L-Galaxies Semi-Analytic Model

• L-Galaxies is a semi-analytic model of galaxy formation that evolves galaxies on dark-matter merger trees using coupled prescriptions for gas accretion, cooling, and feedback.
• It implements detailed treatments of baryonic processes including star formation, AGN feedback, chemical enrichment, and environmental effects across multiple model flavours (H15, H20, A21).
• Its calibration through MCMC techniques against stellar mass and quenched fraction observables facilitates efficient forward modelling for survey interpretation.

L-Galaxies is the Munich semi-analytic model of galaxy formation, a family of SAM implementations that evolves galaxies on top of dark-matter-only merger trees by solving coupled prescriptions for gas accretion, radiative cooling, star formation, stellar and AGN feedback, chemical enrichment, satellite processing, and mergers. In its H15 incarnation, each subhalo carries seven baryonic reservoirs—$M_{\rm hot}$, $M_{\rm cold}$, $M_{\star,{\rm disc}}$, $M_{\star,{\rm bulge}}$, $M_{\star,{\rm halo}}$, $M_{\rm BH}$, and $M_{\rm ejected}$—while later versions introduce radially resolved discs, more detailed enrichment, local-environment stripping, hot-halo structure, dust physics, lightcone outputs, and star-cluster populations (Ayromlou et al., 2020, Yates et al., 2020, Barrera et al., 2022, Hoyer et al., 16 Apr 2025). Across these variants, L-Galaxies serves as a computationally efficient but physically based framework for predicting stellar masses, star-formation histories, gas fractions, morphologies, metallicities, X-ray observables, clustering, and lensing.

1. Genealogy, flavours, and dark-matter backbone

L-Galaxies is built on merger trees extracted from dark-matter simulations such as Millennium, Millennium-II, TNG-DMO, and MillenniumTNG. Friends-of-Friends haloes and identified subhaloes provide the hierarchical skeleton; galaxies are then “painted” onto these trees and advanced snapshot by snapshot, with sub-timestep integration for rapid baryonic processes (Guo et al., 2010, Barrera et al., 2022). In the 2010 model of Guo et al., updated prescriptions were introduced for the transition between rapid infall and cooling-flow accretion, for bulge and disc sizes, for supernova feedback, for the central-to-satellite transition, and for gas and star stripping after infall (Guo et al., 2010). Henriques et al. then reworked the model family so that the H15 version could match the evolution of the stellar mass function and the overall fraction of red galaxies more successfully than earlier variants (Luo et al., 2016).

The three latest flavours compared explicitly in the literature are H15, H20, and A21. They are calibrated with MCMC against the stellar mass function and quiescent fraction, but differ in star-formation, enrichment, and environmental prescriptions (Vani et al., 2024).

Flavour	Distinctive prescriptions	Calibration context
H15	Kennicutt–Schmidt–style law on total cold gas; modified gas reincorporation; ram-pressure stripping threshold in massive hosts	MCMC against stellar mass functions and red fractions
H20	Radial rings; $\mathrm{H}_2$-based star formation; full chemical enrichment tracking	Extension of H15 with resolved discs and delayed enrichment
A21	Local Background Environment stripping for all galaxies; stripping beyond $R_{200}$	Recalibrated at $z=0,1,2$

A recurrent misconception is to treat “L-Galaxies” as a single immutable prescription. The published record instead describes a modular lineage in which the same merger-tree backbone supports materially different physical closures for discs, hot haloes, environmental quenching, metallicity transport, and observational forward modelling (Vani et al., 2024, Barrera et al., 2022).

2. Core mass cycle and governing prescriptions

The canonical L-Galaxies workflow begins with halo growth and baryon infall, which replenish the hot reservoir toward the cosmic baryon fraction. Cooling is then computed with a classical cooling-radius construction. In the H15 description, the cooling radius $M_{\rm cold}$0 is defined by $M_{\rm cold}$1, and the cooling rate is written as

$M_{\rm cold}$2

with $M_{\rm cold}$3 and an isothermal hot-gas profile $M_{\rm cold}$4 in the baseline model (Ayromlou et al., 2020). Guo et al. also distinguish a “hot-halo” regime, where $M_{\rm cold}$5, from a “rapid-infall” regime, where $M_{\rm cold}$6, and note that unlike DLB07 the latter is treated as steady cooling rather than instantaneous collapse (Guo et al., 2010).

Quiescent star formation in H15 follows a Kennicutt–Schmidt–type integrated law,

$M_{\rm cold}$7

with typical fiducial $M_{\rm cold}$8 and $M_{\rm cold}$9 (Ayromlou et al., 2020). In H20 and A21, this is replaced by an annular, $M_{\star,{\rm disc}}$0-based law,

$M_{\star,{\rm disc}}$1

implemented over 12 radial rings (Ayromlou et al., 2020, Vani et al., 2024).

Supernova feedback reheats cold gas and can eject gas beyond the halo. In H15, the injected energy per newly formed stellar mass is

$M_{\star,{\rm disc}}$2

the reheated mass is

$M_{\star,{\rm disc}}$3

and any excess energy yields

$M_{\star,{\rm disc}}$4

Ejected gas later reincorporates on a characteristic timescale (Ayromlou et al., 2020). Guo et al. emphasize that the steep dwarf-galaxy scaling of both reheating and ejection, together with slower reincorporation, is central to delaying low-mass galaxy growth (Guo et al., 2010).

Black-hole growth and AGN feedback appear in quasar and radio modes. In H15, merger-driven quasar growth is parameterized by

$M_{\star,{\rm disc}}$5

while radio-mode accretion takes the form

$M_{\star,{\rm disc}}$6

with the injected energy offsetting cooling in massive systems (Ayromlou et al., 2020). Other L-Galaxies variants retain the same two-mode structure while modifying the detailed scaling with $M_{\star,{\rm disc}}$7 and $M_{\star,{\rm disc}}$8 (Luo et al., 2016, Barrera et al., 2022).

Galaxy mergers redistribute stars into bulges, can trigger starbursts, and drive black-hole growth. In Guo et al., major mergers are defined by baryonic mass ratio $M_{\star,{\rm disc}}$9, minor mergers otherwise, and the collisional starburst efficiency is $M_{\star,{\rm bulge}}$0 (Guo et al., 2010). This merger channel links structural transformation, black-hole fueling, and quenching within the SAM.

3. Satellites, environmental quenching, and the orphan problem

Environmental processing has been one of the most actively revised components of L-Galaxies. In H15, satellites undergo tidal stripping of dark matter and hot gas, and ram-pressure stripping of hot gas only when the host satisfies $M_{\star,{\rm bulge}}$1. The stripping radius is defined through

$M_{\star,{\rm bulge}}$2

and there is no cold-gas ram-pressure stripping in that version (Ayromlou et al., 2020). This design choice mattered strongly in later comparisons: when L-Galaxies was run on IllustrisTNG dark-matter-only trees, Ayromlou et al. found that satellites in groups remained abnormally gas-rich in H15, whereas IllustrisTNG stripped both hot and cold gas self-consistently, out to and beyond $M_{\star,{\rm bulge}}$3, extending to the splashback radius (Ayromlou et al., 2020).

A21 replaces the fixed-threshold treatment with a Local Background Environment method. For each galaxy, the local environment is measured in a shell with inner radius $M_{\star,{\rm bulge}}$4 and outer radius $M_{\star,{\rm bulge}}$5, using at least 30 dark-matter particles. The model then computes

$M_{\star,{\rm bulge}}$6

and compares it to the restoring force per unit area to solve for a ram-pressure stripping radius

$M_{\star,{\rm bulge}}$7

Stripping is applied to centrals, pre-infall flybys, first-order satellites, and orphans, thereby capturing pre-processing before formal infall as well as in-halo stripping (Ayromlou et al., 2020). After recalibration, the global stellar mass function, quenched fractions, and HI mass function remain largely unchanged, but quenched fractions and star-formation rates as functions of environment and halocentric distance improve relative to SDSS and HSC (Ayromlou et al., 2020).

The “orphan” treatment remains a separate, well-defined tension. In the standard L-Galaxies recipe, orphan galaxies are satellites whose subhaloes have fallen below the resolution limit; they lose their remaining hot gas instantaneously, cannot cool new gas, and then form stars only from residual cold gas until merging on a dynamical-friction timescale,

$M_{\star,{\rm bulge}}$8

Harrold et al. show that, at $M_{\star,{\rm bulge}}$9, the over-abundance of low-mass passive galaxies can be attributed solely to these orphans (Harrold et al., 2024). Their ad hoc correction assigns each orphan the median SFR of resolved satellites in the same redshift and supercolour bin,

$M_{\star,{\rm halo}}$0

which largely removes the low-mass passive excess without retuning the galaxy-formation parameters (Harrold et al., 2024). A plausible implication is that orphan handling is not a technical footnote but a first-order determinant of quenched fractions in the low-mass, high-redshift regime.

4. Radial structure, morphology, chemistry, hot gas, dust, and star clusters

Later L-Galaxies variants move beyond one-zone discs. L-Galaxies 2020 represents cold gas and stars in 12 concentric annuli of fixed physical radii $M_{\star,{\rm halo}}$1, uses radial gas inflow $M_{\star,{\rm halo}}$2, and computes molecular fractions with the Krumholz prescription before forming stars locally (Yates et al., 2020). This ring-based formulation underlies subsequent work on resolved metallicity profiles, morphology, and star-cluster populations.

Morphological modelling was revised by Irodotou et al. through a two-component disc-instability criterion that includes both stellar and gaseous discs: $M_{\star,{\rm halo}}$3 They also impose $M_{\star,{\rm halo}}$4, so newly cooled gas loses 20 per cent of its initial specific angular momentum, and include radiative dissipation in gas-rich mergers through $M_{\star,{\rm halo}}$5 (Irodotou et al., 2018). These changes improve morphology fractions, the stellar mass–specific angular momentum relation, and the mass–size relation of bulge-dominated systems (Irodotou et al., 2018).

Chemical enrichment also became more explicit. In the modified L-Galaxies 2020 metallicity model, the fractions of ejecta deposited directly into the hot CGM are set to $M_{\star,{\rm halo}}$6, $M_{\star,{\rm halo}}$7, and $M_{\star,{\rm halo}}$8, rather than the default $M_{\star,{\rm halo}}$9. Yates et al. show that this higher direct CGM enrichment can simultaneously reproduce gas-phase and stellar metallicity profiles, local and high-redshift mass–metallicity relations, COS-Halos CGM abundances, and several IGrM/ICM abundance trends, while keeping the CGM itself spatially unresolved and uniformly enriched within the hot phase (Yates et al., 2020).

Hot-gas structure was reworked by replacing the singular isothermal sphere with the one-dimensional model of Sharma et al. The hot halo is divided into a cool core with $M_{\rm BH}$0 and a stable outer halo with $M_{\rm BH}$1. Cooling is then tied directly to the precipitation core, with $M_{\rm BH}$2 and

$M_{\rm BH}$3

in the slow-mode regime (Zhong et al., 2022). This extension reproduces observed ICM density and temperature profiles and the $M_{\rm BH}$4–$M_{\rm BH}$5 scaling, and it supports mock X-ray observations generated with SOXS, including ROSAT and HUBS configurations (Zhong et al., 2022, Zhong et al., 2023).

Dust and star clusters were later embedded in the same SAM backbone. The dust model includes stellar injection by Type II and Type Ia supernovae and AGB stars, grain growth in molecular clouds and the inter-cloud medium, and destruction by supernova shocks, star formation, and reheating; above $M_{\rm BH}$6 Type II supernovae dominate dust production, whereas below $M_{\rm BH}$7 grain growth becomes dominant and below $M_{\rm BH}$8 the total dust content is dominated by that channel (Vijayan et al., 2019). The 2025 star-cluster extension follows bound cluster formation above $M_{\rm BH}$9, samples an environmentally dependent cluster initial mass function, tracks up to 2000 individual clusters per galaxy, and evolves them under stellar evolution, two-body relaxation, tidal shocks, dynamical friction, and merger-driven repositioning (Hoyer et al., 16 Apr 2025). This suggests that L-Galaxies has become a general baryonic post-processing platform rather than only a stellar-mass-function model.

5. Calibration strategies, numerical realization, and forward modelling

Parameter inference in L-Galaxies is usually MCMC-based. In H15, principal tunable parameters include $M_{\rm ejected}$0, $M_{\rm ejected}$1, $M_{\rm ejected}$2, $M_{\rm ejected}$3, $M_{\rm ejected}$4, $M_{\rm ejected}$5, $M_{\rm ejected}$6, $M_{\rm ejected}$7, $M_{\rm ejected}$8, and environmental stripping parameters, calibrated to match stellar mass functions at $M_{\rm ejected}$9–3 and the red fraction versus mass (Ayromlou et al., 2020). A21 re-calibrates a model with roughly 15 free parameters against stellar mass functions and quenched fractions at $\mathrm{H}_2$0, using a Metropolis-Hastings chain and weighted $\mathrm{H}_2$1-style likelihoods (Ayromlou et al., 2020).

Different observational targets can drive markedly different posterior regions. Martindale et al. added the $\mathrm{H}_2$2 HI mass function to the MCMC constraints and found that a good simultaneous fit to the HI mass function, stellar mass function, and galaxy colours requires a greatly reduced gas surface-density threshold for star formation, with a corresponding reduction in star-formation efficiency (Martindale et al., 2016). They also show that a no-threshold variant can fit the same bulk constraints, but at the cost of weakening the Kennicutt–Schmidt break and raising the low-redshift star-formation-rate density (Martindale et al., 2016). This is an example of a recurring L-Galaxies theme: calibration success against one summary statistic may expose structural deficiencies in another.

The numerical realization has also been modernized. In the MillenniumTNG implementation, L-GALAXIES runs as a post-processing module inside GADGET-4, reads SUBFIND-HBT catalogues from roughly 300 snapshots, distributes tree “forests” over MPI ranks, stores galaxy states in HDF5, and records past-lightcone crossings on the fly during sub-step evolution (Barrera et al., 2022). The continuous-lightcone machinery can generate a full-sky cone to $\mathrm{H}_2$3, a one-octant cone to $\mathrm{H}_2$4, and a $\mathrm{H}_2$5 pencil beam to $\mathrm{H}_2$6, while convergence tests show that the level-2 MillenniumTNG run is converged down to $\mathrm{H}_2$7 for the stellar mass function at $\mathrm{H}_2$8–3 (Barrera et al., 2022). This forward-modelling emphasis is central to the model’s role in survey interpretation.

6. Empirical performance, known tensions, and active revision fronts

L-Galaxies has a long record of empirical success. Guo et al. report an excellent fit to the observed abundance of low-redshift galaxies over 5 orders of magnitude in stellar mass and 9 magnitudes in luminosity, a match to the observed abundance of Milky Way satellites, and good agreement with large-scale clustering as a function of stellar mass and colour; cluster galaxy distributions agree only if orphan galaxies are included (Guo et al., 2010). In a comparison with EAGLE and GALFORM, the galaxy stellar mass functions for $\mathrm{H}_2$9 and the median sSFRs agree to better than $R_{200}$0 dex at $R_{200}$1, although median galaxy sizes can differ by an order of magnitude and the stellar mass–size relation is substantially tighter in EAGLE, pointing to shortcomings in how SA models treat baryonic self-gravity and gas flows (Guo et al., 2015).

The model’s shortcomings are equally well documented. In H15, stronger AGN feedback improves the red fraction of central galaxies and the evolution of the stellar mass function, but central stellar masses in massive haloes become slightly too low, massive satellites remain slightly too blue, and both H15 and G13 produce too many red spirals and too few bulge-dominated galaxies (Luo et al., 2016). The comparison to IllustrisTNG sharpens the environmental and feedback issues: stellar mass functions and individual stellar masses agree to better than $R_{200}$2 dex, yet the transition from low-mass star-forming to high-mass quenched central galaxies occurs at a stellar mass scale $R_{200}$3 dex lower in IllustrisTNG than in L-Galaxies, and TNG predicts lower group-scale halo baryon fractions because its SMBH feedback ejects baryons rather than only preventing cooling (Ayromlou et al., 2020).

At the highest currently tested redshifts, the three latest L-Galaxies flavours remain in qualitatively good agreement with observed global scaling relations out to $R_{200}$4, but they fail more seriously for quenched galaxies. Massive quenched centrals are underproduced by a factor of 5 at $R_{200}$5 and by a factor of 60 by $R_{200}$6, while predicted quenched-galaxy sizes are several times larger than observed and their stellar surface densities are too low (Vani et al., 2024). Ayromlou et al. and later high-redshift comparisons therefore recommend improvements in AGN-driven ejection, environmental stripping outside $R_{200}$7, cold-gas ram-pressure stripping, and merger-driven structural growth (Ayromlou et al., 2020, Vani et al., 2024).

A common misconception is that the main uncertainty in L-Galaxies lies only in parameter values. The literature instead identifies several prescription-level tensions: the preventive character of radio-mode AGN feedback in H15, the treatment of local environmental effects, the handling of orphans once subhaloes disappear, the absence of cold-gas stripping in some flavours, and the simplified coupling between baryons and the dark-matter potential (Guo et al., 2015, Ayromlou et al., 2020, Harrold et al., 2024). The present direction of development is therefore not mere retuning, but replacement of specific physical closures while preserving the speed, flexibility, and large-volume applicability that distinguish semi-analytic models.