ATON: Multi-Domain Research Systems

• ATON is a multi-purpose research platform spanning GPU-accelerated astrophysical simulations, stellar evolution computations, and web-based 3D cultural heritage publication.
• Its astrophysical branch employs moment-based radiative transfer with M1 closure to model cosmic reionization and related stellar processes with high efficiency.
• In cultural heritage, ATON offers an open-access framework for publishing and visualizing optimized 3D models, ensuring FAIR principles and interactive access.

ATON denotes several distinct research systems that share a name but belong to different technical traditions. In astrophysics, it refers both to a radiative-transfer code used to model cosmic reionization and to a stellar-evolution code used for pre-main-sequence, massive-star, AGB, and SAGB calculations. In cultural heritage, it denotes an open-access, self-hosted web framework for publishing optimized 3D models. In all three cases, ATON functions as a core computational or publication layer rather than as a purely descriptive dataset (Asthana et al., 2024, Landin et al., 2022, Barzaghi et al., 2024).

1. Nomenclature and domain structure

The name ATON is therefore polysemous. The cited literature uses it for three technically separate platforms.

ATON usage	Domain	Role in the cited literature
ATON / ATON-HE	Cosmological radiative transfer	Reionization simulations, Ly$\alpha$ forest calibration, UV-background modeling
ATON / aton	Stellar evolution	PMS, massive-star, AGB, SAGB, nucleosynthesis, dust, Rossby-number calculations
ATON	Cultural heritage informatics	Self-hosted web publication and visualization of optimized 3D models

The radiative-transfer branch is associated with the GPU-based, moment-based solver introduced by Aubert and Teyssier and subsequently extended to ATON-HE for helium-inclusive, multifrequency reionization studies. The stellar-evolution branch is associated with Ventura and collaborators and appears with different convection, rotation, and mass-loss choices depending on the target problem. The cultural-heritage branch, developed by CNR-ISPC in 2016, is a web-based dissemination framework used in FAIR-by-design 3D-data workflows (Aubert et al., 2010, Godart et al., 2016, Barzaghi et al., 2024).

2. Radiative-transfer ATON: formulation, numerics, and ATON-HE

In cosmology, ATON is a moment-based solver of the radiative transfer equation with M1 closure. In its GPU implementation, it evolves radiation energy density, flux, and pressure on a uniform Cartesian grid with explicit time integration and a Courant-limited timestep, using the true speed of light rather than a reduced-speed-of-light approximation. In the 2010 large-scale implementation, ATON post-processed RAMSES simulations, used a monochromatic ionizing group with characteristic photon energy $20.27$ eV for a $50{,}000$ K blackbody, and achieved an overall acceleration of about $80\times$ relative to CPU implementations (Aubert et al., 2010).

The core transport system is written in moment form. In the Local Group application, the equations were presented as

$$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$

$$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$

with an M1 Eddington closure

$$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$

where $\hat{\mathbf{n}}=F/|F|$ and $\chi$ is the standard M1 Eddington factor. The same formalism underlies later large-box reionization work, where ATON is characterized as a moment-based solver with M1 closure and, in some studies, a Global Lax–Friedrichs Riemann solver (Ocvirk et al., 2013, Gaikwad et al., 2023).

ATON-HE is the helium-inclusive extension of this framework. It retains the M1 moment method and GPU acceleration but augments the thermochemistry to evolve H I/H II, He I/He II, and He II/He III self-consistently, together with photoheating and cooling. In the late-end reionization suite, the gas density of the Sherwood–Relics simulation was projected onto a $2048^3$ grid in a $20.27$0 cMpc/$20.27$1 box, the comoving-frame RT equation was solved by operator splitting, transport used the Global Lax–Friedrichs flux function, and thermochemistry was integrated implicitly with subcycling. The multifrequency implementation placed bin boundaries at the ionization thresholds of H I, He I, and He II, namely $20.27$2, $20.27$3, and $20.27$4 eV; a full helium-inclusive run from $20.27$5 to $20.27$6 required about $20.27$7 GPU-hours on $20.27$8 NVIDIA A100 GPUs (Asthana et al., 2024).

This radiative-transfer family is used almost entirely in post-processing mode. The gas density field is supplied by hydrodynamical simulations such as RAMSES, CLUES, or Sherwood–Relics, while ATON evolves radiation, ionization fractions, and, depending on the study, gas temperature. A recurring methodological consequence is that ATON captures inhomogeneous radiation transport and self-shielding efficiently on large grids, but the degree of radiation-hydrodynamic back-reaction depends on the surrounding workflow and is often absent in the cited post-processing applications (Aubert et al., 2010, Ocvirk et al., 2014).

3. Reionization science with ATON and ATON-HE

ATON’s main cosmological use is the reconstruction of late hydrogen reionization and the UV background through Ly$20.27$9-forest observables. Calibrated ATON/RAMSES simulations that match the measured evolution of the mean photoionization rate and mean free path reach overlap at $50{,}000$0 and reproduce the accelerated evolution of Ly$50{,}000$1 opacity at $50{,}000$2. At the same time, those galaxy-dominated source models fail to reproduce the high-opacity tail of the $50{,}000$3 distribution at $50{,}000$4, implying spatial UV-background fluctuations on scales substantially larger than predicted when the emissivity is dominated by large numbers of sub-$50{,}000$5 galaxies (Chardin et al., 2015).

That conclusion motivated hybrid ATON-plus-rare-source models. In the $50{,}000$6–$50{,}000$7 analysis of large opacity fluctuations, ATON provided the galaxy-driven radiative-transfer solution and the density, temperature, and peculiar-velocity fields, while a separate halo-based QSO model was superposed. The combined modeling showed that a significant, $50{,}000$8, contribution of ionizing photons from QSOs can explain the large Ly$50{,}000$9 opacity fluctuations on $80\times$0 cMpc/$80\times$1 scales, although the models still struggled with the $80\times$2 cMpc/$80\times$3 trough toward ULAS J0148+0600 (Chardin et al., 2016).

ATON has also become a benchmark for semi-numerical or hybrid forward models. EX-CITE, an Octree-based ionizing-background code, was directly cross-checked against an ATON radiative-transfer simulation on the same Sherwood density field. The comparison showed very similar large-scale morphology in the ionizing-background and neutral-fraction fields and, more importantly, recovery of the true ATON values of $80\times$4 and $80\times$5 within $80\times$6. Applied to $80\times$7 high-$80\times$8 quasar sightlines in $80\times$9 bins spanning $$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$0, the forward model inferred $$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$1 decreasing by about $$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$2 and $$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$3 increasing by about $$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$4 from $$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$5 to $$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$6, consistent with reionization completing by $$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$7 (Gaikwad et al., 2023).

A distinct use of ATON appears in damping-wing analyses of quasars at $$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$8. In that application, ATON supplied a grid of reionization models and line-of-sight radiative-transfer realizations around quasar host haloes. The inferred ATON-based volume-averaged neutral fractions were

$$\frac{\partial E}{\partial t} + \nabla \cdot F = S_E - c\,\kappa_E\,E,$$9

$$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$0

$$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$1

with quasar lifetimes $$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$2 Myr across all bins. These results place ATON within the observational program of reconstructing the chronology of the final stages of reionization from stacked quasar spectra (Ďurovčíková et al., 2024).

ATON-HE extends this program to source-population and photon-budget studies calibrated to E-XQR-30 or XQR-30 data. In late-end reionization simulations targeted at JWST Ly$$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$3 emitters, a fiducial model with midpoint $$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$4, an Early model with midpoint $$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$5, and an Extremely Early model with midpoint $$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$6 were all made consistent with Ly$$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$7-forest mean transmission at $$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$8. A central result is that haloes massive enough to host observed Ly$$\frac{\partial F}{\partial t} + c^2 \nabla \cdot P = S_F - c\,\kappa_F\,F,$$9 emitters are highly biased: the fraction of haloes with $$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$0 embedded in bubbles of radius $$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$1 pMpc approaches unity well before the ionized volume filling factor does. In the fiducial history this occurs by $$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$2–$$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$3, while the presence of abundant Ly$$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$4 emission out to $$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$5 likely requires earlier histories (Asthana et al., 2024).

The photon-budget analysis based on ATON-HE and JWST $$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$6 measurements pushes the code into a different inference regime. With emissivities calibrated to XQR-30, the Fiducial, Early, and Extremely Early models yield escape fractions of $$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$7 at $$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$8 and $$P = \mathcal{D}E, \qquad \mathcal{D} = \frac{1-\chi}{2}\,\mathbf{I} + \frac{3\chi-1}{2}\,\hat{\mathbf{n}}\otimes\hat{\mathbf{n}},$$9 at $\hat{\mathbf{n}}=F/|F|$0, while the inferred effective clumping factors lie in the range $\hat{\mathbf{n}}=F/|F|$1–$\hat{\mathbf{n}}=F/|F|$2. An Oligarchic model in which faint galaxies emit no ionizing photons requires $\hat{\mathbf{n}}=F/|F|$3 at $\hat{\mathbf{n}}=F/|F|$4, and is therefore disfavored at very high redshift (Asthana et al., 2024).

The same helium-inclusive framework has been used to test faint-AGN scenarios motivated by JWST. A QSO-assisted model in which $\hat{\mathbf{n}}=F/|F|$5 of haloes host AGN with $\hat{\mathbf{n}}=F/|F|$6 Myr lifetimes and AGN contribute $\hat{\mathbf{n}}=F/|F|$7 of the hydrogen-ionizing emissivity of the stellar field requires an emissivity factor $\hat{\mathbf{n}}=F/|F|$8 lower than the galaxy-only models toward the end of reionization and reproduces the observed $\hat{\mathbf{n}}=F/|F|$9 distribution well. A QSO-only model, by contrast, is inconsistent with the observed Ly$\chi$0 optical-depth distribution and produces excessively high IGM temperatures at $\chi$1 unless the escape fraction of He II-ionizing photons is low (Asthana et al., 2024).

ATON has also been applied on Local Group scales. In CLUES-based simulations of the Milky Way–M31 system, ATON showed that reionization of the progenitors is patchy and locally inside-out; in all but the most extreme source model, the Milky Way and M31 reionize internally despite their proximity, with durations between $\chi$2 Myr and $\chi$3 Myr depending on emissivity and source suppression (Ocvirk et al., 2013). In the improved feedback-enabled version, the average reionization redshift of present-day satellites remained higher near galaxy centers, and in the lowest-emissivity scenario outer satellites were reionized about $\chi$4 Myr later than inner satellites. High-emissivity or externally driven reionization flattened that gradient (Ocvirk et al., 2014).

4. Stellar-evolution ATON: structure, rotation, and instability calculations

In stellar astrophysics, ATON is a one-dimensional stellar-evolution code used with different physical closures according to the scientific problem. In rotating pre-main-sequence work, ATON 2.3 coupled rotation to the structure equations through the Kippenhahn–Thomas method, included angular-momentum transport and magnetic-wind braking prescriptions, and computed both local and global convective turnover times. The local time was defined at one-half a mixing length above the base of the convective envelope,

$\chi$5

while the global time was

$\chi$6

Within that framework, increasing convection efficiency decreases $\chi$7, FST models yield still lower values than MLT, the presence of rotation shifts $\chi$8 toward slightly higher values, and non-gray boundary conditions yield values of $\chi$9 smaller than in the gray approximation (Landin et al., 2010).

The Rossby-number analysis of fully and partially convective stars used ATON over $2048^3$0–$2048^3$1 with MLT $2048^3$2, non-gray atmospheres, and differential rotation under local angular-momentum conservation. There the standard location for $2048^3$3, defined with respect to the base of the convective zone, becomes unusable in fully convective stars because $2048^3$4 and $2048^3$5 can exceed the stellar radius. The preferred alternative is an $2048^3$6-scaled interior location calibrated as a function of mass and age. When those ATON-derived $2048^3$7 values are combined with observed periods for $2048^3$8 stars, the resulting solar-anchored rotation–activity fit yields

$2048^3$9

The paper interprets this as evidence that a tachocline is not required to generate the observed rotation–activity relation (Landin et al., 2022).

ATON has also been used to generate massive-star grids for pulsational stability calculations. In the IACOB study, non-rotating tracks from $20.27$00 to $20.27$01 were computed with MLT, the Schwarzschild criterion, OPAL opacities, and no convective core overshooting, and were then interfaced to the adiabatic code LOSC and the non-adiabatic code MAD. The resulting instability maps extended to degrees $20.27$02–$20.27$03 and showed the widening of high-degree instability domains across the spectroscopic HR diagram. However, the comparison with single-snapshot line-broadening measurements of about $20.27$04 O and B-type stars indicated that heat-driven oscillations alone cannot explain the large macroturbulent broadening detected in O stars and B supergiants (Godart et al., 2016).

5. AGB, nucleosynthesis, abundances, and dust in ATON models

ATON is especially prominent in AGB and SAGB research because its convection and mass-loss prescriptions strongly affect hot bottom burning, neutron sources, and dust chemistry. In the Li and Ca abundance study of massive Galactic O-rich AGB stars, ATON models were used as a reference for solar-metallicity HBB. HBB occurs when the base of the convective envelope becomes hot enough to activate proton-capture reactions, with a commonly quoted threshold of $20.27$05 MK. Under these conditions the Cameron–Fowler chain

$20.27$06

raises the surface lithium abundance. The ATON peak values reported in that comparison rise from $20.27$07 dex at $20.27$08 to $20.27$09 dex at $20.27$10 and $20.27$11, with strong oscillations on $20.27$12 yr timescales. The observed Li-rich and super-Li-rich O-rich AGB stars agreed with ATON, Monash, and NuGrid/MESA, whereas FRUITY predicted no HBB lithium production at near-solar metallicity (Pérez-Mesa et al., 2019).

The first s-process post-processing calculations based on ATON structures were built with the snuppat framework for $20.27$13, $20.27$14, and $20.27$15 at $20.27$16. These models adopt FST convection, an envelope-overshoot treatment that forms $20.27$17C pockets, and a full $20.27$18-isotope network from neutrons to $20.27$19Po. Their effective $20.27$20C abundance is defined as

$20.27$21

and the network integration uses the Patankar–Euler–Deuflhard explicit update

$20.27$22

The combination of ATON’s relatively high intershell $20.27$23C and an advective overshoot prescription produces s-process abundance patterns that favor the second peak over the first peak across the explored masses, and can maintain significant s-processing even in $20.27$24 models. The authors explicitly note that this may be in contradiction with some observations of massive AGB stars (López et al., 2021).

ATON has also been coupled to a stationary wind/dust model for low-metallicity AGB and SAGB stars. In that framework ATON supplies the wind module with $20.27$25, $20.27$26, $20.27$27, $20.27$28, and the full surface composition at each timestep, while dust growth is computed under the assumptions of a spherically symmetric, time-independent wind. At $20.27$29, the predicted total dust mass ranges from $20.27$30 for the $20.27$31 model up to about $20.27$32 for the $20.27$33 model, while ONe-core SAGB stars release $20.27$34. The chemistry is sharply mass dependent: stars with $20.27$35 produce carbon-rich dust, whereas more massive stars undergoing HBB do not reach the carbon-star stage and instead produce silicates and iron (Ventura et al., 2011).

Taken together, these AGB applications show that ATON is not merely a structural code in this literature. It serves as the upstream provider of temperatures, convective boundaries, dredge-up histories, mass-loss rates, and surface abundances from which lithium synthesis, s-process patterns, isotope budgets, and dust yields are subsequently inferred (Pérez-Mesa et al., 2019, López et al., 2021, Ventura et al., 2011).

6. ATON as a cultural-heritage web framework

Outside astrophysics, ATON is an open-access, self-hosted web-based framework for hosting and visualizing 3D cultural-heritage assets. In the Aldrovandi Digital Twin, it is the publication endpoint for optimized Digital Cultural Heritage Objects. The workflow described in that project proceeds from acquisition of Cultural Heritage Objects by SfM photogrammetry or structured-light scanning, to processing into RAWp, authorial modeling into DCHO, optimization into DCHOo, export of DCHOo in glTF, metadata creation in RDF, provenance capture through OCDM, and finally upload to ATON, where each model receives a unique alphanumeric identifier and becomes publicly accessible through a web viewer (Barzaghi et al., 2024).

Within that FAIR-by-design pipeline, ATON’s contribution is specific and delimited. It supports findability through its internal identifiers, accessibility through web-based delivery of glTF models, and interoperability through reliance on open-source software, solid web standards, and an open, program-neutral format optimized for interactive Web3D applications. The broader FAIR stack remains external to ATON proper: IRIs are issued via w3id.org, metadata records are represented as RDF named graphs, CIDOC-CRM and CRMdig encode object and process semantics, CHAD-AP formalizes the application profile, provenance snapshots use OCDM, and long-term preservation is delegated to Zenodo rather than to ATON itself (Barzaghi et al., 2024).

The Aldrovandi study is explicit that ATON is a dissemination layer rather than a preservation repository. That distinction matters because 3D-cultural-heritage workflows maintain multiple versions of each object—RAWp, DCHO, and DCHOo—with very different storage profiles, and because FAIR reuse depends on metadata, provenance, licensing, and repository deposit in addition to interactive visualization. In that ecosystem, ATON occupies the web-publication layer rather than the archival one (Barzaghi et al., 2024).