RIGEL Model: High-Res Galaxy Simulation

• The RIGEL model is a high-resolution astrophysical simulation framework that explicitly captures stellar feedback and radiative processes in galaxy evolution.
• It employs state-of-the-art techniques such as on-the-fly radiative transfer with multiple spectral bins and moving-mesh hydrodynamics to resolve star-by-star feedback.
• Its simulations reveal key astrophysical insights, including rapid gas dispersal, strong SFR–metallicity correlations, and distinct supernova feedback channels.

The RIGEL model is a suite of physically motivated, high-resolution computational frameworks developed for simulating and analyzing complex astrophysical systems. Deployed in studies spanning massive social graphs, blue supergiant stellar structure, and the multiphase interstellar medium (ISM) of dwarf galaxies, the RIGEL models share a common emphasis on capturing the multiscale feedback and structural complexity of their respective domains. The following sections focus on the RIGEL model for galaxy simulations, including its numerical innovations, feedback mechanisms, and key astrophysical implications, supplemented by context from other domains in which the RIGEL name has been employed.

1. Framework and Methodological Basis

The RIGEL model as introduced in recent galaxy simulation work (Deng et al., 14 May 2024, Zhang et al., 2 Oct 2025, Deng et al., 8 Oct 2025) is a state-of-the-art radiation hydrodynamics (RHD) framework embedded within the AREPO-RT code. It achieves solar-mass resolution ($\sim 1\,M_\odot$ per gas element), enabling self-consistent and explicit tracking of individual massive stars and their multifaceted feedback into the ISM. The method represents stellar populations via stochastically sampled star particles according to the initial mass function (IMF), tracking each star's radiative, mechanical, and chemical outputs as a function of age, mass, and metallicity, with physical prescriptions drawn from comprehensive stellar evolution libraries.

A core computational feature is on-the-fly radiative transfer, utilizing a moment-based M1-closure scheme with up to seven spectral bins (infrared through HeII-ionizing). Hydrodynamics employ the moving-mesh paradigm, maintaining quasi-Lagrangian control over mass resolution and thus resolving cold, dense gas structures relevant for star formation.

2. Explicit Feedback Physics: Star-by-Star and Channel Differentiation

The RIGEL framework is distinguished by its star-by-star feedback implementation, which explicitly models the following processes for each resolved massive star:

• Photoionization: Generation of H II regions and alteration of local ionization balance.
• Photoheating: Thermal input to the ISM, raising local temperatures and modifying pressure support.
• Radiation Pressure: Inclusion (where evaluated) of momentum injection from absorbed and scattered photons.
• Stellar Winds and Supernovae: Direct injection of mechanical energy and mass, with SN explosions tracked at fixed resolution.

This fidelity is critical in distinguishing feedback events by environment. High numerical resolution allows the RIGEL model to resolve:

• Diffusive Channel: Supernovae in low-density environments expand to large cooling radii and efficiently drive galactic outflows (hot phase, $\sim$kpc scales).
• Local Suppression Channel: Supernovae within dense clouds disrupt star-forming regions locally (pc scales), quenching further star formation in situ.

Analytic expressions used include, for example, the SN cooling radius:

$$r_{\rm cool} = 22.6\,{\rm pc}\,\left(\frac{E_{\rm SN}}{10^{51}\,\text{erg}}\right)^{0.29} \left(\frac{\rho_{\rm local}}{1\,{\rm cm}^{-3}}\right)^{-0.42}$$

where $E_{\rm SN}$ is the explosion energy and $\rho_{\rm local}$ the ambient density. Accurate evaluation of $r_{\rm cool}$ is only possible with cells of $\lesssim10^2$--$10^3\,M_\odot$.

3. Simulation Design and Thermochemistry

Simulations utilizing the RIGEL model are typically performed on isolated or merging dwarf galaxies, with imposed resolution of 1--2 solar masses per grid element (Deng et al., 14 May 2024, Deng et al., 8 Oct 2025). Thermochemistry combines non-equilibrium solvers for H, He, and associated ions with equilibrium treatment for cooling molecules and metals (C, O, CO, etc.), spanning the full thermal range ($<100$ K to $>10^4$ K) of the ISM.

The RIGEL model also introduces stochastic star formation. The star formation probability per timestep is given by:

$P_{\rm SF} = \Delta t / t_{\rm ff}$

with $t_{\rm ff}$ the local free-fall time. The simulation advances via mesh refinement/splitting algorithms preserving the high mass resolution.

Radiative transfer is computed in each spectral bin using the M1 approximation, solving for energy density and flux and accounting for the absorption, scattering, and emission processes relevant for each gas phase.

4. Star Formation and Feedback Regulation: Key Results and Formulas

The model robustly demonstrates several emergent results:

• Radiative feedback rapidly (<1 Myr) disperses gas in star-forming clouds immediately after the birth of massive stars, significantly reducing the age spread of stellar clusters ($<2$ Myr) and suppressing runaway growth of individual clusters; the cluster initial mass function steepens to a slope of $\approx-2$ (Deng et al., 14 May 2024).
• Strong SFR–metallicity correlation: Higher metallicity promotes increased SFR and stronger ISRF due to enhanced cooling and a larger reservoir of cold dense gas.
• Mass-loading factor ($\eta_M$) increases under radiative feedback: With radiative feedback enabled, $\eta_M\sim50$; when radiative feedback is turned off, this value drops by an order of magnitude.
• Merger-driven starbursts (Deng et al., 8 Oct 2025): Simulated mergers yield a $\sim$130$\times$ increase in global SFR and two orders-of-magnitude shorter global gas depletion times, but local cloud depletion times and integrated star formation efficiencies (SFEs) remain nearly invariant. The SFE–surface density relation is:

$$\epsilon_{\rm int} = \frac{\sqrt{\Gamma^2 + (4\beta-2)\Gamma + 1} - (2\beta-1)\Gamma - 1}{2(1-\beta)\Gamma}$$

where $\Gamma$ quantifies the ratio of gravity to feedback momentum and $\beta$ encodes geometric/cloud structure effects.

Cloud life cycles display an exponential distribution, supporting the interpretation that local feedback, rather than large-scale environment or merger-induced compressive effects, dominates cloud-scale SFE regulation.

5. Comparison with Alternate Models and Resolution Effects

The RIGEL model has been directly compared to the LYRA and SMUGGLE frameworks (Zhang et al., 2 Oct 2025). LYRA provides a similar high-resolution baseline but lacks explicit radiative feedback, while SMUGGLE, designed for coarser simulations ($\sim$200$\,M_\odot$ cells), uses kinetic momentum injection based on unresolved phase approximations. Only RIGEL (and, to a slightly lesser extent, LYRA) can robustly distinguish supernova feedback channels and capture the local density dependence of SN energy coupling; SMUGGLE and similar coarse-resolution models lose the ability to predict whether SNe will drive kpc-scale outflows or only disrupt local star-forming regions.

This distinction is crucial for physically motivated calibration of galaxy formation and CGM enrichment, as “subgrid” feedback models cannot encapsulate the small-scale physics that governs global galaxy evolution without direct high-resolution data for calibration.

6. Broader Astrophysical Context and Notable Extensions

Although primarily referenced in the domain of galaxy-scale RHD, the RIGEL name has also appeared in other astrophysical contexts. In blue supergiant asteroseismology (Moravveji et al., 2012, Chesneau et al., 2014), “RIGEL models” refer to highly observed and theoretically constrained representations of pre-SN massive stars, focusing on internal mixing, pulsation, and wind variability. Observational constraints from asteroseismology, high-resolution photometry, and interferometry serve as crucial calibration points for theoretical models of stellar evolution, mass loss, and wind dynamics.

Moreover, the RIGEL graph coordinate system (Zhao et al., 2011) applies a hyperbolic embedding for rapid and accurate estimation of node distances and shortest paths in massive social networks, emphasizing computational scalability and parallelism rather than astrophysical modeling.

7. Summary Table: Core Features of RIGEL in Dwarf Galaxy Simulations

Feature	Implementation in RIGEL	Astrophysical / Computational Impact
Explicit radiative feedback	Star-by-star, on-the-fly RT (M1, 7 bins)	SFR regulation, resolves age spread, ISRF scaling
Mass resolution	$\sim$1–2 $M_\odot$ per gas element	Resolves feedback channels; captures SNe phasing
Thermochemistry	Nonequilibrium + equilibrium (metals, molecules)	Multiphase ISM, heating/cooling across phases
Feedback channels	Local quenching vs. outflow driving	Predicts outflow morphology, SFR suppression
SFE prescription	Analytic $\epsilon_{\rm int}$–$\Sigma_{\rm tot}$ relation	Cloud and galaxy-scale star formation efficiency
Merger modeling	Full RHD with cloud tracking and decorrelation	Starburst triggering and cluster formation

Models designated RIGEL thus represent advanced, physically explicit approaches to multiphysics simulation in astrophysics, achieving predictive power by merging stellar evolution, radiative transfer, and high-resolution hydrodynamics in both isolated and interacting galaxy systems. Their development and usage mark an essential trend toward resolving the multiscale nonlinear feedback processes driving structure formation across cosmic environments.