuli or rings (Guo et al., 2010, Ayromlou et al., 2020).

The timestep logic is modular. In the dust-integrated implementation, each timestep proceeds through star formation, supernova-rate estimation from the star-formation history, metal production and redistribution, source-specific dust injection, molecular-cloud grain growth, dust destruction, and a final update of global dust, dust-to-gas, and dust-to-metal ratios. That ordering illustrates a more general point about L-Galaxies: later modules depend on earlier modules to supply rates, metallicities, phase masses, temperatures, and feedback fluxes (Vijayan et al., 2019).

The older Guo et al. branch used a threshold-based quiescent star-formation law,

$$\dot{M}_\star = \alpha_{\rm SF}\,\frac{(M_{\rm gas}-M_{\rm crit})}{t_{\rm dyn,disk}},$$

with

$125$0

while retaining burst modes in mergers and disc instabilities (Martindale et al., 2016). Cooling in this lineage was tied to a hot halo treated as an isothermal atmosphere, with a cooling radius $125$1 separating slow-cooling and rapid-infall regimes, and a halo dynamical time $125$2 setting the characteristic cooling timescale (Guo et al., 2010).

Black-hole growth and AGN feedback are built into all modern flavours. The 2024 comparison of the three latest model flavours states the hot-gas radio-mode accretion law as

$125$3

with associated heating power

$125$4

where $125$5, and emphasizes that AGN feedback suppresses cooling rather than ejecting gas from haloes in those flavours (Vani et al., 2024). This preventative character of AGN feedback is central to several later tensions with hydrodynamical simulations and with the abundance of quenched massive galaxies at high redshift.

3. Radial resolution, cold gas phases, and chemical enrichment

The most important structural reworking of the model came with L-GALAXIES 2020, which resolved galactic discs into 12 concentric rings and computed star formation, gas partitioning, and enrichment locally. Ring outer edges are fixed at

$125$6

and newly cooled gas is deposited with an exponential surface-density profile

$125$7

where

$125$8

This setup produces inside-out growth while preserving a direct link between halo angular momentum and disc structure (Henriques et al., 2020).

Cold gas is partitioned into HI and H$125$9 ring by ring using the Krumholz-McKee-Tumlinson framework, implemented through the molecular fraction

$z=0,1,2,3$0

with $z=0,1,2,3$1, $z=0,1,2,3$2, and $z=0,1,2,3$3 defined in terms of metallicity and gas surface density, and with a metallicity-dependent clumping factor $z=0,1,2,3$4 applied to the azimuthally averaged gas surface density. Molecular and atomic components then follow

$z=0,1,2,3$5

Star formation becomes explicitly H$z=0,1,2,3$6-based: $z=0,1,2,3$7 with $z=0,1,2,3$8 in L-GALAXIES 2020 (Henriques et al., 2020).

Chemical enrichment is no longer approximated as purely prompt recycling. Instead, L-GALAXIES 2020 applies the delayed-enrichment framework of Yates et al. ring by ring, using Portinari et al. for SN II yields and lifetimes, Marigo for AGB yields, and Thielemann et al. for SN Ia yields, with a SN Ia delay-time distribution proportional to $z=0,1,2,3$9. The ejection rate of element $_2$0 from a stellar population is written as

$_2$1

This local enrichment model stores ring-resolved star-formation and enrichment histories and computes ring-level reheating, ejection, and metallicity evolution self-consistently (Henriques et al., 2020).

A later metallicity-focused modification demonstrated that increasing direct CGM enrichment by supernovae can simultaneously reproduce gas-phase and stellar metallicity radial profiles and the evolution of gas and stellar mass-metallicity relations. In that version, a direct CGM enrichment fraction of $_2$2 for SN II is preferred, with $_2$3, $_2$4, and $_2$5, while the radial inflow parameter is lowered to $_2$6 (Yates et al., 2020).

4. Structural evolution, environment, and satellite treatment

Galaxy sizes in L-Galaxies are tied to angular momentum and halo structure. In the resolved and semi-resolved branches, discs form by angular-momentum-conserving cooling, with scale length related to halo spin following Mo, Mao & White. One common expression quoted in the size-metallicity study is

$_2$7

while the 2018 morphology update writes gaseous and stellar disc scale lengths as

$_2$8

That same work argues that matching the observed stellar disc scale length-mass relation at $_2$9 requires cooled gas to retain $z=0,2$0 of the halo’s specific angular momentum, corresponding to a $z=0,2$1 loss during cooling (Irodotou et al., 2018).

Bulge growth is split between mergers and disc instabilities. The 2018 update introduced a two-component instability criterion that includes both stellar and gaseous discs, with component stability parameters

$z=0,2$2

where $z=0,2$3 and $z=0,2$4. Gas is first converted to stars in a bar-driven episode until marginal stability is restored or the gas component itself reaches marginal stability; if instability remains, stars are transferred from disc to bulge. Merger remnant sizes are then computed from energy conservation with an explicit radiative-loss term,

$z=0,2$5

with $z=0,2$6 adopted for the dissipation efficiency. These modifications improve the morphology-mass relation, the stellar specific-angular-momentum relation, and the mass-size relation of bulge-dominated systems (Irodotou et al., 2018).

Environmental treatment is equally central. L-Galaxies distinguishes centrals, satellites with resolved subhaloes, and orphans. In the environmental-dependence extension, these are denoted type 0, type 1, and type 2, respectively, and the model measures a local background environment for every galaxy directly from dark-matter particle data. Ram pressure is computed as

$z=0,2$7

and the stripping radius for hot halos follows from the force balance

$z=0,2$8

with stripping then applied to all galaxies, centrals and satellites, at all halocentric distances. In that implementation, satellites near massive haloes can lose more than $z=0,2$9–$z=0$0 of their hot gas before infall, and low-mass centrals within $z=0$1 of clusters can lose up to $z=0$2 of their hot reservoirs (Ayromlou et al., 2020).

Orphans remain a major modeling issue. A 2024 analysis of passive-galaxy abundances found that the overabundance of low-mass passive galaxies in L-Galaxies at $z=0$3 can be attributed solely to orphans, which comprise at least $z=0$4 of the model quiescent population in the lightcone. Replacing orphan star-formation properties with those of resolved satellites at similar redshift and supercolour largely fixes the low-mass passive discrepancy and reduces passive-SMF $z=0$5 by $z=0$6, while leaving the star-forming SMF essentially unchanged (Harrold et al., 2024).

5. Extended physical modules and observable interfaces

A major extension of L-Galaxies concerns interstellar dust. The detailed dust model introduces a two-phase cold ISM consisting of molecular clouds and inter-cloud medium, and follows dust production by SN II, SN Ia, and AGB stars; grain growth in molecular clouds only on pre-existing grains; and destruction by SN shocks, star formation, and reheating. Source injection is parameterized as

$z=0$7

and grain growth in molecular clouds follows

$z=0$8

This model predicts that above $z=0$9, SN II are the primary source of dust; below $z=0,1,2$0, grain growth in molecular clouds dominates the dust-production rate; and below $z=0,1,2$1, the total dust content is dominated by grain growth. It also introduces a fitted $z=0,1,2$2 relation that can be used to infer dust-to-metal ratios at any redshift (Vijayan et al., 2019).

Hot gaseous haloes have also been reworked beyond the traditional isothermal sphere. In the 2022 hot-gas implementation, the radial structure of the hot phase follows the one-dimensional precipitation framework of Sharma et al., dividing haloes into a cool core with $z=0,1,2$3 and a stable outer halo with $z=0,1,2$4. The resulting flatter inner density profiles produce lower X-ray luminosities than an isothermal sphere, while cool-core regions have temperatures above $z=0,1,2$5, with a larger $z=0,1,2$6 ratio in smaller haloes. The model reproduces observed radial profiles of hot-gas density and the scaling relations of X-ray luminosity and temperature, and argues that ionized gas in the unbounded reservoir and low-temperature intergalactic gas in low-mass haloes are likely major components of the halo “missing baryons” (Zhong et al., 2022).

This hot-gas framework has been taken further into mock-observation pipelines. A 2023 extension of L-Galaxies 2015 introduces explicit radial distributions of halo hot gas and constructs mock X-ray lightcones, spectra, and images. Using SOXS and APEC, it generates mock ROSAT and HUBS observations and finds that the synthetic data match current X-ray observations, that HUBS should survey resolved cluster hot baryons effectively below $z=0,1,2$7, and that point-like sources at $z=0,1,2$8 can still provide informative emission-line spectra. The same work emphasizes the advantage of coupling large SAM volumes to flexible mock-observation pipelines (Zhong et al., 2023).

Recent extensions reach beyond gas and dust. A 2025 variation of L-Galaxies 2020 forms and evolves individual massive star clusters above $z=0,1,2$9 in the resolved discs, stores up to $z=0$0 clusters per galaxy, and evolves them through stellar evolution, two-body relaxation, tidal shocks, dynamical friction, and merger-driven repositioning. That module reproduces the relation between the brightest young cluster and host-galaxy star-formation rate, the young-cluster mass function, and mean cluster metallicity trends with host mass (Hoyer et al., 16 Apr 2025).

6. Calibration, predictive power, and unresolved tensions

L-Galaxies has consistently been calibrated against a small set of low-redshift or multi-redshift observables and then stress-tested on others. In the EAGLE comparison, the Guo et al. branch, modestly recalibrated for the eagleDMO trees, matches the galaxy stellar mass function and median specific star-formation rates to within $z=0$1 dex for $z=0$2 at $z=0$3, and its sSFR evolution closely follows the mass assembly history of dark-matter haloes. The same comparison, however, finds that median galaxy sizes can differ by up to an order of magnitude between models in some cases, and argues that semi-analytic models should revise how they treat baryonic self-gravity and halo contraction, because L-GALAXIES ignores baryonic self-gravity when computing disc sizes and dynamics (Guo et al., 2015).

Object-by-object comparison with IllustrisTNG sharpens those tensions. Running L-GALAXIES on the TNG dark-matter-only trees yields stellar masses that agree with TNG to better than $z=0$4 dex, but star-formation rates, gas contents, and halo baryon fractions differ more strongly. At $z=0$5, the transition between low-mass star-forming galaxies and high-mass quenched galaxies occurs at a stellar mass scale $z=0$6 dex lower in TNG than in L-GALAXIES, and TNG satellites are less star-forming and less gas-rich out to $z=0$7–$z=0$8. This indicates that environmental processes such as ram-pressure stripping are stronger and operate over a broader host-mass range in the hydrodynamical model, suggesting that L-Galaxies needs more local environmental prescriptions (Ayromlou et al., 2020).

Despite such tensions, the model remains competitive in large-scale forward modelling. The continuous-lightcone implementation for MillenniumTNG outputs galaxies directly on fully continuous past lightcones, potentially over the full sky and out to high redshift, for all galaxies more massive than $z=0$9. It interpolates galaxy orbits and halo properties between snapshots, carries adaptive star-formation histories for on-the-fly photometry, and shows that projected clustering on lightcones agrees with snapshot-based estimates to within $z\simeq 10$0–$z\simeq 10$1 at $z\simeq 10$2–$z\simeq 10$3 Mpc, with larger differences only at very small scales or near BAO scales because of box-size and anisotropy effects (Barrera et al., 2022).

The strongest current challenges are concentrated at high redshift and in quenched structural evolution. The 2024 comparison of three recent flavours finds that L-Galaxies is in qualitatively good agreement with observed global scaling relations up to $z\simeq 10$4, including the overall behaviour of total stellar mass functions, cosmic star-formation-rate density, and the main sequence of star-forming galaxies. Yet the same study reports that the abundance of massive quenched centrals is underpredicted at $z\simeq 10$5, reaching a discrepancy of a factor of $z\simeq 10$6 by $z\simeq 10$7, and that quenched sizes are several times larger than observed. It therefore proposes improving AGN feedback and merger-related structural prescriptions, potentially by making AGN feedback more ejective and by revisiting remnant-size modeling (Vani et al., 2024).

More focused diagnostics show that the model can nevertheless isolate physically interpretable relations. In the 2025 size-stellar-metallicity study, L-GALAXIES reproduces the observed anti-correlation between size and stellar metallicity at fixed stellar mass, but with a stronger amplitude than seen in MaNGA: Spearman’s $z\simeq 10$8 in the model versus $z\simeq 10$9 observationally. Within that framework, the relation is attributed not to gravitational potential depth or star-formation history, but to higher star-formation efficiencies and more metal-rich recycled inflows in smaller galaxies at fixed stellar mass (Wang, 2 Oct 2025).

Weak-lensing tests also show that the model’s empirical performance depends on the chosen flavour. In galaxy-galaxy-galaxy lensing using KiDS+VIKING+GAMA, the Henriques et al. 2015 implementation agrees with all colour-selected samples and all but one stellar-mass-selected sample at $$\dot{M}_\star = \alpha_{\rm SF}\,\frac{(M_{\rm gas}-M_{\rm crit})}{t_{\rm dyn,disk}},$$0 confidence, with deviations restricted to lenses below $$\dot{M}_\star = \alpha_{\rm SF}\,\frac{(M_{\rm gas}-M_{\rm crit})}{t_{\rm dyn,disk}},$$1 at scales below $$\dot{M}_\star = \alpha_{\rm SF}\,\frac{(M_{\rm gas}-M_{\rm crit})}{t_{\rm dyn,disk}},$$2 Mpc. This suggests that, even where global tensions persist, the model can already reproduce non-trivial third-order statistics of halo occupation and matter distribution (Linke et al., 2020).

A recurring misconception is that L-Galaxies is a single immutable prescription. The literature instead presents it as a family of semi-analytic implementations sharing merger-tree logic and baryon bookkeeping while differing in star-formation law, metal return, environmental stripping, hot-gas structure, and output methodology. Another misconception is that its remaining discrepancies are purely calibration failures. The comparative studies suggest a more specific interpretation: several tensions arise from identifiable modeling choices, including preventative rather than ejective AGN feedback, incomplete treatment of baryonic self-gravity, simplified environmental processing of satellites and orphans, and size prescriptions that remain too diffuse for quenched systems at early times (Guo et al., 2015, Ayromlou et al., 2020, Vani et al., 2024).