Galacticus: Modular Galaxy Formation Model

• Galacticus is a free, open-source semi-analytic model of galaxy formation that uses a modular, component-based architecture to simulate key physical processes.
• It integrates galaxy evolution via dark matter merger trees and adaptive ODE solvers, enabling rapid exploration of various astrophysical prescriptions.
• The framework supports efficient calibration, constrained merger trees, and versatile applications ranging from low-redshift surveys to dark matter subhalo analyses.

Galacticus is a free and open source semi-analytic model of galaxy formation designed to be highly modular, so as to facilitate expansion and the exploration of alternative descriptions of key physical ingredients. In its foundational formulation, it evolves galaxies through a merging hierarchy of dark matter halos, provides specific implementations of cooling, star formation, feedback, chemical enrichment, and related processes, and was explicitly presented both as a model and as a framework for rapid exploration of galaxy-formation physics (Benson, 2010).

1. Architecture and software organization

Galacticus is organized around a highly modular, component-based architecture in which every piece of physics—from halo mass functions to stellar population synthesis—lives in an interchangeable module. Each halo node may contain any subset of components such as DarkMatterHalo, HotHaloGas, ExponentialDisk, HernquistSpheroid, and BlackHole, and for each component there can be multiple implementations selected by input parameters. Components exchange mass, metals, energy, and angular momentum through named pipes such as CoolingGas, GasOutflow, and EnergyInput, while each component exposes routines to initialize properties, compute time derivatives, and respond to tree events including halo mergers, satellite mergers, and promotions (Benson, 2010).

The numerical core is centralized. At each step the code gathers the active components in a node, assembles their coupled ordinary differential equations, and hands them to GSL’s Runge–Kutta–Fehlberg (4,5) integrator. Components can trigger interrupts, for example when cooling begins or when a merger event must be processed, after which integration resumes. This architecture makes the code event-driven at the level of merger-tree evolution while keeping baryonic evolution in a unified ODE framework (Benson, 2010).

Later descriptions emphasize the software layering as well as the physics modularity. Galacticus is described as written in C++ with a layer of Python and XML wrappers for steering and I/O, with a plugin system in which each physics process implements a fixed interface and may be swapped out at run time via an XML parameter file. Outputs are written in HDF5, and the code supports on-the-fly merger-tree construction as well as reading pre-computed trees (Nadler et al., 2022). A recurrent misconception is therefore that Galacticus denotes a single fixed galaxy-formation prescription; the cited literature instead consistently presents it as a configurable framework with interchangeable modules.

2. Merger trees, time resolution, and constrained assembly histories

Galacticus can either read precomputed trees from HDF5 or generate them on the fly using extended Press–Schechter Monte Carlo algorithms. In the foundational implementation, the merger-tree builder uses modified Press–Schechter parameters calibrated to N-body results, and tree evolution proceeds by walking to the earliest unresolved progenitor, evolving it forward until it reaches its parent’s time, then handling satellite infall and later mergers. Different branches may be at different cosmic times, and interactions occur when a satellite merges into its host (Benson, 2010).

A distinct numerical issue is temporal resolution. In a dedicated convergence study, Galacticus merger trees were built free of any fixed time grid and then re-gridded onto discrete snapshots with the mergerTreeRegridTimes utility. When snapshots span $z=20$ to $z=0$, at least 128 snapshots are required to achieve convergence to within 5% for galaxy masses. The convergence rate depends only weakly on whether snapshots are spaced uniformly in expansion factor, uniformly in $\ln a$, or uniformly in $\ln \delta_c$, although spacing uniform in $\ln a$ or $\ln \delta_c$ is marginally better at high redshift (Benson et al., 2011). This result is methodologically important because Galacticus solves baryonic ODEs with an adaptive timestepper rather than tying timesteps to halo snapshots; the snapshot grid primarily constrains the merger-tree representation, not the internal ODE step size.

Galacticus has also been extended to generate merger trees that satisfy user-specified constraints. In the constrained framework, the standard EPS builder is augmented with Brownian bridges so that branches are guaranteed to achieve a desired halo mass at a chosen redshift, or to satisfy positive or negative assertions such as the presence or absence of a major merger in a given interval. This constrained merger-tree implementation is implemented in Galacticus and reported to be thousands of times more efficient than existing methods when targeting rare systems such as luminous high-redshift JWST candidates (Nadler et al., 2022).

3. Physical prescriptions and configurable subgrid models

The “Standard” implementations documented for Galacticus include gas cooling, star formation, supernova and AGN feedback, and chemical enrichment. The cooling rate follows the White & Frenk formalism, with a cooling radius defined by equating the cooling time to an available time and a rate

$$\dot M_{\rm cool} = 4\pi r_{\rm cool}^2 \rho_{\rm hot}(r_{\rm cool}) \dot r_{\rm cool}.$$

Disk and spheroid star formation follow Schmidt-like laws, with

$\dot M_* = M_{\rm gas}/\tau_*,$

where the timescale depends on dynamical time and circular velocity. Supernova-driven winds are parameterized by a power-law dependence on velocity, while AGN feedback includes both radio-mode heating and a quasar-mode mechanical wind. Chemical enrichment can be treated with an instantaneous recycling approximation or with non-instantaneous modules that convolve the full star-formation history with tabulated return rates and yields (Benson, 2010).

The list of shipped or described modules is broader than the foundational “Standard” set. Later summaries enumerate dark matter halo growth, gas cooling, star formation, supernova and AGN feedback, chemical enrichment, disk instabilities, galaxy mergers, black-hole growth, radiative transfer, spectral synthesis, and I/O. This suggests that Galacticus has been used as a modular host for both conventional semi-analytic prescriptions and more specialized astrophysical treatments (Nadler et al., 2022).

Specific applications illustrate how these modules are tuned or replaced. In Milky Way satellite modeling, Galacticus is configured with a cooling-velocity threshold $v_{\rm cooling}\approx18.5\,\mathrm{km/s}$, reionization suppression with $z_{\rm reion}=9$ and $z=0$0, pressure-regulated disk star formation following Blitz & Rosolowsky, and ram-pressure and tidal stripping prescriptions with $z=0$1 (Weerasooriya et al., 2022). In emission-line applications, star-formation histories, gas metallicities, H II region densities, and ionizing photon rates from Galacticus are passed to CLOUDY-based look-up tables to compute $z=0$2, $z=0$3, and related line luminosities (Zhai et al., 2021). These examples do not define a unique default model; they document the range of physically distinct prescriptions that have been embedded within the same software structure.

4. Calibration, convergence studies, and computational acceleration

The example model in the original Galacticus paper used roughly 100 parameters and was calibrated against several low-redshift observables, including luminosity functions, the black-hole–bulge-mass relation, the HI mass function, the color–magnitude diagram, the Tully–Fisher relation, cosmic star-formation history, and disk scale-length distributions. The same paper also emphasized numerical convergence tests, including sensitivity to ODE tolerance, time-step parameters, and merger-tree mass resolution (Benson, 2010).

Subsequent work has pursued more formal and more computationally efficient calibration strategies. An accelerated calibration framework replaces a full stellar mass function likelihood with a fast likelihood based on the stellar-to-halo mass relation evaluated at three target halo masses with $z=0$4 halos each, so that only 27 trees are evolved per likelihood evaluation. In that implementation, each likelihood costs $z=0$5 CPU-hours, approximately $z=0$6 faster than simulating a full population, and Differential Evolution MCMC is then used to sample Galacticus parameters. The resulting low-redshift stellar mass function matches data well, but joint fits to low- and high-redshift SHMR and the low-redshift stellar mass–size relation indicate that the explored seven-parameter model lacks sufficient flexibility to reconcile all datasets simultaneously (Robertson et al., 29 Aug 2025).

Two distinct surrogate strategies have also been built around Galacticus outputs. In strong-lensing applications, a normalizing flow was trained on 300 Galacticus realizations, learning a 6D joint distribution of subhalo properties and reproducing the Galacticus distribution with KS statistics $z=0$7. Once trained, the emulator generates a full subhalo population in $z=0$8, compared with $z=0$9 for a direct Galacticus SAM realization in that setup (Lonergan et al., 21 Apr 2025). At the galaxy-catalog level, a conditional graph neural network surrogate trained on merger trees from Uchuu and Galacticus predicts stellar mass, luminosity, angular momentum, gas metal mass, and specific star formation rate across $\ln a$0; for stellar mass at $\ln a$1, the reported scatter is $\ln a$2–$\ln a$3 dex with $\ln a$4–$\ln a$5, and processing the whole UchuuMicro using Galacticus on a single CPU takes $\ln a$6 hours while the GNN surrogate needs $\ln a$7 minute (Li et al., 25 Apr 2026).

5. Applications to observed galaxy populations

Galacticus has been used extensively to model dwarf galaxies, emission-line galaxies, massive red-selected systems, high-redshift galaxies, and galaxies embedded in cluster environments. In a Milky Way satellite application, the code was constrained to reproduce the observed cumulative luminosity function and luminosity–metallicity relation down to the ultra-faint regime, and the resulting modeled dwarfs also matched half-light radii, velocity dispersions, and mass-to-light ratios at $\ln a$8 down to $\ln a$9; their star-formation histories were reported to be consistent with those of Local Group dwarfs (Weerasooriya et al., 2022). A related Centaurus A study modeled dwarfs within a 700 kpc region around the host, approximately its splashback radius, using prescriptions and parameters previously tuned to match Milky Way satellites; it approximately replicated cumulative luminosity functions and luminosity–metallicity and luminosity half-light-radii relations, and provided predictions for velocity dispersions and star-formation histories (Weerasooriya et al., 2023).

For survey forecasting, Galacticus has been combined with CLOUDY-based line-emission modeling and dust attenuation prescriptions to predict H$\ln \delta_c$0 and [OIII] samples for Euclid-, WFIRST-, and Roman-like surveys. One early H$\ln \delta_c$1 study reported Euclid-like counts of 3900–4800 galaxies per square degree for a blended flux limit of $\ln \delta_c$2, and 10400–15200 galaxies per square degree for a WFIRST-like survey with a blended flux limit of $\ln \delta_c$3 (Merson et al., 2017). A later Roman mock-catalog study found that at $\ln \delta_c$4, a Euclid-like survey to $\ln \delta_c$5 is 97% complete, while a Roman HLWASS to $\ln \delta_c$6 is 94.6% complete and becomes 98% complete at $\ln \delta_c$7 (Zhai et al., 2021). Clustering analyses based on Galacticus mocks measured linear bias $\ln \delta_c$8 for H$\ln \delta_c$9 over $\ln a$0 and $\ln a$1 for [OIII] over $\ln a$2, while also noting that a double-peaked central-galaxy HOD emerges and that its origin remains under investigation (Zhai et al., 2021). The longer arc of these ELG studies also identifies a recurrent limitation: dust calibrations that match low-redshift counts do not automatically guarantee agreement at higher redshift (Zhai et al., 2019).

In massive-galaxy work, Galacticus was used within the MultiDark-Galaxies suite to build CMASS-like mocks at $\ln a$3. The resulting catalogs showed good agreement with observations regarding the galaxy-halo connection, but the original CMASS-like mock over-estimated the projected two-point clustering amplitude because of a smaller number density, a lack of blue objects, and an intrinsic scatter in stellar mass at fixed halo mass of $\ln a$4 dex; an alternative down-sampled mock matched the clustering within $\ln a$5 (Stoppacher et al., 2019).

At much higher redshift, Galacticus has been used to compare stellar-mass growth in the $\ln a$6 epoch with JWST inferences. In that study, the shape of the integrated stellar mass as a function of redshift agreed without parameter adjustment, while agreement in amplitude required lowering feedback by a factor of 3 relative to later-universe calibrations. The model then reproduced a burst fraction of $\ln a$7 at $\ln a$8, close to the $\ln a$9 reported from the data, while also identifying short $\ln \delta_c$0–$\ln \delta_c$1 Myr starbursts and substantial stellar and/or gas-rich mergers in some systems (Dressler et al., 2 Feb 2026).

Galacticus has also been coupled to external hydrodynamics. In an intracluster-medium study, the code was interfaced with FLASH4 so that winds and ram-pressure stripping predicted for individual galaxies could be injected as source terms into an Eulerian hydro simulation; of the wind models tested, the native Galacticus outflow-reservoir prescription reproduced mean ICM metallicities of $\ln \delta_c$2–$\ln \delta_c$3 within the inner 1 Mpc at $\ln \delta_c$4 (Höller et al., 2014).

6. Dark-matter and subhalo applications

Although Galacticus is principally a semi-analytic model of galaxy formation, several studies use it as a subhalo-evolution framework for dark-matter phenomenology. In a strong-lensing context, Galacticus evolves infalling progenitors with orbital decay, tidal stripping and heating, density-profile evolution, and dynamical friction, and a normalizing-flow emulator trained on those populations produces lensing signatures comparable to both direct Galacticus runs and an empirical subhalo model under the fiducial dark matter model (Lonergan et al., 21 Apr 2025).

Warm-dark-matter applications modify the linear power spectrum, the smoothing filter used in $\ln \delta_c$5, and the concentration–mass relation. In one comparative study against the COZMIC suite, Galacticus replaced the CDM power spectrum with a WDM transfer function, used a sharp-$\ln \delta_c$6 filter, and assigned WDM concentrations through the Schneider collapse-matching prescription. Both Galacticus and the N-body suite predicted suppression of low-mass subhalos with decreasing thermal relic mass and lower $\ln \delta_c$7 with larger $\ln \delta_c$8 than in CDM at fixed mass; Galacticus provided more statistically precise results because of a larger sample size (Lonergan et al., 31 Oct 2025).

A further extension added prompt $\ln \delta_c$9 cusps expected at the free-streaming scale of warm dark matter. In that implementation, Galacticus drew cusp amplitudes when halos first crossed $$\dot M_{\rm cool} = 4\pi r_{\rm cool}^2 \rho_{\rm hot}(r_{\rm cool}) \dot r_{\rm cool}.$$0, evolved cusp-plus-NFW profiles under tidal losses, and translated the resulting profiles into stellar velocity dispersions for ultra-faint satellites. Comparison to Tucana V, Triangulum II, and Segue 1 then yielded lower bounds on a thermal-relic WDM mass of $$\dot M_{\rm cool} = 4\pi r_{\rm cool}^2 \rho_{\rm hot}(r_{\rm cool}) \dot r_{\rm cool}.$$1 keV at 95 percent confidence and $$\dot M_{\rm cool} = 4\pi r_{\rm cool}^2 \rho_{\rm hot}(r_{\rm cool}) \dot r_{\rm cool}.$$2 keV at 90 percent confidence (Delos et al., 3 Dec 2025).

Taken together, these uses reinforce a central feature already visible in the earliest descriptions: Galacticus is not restricted to a single observational domain or to a single parameterization of baryonic physics. The literature instead presents it as a modular semi-analytic framework whose merger-tree machinery, ODE-based component evolution, and replaceable submodules have been adapted to problems ranging from dwarf-galaxy star-formation histories to strong-lensing substructure and warm-dark-matter constraints (Benson, 2010).