GADGET4-Osaka: Advanced Galaxy Simulation Framework

• GADGET4-OSAKA is a simulation framework derived from GADGET-4, integrating PM gravity, SPH hydrodynamics, and advanced feedback modules for diverse galaxy formation applications.
• The code employs adaptive Tree–PM gravity, varied SPH formulations, and hierarchical time integration to accurately resolve processes from isolated galaxies to cosmological volumes.
• Its modular design supports detailed dust evolution, SKIRT-based radiative transfer, and kinetic AGN jet launching, enabling precise calibration against observed galaxy properties.

GADGET4-OSAKA is a modified version of the public GADGET-4 code developed by the Osaka group for galaxy-formation and gas-dynamical simulations spanning cosmological volumes, cosmological zoom-ins, isolated galaxies, explicit dust evolution, and AGN jet propagation. In the published implementations, it combines large-scale PM gravity with hierarchical short-range multipole methods, SPH hydrodynamics, GRACKLE cooling and chemistry, CELib-based stellar evolution and enrichment, and Osaka feedback modules; study-specific branches further add grain-size–resolved dust physics and reservoir-based jet launching (Oku et al., 2024, Tomaru et al., 30 Oct 2025, Giessen et al., 2024, Dong et al., 29 Aug 2025). Its recent uses include the CROCODILE cosmological suite, the CROCODILE-DWARF zoom-ins of field dwarfs, AGORA validation runs, and isolated-galaxy calculations of dust radial structure, PAH indicators, and attenuation curves (Granizo et al., 22 Dec 2025, Matsumoto et al., 2024, Matsumoto et al., 28 Aug 2025).

1. Code lineage and computational scope

Published descriptions present GADGET4-OSAKA as the “Osaka branch” of GADGET-4, retaining the parent code’s parallel architecture while augmenting it with improved subgrid physics and chemistry modules (Tomaru et al., 30 Oct 2025). In CROCODILE-DWARF it is described as a “highly parallel Tree–PM + SPH code” built on the public framework and coupled to \textsc{CELib} and \textsc{grackle} (Tomaru et al., 30 Oct 2025). In the AGORA validation study it appears as the implementation of the CROCODILE model inside the AGORA calibration workflow, where the resulting simulations were contributed to the AGORA CosmoRun suite (Granizo et al., 22 Dec 2025).

The scope of applications is unusually broad. Cosmological galaxy-formation runs in CROCODILE include supernova feedback with a metallicity- and redshift-dependent, top-heavy IMF and an AGN feedback model (Oku et al., 2024). Cosmological dwarf-galaxy zoom-ins target isolated halos of $\sim 10^{10}\,M_\odot$ at $z=0$ and analyze structural and kinematic diversity (Tomaru et al., 30 Oct 2025). Isolated-galaxy studies add explicit grain-size evolution and SKIRT post-processing to connect simulated ISM dust physics to PAH diagnostics, dust surface densities, and attenuation curves (Matsumoto et al., 2024, Giessen et al., 2024, Matsumoto et al., 28 Aug 2025). A separate configuration simulates purely kinetic bipolar AGN jets and benchmarks SPH-based jet propagation against self-similar analytic expectations (Dong et al., 29 Aug 2025).

This body of work suggests that GADGET4-OSAKA is best understood as a simulation framework rather than a single immutable parameter set. The common substrate is the GADGET-4-derived gravity and SPH infrastructure together with Osaka feedback, CELib enrichment, and GRACKLE thermochemistry, while neighbor numbers, star-formation thresholds, feedback tunings, and auxiliary physics are configured according to the scientific problem (Oku et al., 2024, Granizo et al., 22 Dec 2025).

2. Gravity, SPH, and time integration

The gravity solver is described in closely related but not identical ways across publications. CROCODILE-DWARF specifies a hybrid Tree–PM Poisson solver in which a long-range Particle–Mesh computation on a regular grid handles low-frequency modes and a hierarchical oct-tree handles short-range forces through a multipole expansion up to quadrupole order (Tomaru et al., 30 Oct 2025). The same study states that GADGET4-OSAKA employs an adaptive opening criterion tuned to ensure better force accuracy in the dense inner regions of dwarf halos, thereby reducing two-body noise without an appreciable increase in cost (Tomaru et al., 30 Oct 2025). In the AGORA comparison, the gravity module is summarized as “FMM–PM (4th order)” for GADGET4-OSAKA, in contrast to “TreePM (2nd order)” for its predecessor (Granizo et al., 22 Dec 2025). CROCODILE additionally reports 3D Peano–Hilbert domain decomposition and hybrid MPI + OpenMP parallelization (Oku et al., 2024).

The hydrodynamics layer is SPH-based throughout, but the exact formulation depends on the application. Published descriptions include the improved density-independent SPH formulation of GADGET-4 (Tomaru et al., 30 Oct 2025), pressure–entropy SPH (Matsumoto et al., 2024, Dong et al., 29 Aug 2025), pressure–energy SPH (Granizo et al., 22 Dec 2025), and density-entropy SPH with improved artificial-viscosity switches (Matsumoto et al., 28 Aug 2025). The Wendland C4 kernel is repeatedly used, with reported neighbor numbers of $\sim 50$, $100$, $120\pm2$, $128\pm4$, and $200$ in different setups (Matsumoto et al., 2024, Tomaru et al., 30 Oct 2025, Oku et al., 2024, Granizo et al., 22 Dec 2025, Dong et al., 29 Aug 2025). Artificial viscosity is likewise problem-dependent: the code is reported with a Cullen–Dehnen switch, Monaghan–Gingold–Lattanzio viscosity, a Balsara shear-limiter, and artificial conduction terms introduced to suppress pressure blips or smooth contact discontinuities (Tomaru et al., 30 Oct 2025, Matsumoto et al., 2024, Dong et al., 29 Aug 2025).

Representative SPH discretizations are given explicitly in the dwarf-galaxy study:

$\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$

and

$$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$

with corresponding energy equations including radiative cooling and UV-background heating terms (Tomaru et al., 30 Oct 2025).

Time integration is hierarchical and adaptive across the code family. CROCODILE-DWARF uses GADGET-4’s global kick–drift–kick leapfrog integrator with individual subcycling in powers of two, and chooses each particle timestep as the minimum of a CFL condition, an acceleration criterion, and a synchronization constraint from neighboring particles (Tomaru et al., 30 Oct 2025). CROCODILE emphasizes hierarchical individual time-steps with a second-order predictor-corrector and a signal-velocity time-step limiter, with mutual “wake-up” of neighboring particles when strong feedback is injected (Oku et al., 2024). Isolated dust simulations also use individual hierarchical timesteps with subcycling for rapid dust growth and destruction (Matsumoto et al., 2024).

3. Thermochemistry, star formation, and feedback

GRACKLE provides the thermochemical backbone in multiple GADGET4-OSAKA applications. Published configurations include non-equilibrium primordial chemistry for species such as H, H$^+$, He, He$z=0$0, He$z=0$1, $z=0$2, H$z=0$3, H$z=0$4, H$z=0$5, D, D$z=0$6, and HD, combined with metal-line cooling from precomputed \textsc{Cloudy} tables and UV-background photo-heating (Tomaru et al., 30 Oct 2025). CROCODILE uses non-equilibrium chemistry of 12 species, \textsc{Cloudy} metal cooling, and a Haardt & Madau UVB turning on at $z=0$7 (Oku et al., 2024), whereas CROCODILE-DWARF reports the Haardt & Madau (2012) UVB turned on at $z=0$8 together with self-shielding corrections (Tomaru et al., 30 Oct 2025).

Star formation follows a Schmidt-type or volumetric Kennicutt–Schmidt law, but the threshold depends on the application. In CROCODILE-DWARF, gas above $z=0$9 and below $\sim 50$0 is eligible, with

$\sim 50$1

and stochastic conversion of gas particles into collisionless star particles of the same mass (Tomaru et al., 30 Oct 2025). The isolated-galaxy dust study uses stochastic star formation once $\sim 50$2 with efficiency $\sim 50$3 (Giessen et al., 2024). The MW-like attenuation-curve study adopts $\sim 50$4, $\sim 50$5, and $\sim 50$6 (Matsumoto et al., 28 Aug 2025). CROCODILE uses $\sim 50$7 with thresholds $\sim 50$8 and $\sim 50$9 (Oku et al., 2024). AGORA validation reports $100$0 in the isolated run and $100$1 in the cosmological run, together with a Jeans pressure floor

$100$2

(Granizo et al., 22 Dec 2025).

The stellar feedback model is one of the code’s defining features. CELib supplies Type II SNe, Type Ia SNe, and AGB mass return, yields, and delay-time distributions (Tomaru et al., 30 Oct 2025, Giessen et al., 2024). CROCODILE-DWARF tracks 16 isotopic species and injects feedback through a thermal channel based on stochastic heating of $100$3 neighbors to a target entropy $100$4 and a momentum channel calibrated on high-resolution superbubble simulations (Tomaru et al., 30 Oct 2025). In that suite, the default CELib energy per solar mass formed is multiplied by 2, to $100$5, to mimic missing early stellar feedback and compensate for finite resolution (Tomaru et al., 30 Oct 2025).

The AGORA validation isolates two feedback ingredients as essential. Mechanical momentum injection distributes a terminal momentum per SN calibrated from high-resolution SN remnant simulations,

$100$6

while stochastic thermal heating raises selected neighbors to a target entropy

$100$7

with probability based on the available thermal budget and the required entropy jump (Granizo et al., 22 Dec 2025). In CROCODILE, the supernova model is further modified by a metallicity- and redshift-dependent, top-heavy IMF and a hot galactic-wind channel, while AGN feedback follows a stochastic heating model with $100$8 (Oku et al., 2024).

4. Dust, radiative transfer, and jet modules

A major extension of GADGET4-OSAKA is its explicit treatment of dust mass and grain-size distributions in isolated-galaxy studies. These implementations track grain radii between $100$9 and $120\pm2$0 in 30 logarithmic bins (Giessen et al., 2024, Matsumoto et al., 2024, Matsumoto et al., 28 Aug 2025). Dust is fully coupled to gas, with no separate drift term, and the evolution of each bin includes stellar dust production, accretion, shattering, coagulation, sputtering, and astration (Giessen et al., 2024). The radial-properties study uses a two-phase subgrid ISM model in which each gas particle is split into a dense cloud with $120\pm2$1 and $120\pm2$2 and a diffuse ambient phase, with dense-cloud mass fraction

$120\pm2$3

for tunable $120\pm2$4–$120\pm2$5 (Giessen et al., 2024). Dust diffusion can be included through a Smagorinsky-type turbulent mixing model (Giessen et al., 2024).

The dust module is routinely coupled to SKIRT for post-processing radiative transfer. In the PAH-indicator study, GADGET4-OSAKA provides per-particle grain-size distributions, which are mapped onto a SKIRT grid where carbonaceous grains smaller than $120\pm2$6 are treated as neutral or ionized PAHs and larger grains are split into silicate and graphite according to local Si and C abundances (Matsumoto et al., 2024). The attenuation-curve study uses the same pipeline to analyze the optical–UV slope, the $120\pm2$7 bump, scattering, and star–dust geometry (Matsumoto et al., 28 Aug 2025).

A second major extension is the AGN jet module. In the jet-evolution study, GADGET4-OSAKA launches purely kinetic bipolar jets with fixed power $120\pm2$8, launch velocity $120\pm2$9, and cone half-angle $128\pm4$0 (Dong et al., 29 Aug 2025). Injection uses a pre-allocated reservoir of particles activated in pairs. Three spatial schemes are tested: Reservoir–Grid, Reservoir–Random, and Spawning–Random (Dong et al., 29 Aug 2025).

Domain	Added module(s)	Representative use
Isolated galaxies	Grain-size–resolved dust evolution, two-phase ISM, SKIRT	Dust radial profiles, PAH indicators, attenuation curves
Cosmological galaxy formation	Osaka SN feedback, AGN feedback, CELib, GRACKLE	CROCODILE and CROCODILE-DWARF
AGN jet simulations	Reservoir-based kinetic jet launching	Self-similar jet-lobe evolution

These extensions are not ancillary. They alter the code’s phenomenology in ways that are explicitly measured: dust studies track small-to-large grain ratios and PAH fractions, while the jet study shows that lobe morphology and energetics are highly sensitive to artificial viscosity and launch geometry (Giessen et al., 2024, Matsumoto et al., 2024, Dong et al., 29 Aug 2025).

5. Resolution scales, diagnostics, and computational performance

The numerical resolution reported for GADGET4-OSAKA spans several orders of magnitude. CROCODILE-DWARF uses effective zoom-in resolution $128\pm4$1 in a $128\pm4$2 parent box, with $128\pm4$3, initial gas particle mass $128\pm4$4, and Plummer-equivalent softenings $128\pm4$5 and $128\pm4$6 (Tomaru et al., 30 Oct 2025). The CROCODILE fiducial cosmological run uses a $128\pm4$7 box with $128\pm4$8 particles, $128\pm4$9, $200$0, and $200$1 capped at $200$2 (Oku et al., 2024). The AGORA isolated disk uses $200$3 with minimum SPH smoothing $200$4, while the AGORA cosmological zoom switches from $200$5 comoving pc until $200$6 to $200$7 proper pc thereafter (Granizo et al., 22 Dec 2025). In isolated MW-like dust simulations, $200$8 and the minimum SPH smoothing is $200$9 (Matsumoto et al., 28 Aug 2025).

The code employs an extensive diagnostic apparatus. For dwarf-galaxy kinematics, CROCODILE-DWARF uses orbital circularity

$\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$0

and the global disk fraction

$\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$1

together with the gas kinematic ratio $\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$2 (Tomaru et al., 30 Oct 2025). The jet study uses slice maps of temperature, density, entropy, pressure, velocity, and Mach number, as well as phase diagrams in the $\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$3–$\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$4, $\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$5–$\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$6, and thermal-versus-ram-pressure planes (Dong et al., 29 Aug 2025). CROCODILE outputs on-the-fly FoF and Subfind catalogs and uniform mesh dumps of density, temperature, and metallicity for IGM analysis (Oku et al., 2024).

Parallel performance is inherited from GADGET-4’s hybrid MPI + OpenMP design. CROCODILE-DWARF reports runs with $\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$7 MPI ranks and 2–4 OpenMP threads per rank, and notes that GADGET-4, and hence GADGET4-OSAKA, is known to show near-ideal weak scaling to $\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$8 ranks on modern supercomputers (Tomaru et al., 30 Oct 2025). Typical computational cost per dwarf zoom-in is $\rho_i = \sum_j m_j\,W(|r_i-r_j|,h_i),$9–$$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$0 CPU h (Tomaru et al., 30 Oct 2025), while the CROCODILE fiducial cosmological run costs $$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$1 CPU-h on SQUID with AVX-512 SPH loops (Oku et al., 2024).

6. Validation, scientific outcomes, and limitations

The scientific return of GADGET4-OSAKA is documented through several validation programs. In CROCODILE-DWARF, the simulated galaxies reproduce the observed stellar-to-halo mass, mass–metallicity, and size–mass relations, yielding stellar masses of $$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$2–$$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$3 and metallicities consistent with Local Group dwarfs (Tomaru et al., 30 Oct 2025). The same suite finds that early-assembling, high-concentration halos form stars efficiently and become gas-poor by $$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$4, while late-assembling, low-concentration halos remain gas-rich because of delayed star formation and rejuvenated gas accretion; it also identifies a clear anti-correlation between rotational support and the cumulative merger mass fraction (Tomaru et al., 30 Oct 2025). In some cases, late-time mergers induce extended gas disks by delivering fresh gas and angular momentum (Tomaru et al., 30 Oct 2025).

The AGORA validation study shows that mechanical momentum injection is necessary to suppress unphysical gas fragmentation and regulate star formation, while stochastic thermal heating is essential for driving a hot, metal-enriched gaseous halo and establishing a multiphase CGM (Granizo et al., 22 Dec 2025). Quantitatively, the isolated disk at $$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$5 has $$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$6 and $$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$7 clumps in GADGET4-OSAKA, compared with $$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$8 and $$\frac{d\mathbf v_i}{dt} = -\sum_j m_j \left[ \frac{P_i}{\rho_i^2} + \frac{P_j}{\rho_j^2} + \Pi_{ij} \right] \nabla_i W_{ij},$$9–20 self-bound clumps in the predecessor code (Granizo et al., 22 Dec 2025). In the cosmological AGORA Cal-4 run, the GADGET4-OSAKA halo contains cold filaments at $^+$0, a warm–hot interface at $^+$1–$^+$2, and a hot volume-filling halo at $^+$3 extending to $^+$4 (Granizo et al., 22 Dec 2025).

At cosmological volume scale, CROCODILE reports that the stellar-mass function, star-formation main sequence, and mass–metallicity relation show promising agreement with observations, especially for the Fiducial run (Oku et al., 2024). The same work concludes that SN feedback is a key driver of IGM chemical enrichment, while AGN feedback produces metal-rich bipolar outflows extending over a few Mpc scales (Oku et al., 2024).

The dust and jet studies also expose current limitations. The radial dust-properties calculation reproduces the radial profile of dust mass surface density in NGC628 but overestimates the small-to-large grain ratio, with simulated SLRs exceeding observed values by $^+$5 (Giessen et al., 2024). The PAH-signature study finds that the NGC 628-like simulation underestimates the PAH mass fraction throughout the galaxy by a factor of $^+$6 on average, possibly because of efficient PAH loss by coagulation (Matsumoto et al., 2024). The attenuation-curve study shows that the slope–$^+$7 relation is driven by variations in star–dust geometry and the amount of scattered photons escaping the galaxy, with additional contributions from grain-size distribution and the fraction of obscured young stars (Matsumoto et al., 28 Aug 2025). The AGN jet benchmark demonstrates that global lobe length converges with resolution to within $^+$8 across a two-order-of-magnitude mass-resolution span, but also that lobe morphology and the partitioning of thermal and kinetic energy are highly sensitive to the artificial-viscosity prescription (Dong et al., 29 Aug 2025).

A recurring misconception would be to treat GADGET4-OSAKA as a single, fully fixed “model.” The published record points instead to a family of closely related implementations that share a GADGET-4-derived SPH and gravity infrastructure plus Osaka feedback, while differing in gravity order, SPH form, neighbor number, star-formation threshold, and optional dust or jet modules (Granizo et al., 22 Dec 2025, Tomaru et al., 30 Oct 2025). This suggests that comparisons across results should track the exact configuration, not only the code name.