CHIMES Non-equilibrium Chemistry Module

• CHIMES Non-equilibrium Chemistry Module is a comprehensive network that models hundreds of atomic, ionic, and molecular species without assuming chemical equilibrium.
• It integrates advanced radiative, hydrodynamic, and dust processes using adaptive implicit solvers to capture transient behavior in the interstellar medium.
• Hybrid schemes balance computational cost with precision, reproducing key observables within 10–20% accuracy across a range of astrophysical benchmarks.

The CHIMES (CoolING and Molecular EvolutionS) non-equilibrium chemistry module is a comprehensive chemical kinetics and cooling network designed for integration into astrophysical simulations, especially those modeling the multiphase interstellar medium (ISM) and star-forming environments in galaxies. Developed initially by Richings, Schaye, and Oppenheimer (2014), CHIMES tracks the time-dependent abundances of hundreds of atomic, ionic, and molecular species without imposing chemical equilibrium, allowing it to model the thermo-chemical evolution of gas subject to rapidly varying physical conditions characteristic of the ISM, star formation, and feedback processes (Richings et al., 2014, Thompson et al., 2024, Richings et al., 2022, Ploeckinger et al., 18 Jun 2025, Chan et al., 18 Aug 2025). The module is widely used in modern galaxy formation codes, notably in GIZMO with FIRE-2 physics, and in the SWIFT and SPARCS frameworks, providing a flexible and physically consistent treatment of non-equilibrium chemistry, radiative heating/cooling, and dust and cosmic ray physics.

1. Chemical Species, Reaction Network, and Physical Processes

CHIMES evolves a reaction network comprising up to 157 species, including all relevant ionization stages of hydrogen, helium, and the primary astrophysical metals (C, N, O, Ne, Mg, Si, S, Ca, Fe), as well as important molecular species and their intermediates:

• All ionization and negative states of H and He (e.g., H I, H II, H⁻; He I, He II, He III)
• All states of C, N, O, Ne, Mg, Si, S, Ca, Fe (neutral through fully stripped ions, C⁻, O⁻)
• 20 molecular species: H₂, H₂⁺, H₃⁺, OH, H₂O, O₂, CO, CO⁺, HCO⁺, HOC⁺, OH⁺, H₂O⁺, H₃O⁺, O₂⁺, C₂, CH, CH₂, CH₃⁺, CH⁺, CH₂⁺
• Electrons as a distinct population

The integrated reaction network (derived from Richings et al. 2014 and subsequent expansions) incorporates:

• Gas-phase collisional ionization and recombination, radiative and dielectronic processes
• Charge-exchange reactions
• Grain-surface chemistry (notably, H₂ formation)
• Photochemical reactions, including photoionization and photodissociation, with process rates modulated by local UV fields, dust, and self-shielding
• Cosmic-ray ionization and secondary electron cascades
• Full coupling to dust and metal depletion schemes for accurate gas-phase abundance accounting

These reactions drive the evolution, destruction, and creation of each species under explicitly non-equilibrium conditions, allowing the network to capture rapid transients, recombination lags, and molecule formation/dissociation relevant for galactic environments (Richings et al., 2014, Thompson et al., 2024).

2. Kinetic Equations, Rate Coefficients, and Solver Formulation

The temporal evolution of species abundances is governed by a coupled, stiff system of ODEs, capturing both one-body (e.g., photo-processes, cosmic rays) and two-body (collisions, molecular reactions) channels. The system for number density $n_i$ of each species $i$ is generically:

$$\frac{d n_i}{dt} = \sum_j k_{j \to i}(T, J) n_j - \sum_k k_{i \to k}(T, J) n_i$$

where each $k_{j \to i}$ exhibits Arrhenius-like temperature dependence, often parameterized as $k(T) = \alpha T^\beta \exp(-\gamma/T)$. Photoprocesses are computed from frequency-binned local and extragalactic radiation fields, modulated by self-shielding and dust attenuation (Richings et al., 2014, Ploeckinger et al., 18 Jun 2025, Thompson et al., 2024).

For chemistry integrated with radiation hydrodynamics (e.g., in SPARCS), photoionization and photon transport equations are also solved in tandem, tracking photon number densities and their attenuation over hydrodynamic and radiative time steps (Chan et al., 18 Aug 2025). Dust-catalyzed H₂ formation, recombination on grains, and photoelectric heating rates are updated according to empirically or theoretically calibrated cross-sections and efficiencies, with explicit dependence on grain properties and dust-to-gas ratios.

Each hydrodynamic element (cell or particle) solves its local ODEs independently per timestep, leveraging implicit time-integration schemes (backward-Euler, BDF) with adaptive sub-stepping to resolve the shortest relevant reaction or cooling timescales. Solver implementations are based on CVODE from the SUNDIALS library or closely related BDF Newton-iteration frameworks (Thompson et al., 2024, Richings et al., 2022). Tolerances are typically set at relative $10^{-4}$–$10^{-6}$ and absolute $10^{-10}$–$10^{-13}$ to ensure mass and charge conservation.

3. Integration with Hydrodynamics, Radiation, and Dust Physics

CHIMES is operator-split into contemporary hydrodynamical simulation platforms, including GIZMO (FIRE-2), SWIFT, and SPARCS. The typical operator-splitting scheme involves updating hydrodynamic quantities (density, velocity, internal energy) via Godunov-type solvers, then holding these fixed during a chemistry/cooling substep in which CHIMES updates species and energy under constant densities/temperatures (Thompson et al., 2024, Richings et al., 2022). This maintains physical accuracy when hydrodynamic and chemical timescales are disparate.

Radiation fields are treated via multi-frequency binning, local stellar sources (e.g., LEBRON tree algorithm), and external backgrounds (e.g., UVB models), with attenuation determined by local shielding length scales—often a Sobolev-type length $$L_{\rm sh} = \frac{1}{2} \left( \rho/|\nabla\rho| + h_{\rm int} \right)$$—and species column densities. Dust-to-metals and depletion factors are determined empirically as functions of gas density (e.g., Jenkins 2009, De Cia et al. 2016), and used for both grain chemistry and the scaling of photoelectric heating (Richings et al., 2022, Thompson et al., 2024).

The chemistry module passes back updated abundances and thermal states to the hydrodynamic solver for the next global timestep, enabling consistent coupling of chemical, radiative, and dynamical evolution.

4. Cooling, Heating, and the Role of Non-equilibrium Effects

Thermal balance in CHIMES couples cooling and heating to explicit species abundances, incorporating:

• Collisional line and continuum cooling from H, He, and heavy metals through data tables (e.g., Oppenheimer & Schaye 2013)
• Molecular rovibrational (H₂) and rotational (CO, H₂O, OH, HD) cooling using analytic or tabulated fits (notably Glover & Abel 2008; Glover 2010)
• Dust-gas collisional energy transfer and photoelectric heating
• Compton cooling by the CMB and optically thin radiative mechanisms

Non-equilibrium chemistry yields quantitatively distinct outcomes compared to equilibrium, notably:

• Recombination lags lead to elevated electron abundances during rapid cooling, increasing the net cooling rate by up to two orders of magnitude at $i$0 K compared to equilibrium predictions (Richings et al., 2014).
• H₂ and CO formation/dissociation rates, line intensities, and the conversion factor $i$1 are affected at the tens-of-percent level in massive galaxies (e.g., $i$225% lower H₂ mass and CO luminosity in non-equilibrium, but $i$3 robust to within 5%), though effects are stochastic and larger in bursty low-mass galaxies (Thompson et al., 2024).

5. Hybrid Equilibrium/Non-equilibrium Schemes and Computational Trade-Offs

For large cosmological domains or applications where full non-equilibrium chemistry is computationally intensive, CHIMES supports hybrid approaches (Ploeckinger et al., 18 Jun 2025):

• A small non-equilibrium “live” network (e.g., H+He or a few metals) is evolved explicitly, while other elements and molecules use equilibrium tables parameterized on local conditions (density, temperature, metallicity, shielding, etc.)
• The total electron density is the sum of the non-equilibrium and equilibrium contributions, ensuring consistent coupling to cooling rates and thermal evolution
• CPU costs scale roughly linearly with network size: pure H+He chemistry is %%%%13$k_{j \to i}$14%%%% the cost of table interpolation; including O increases this to $i$61.85$i$7; the full 157-species network is %%%%17$i$118%%%% slower and often only used in high-resolution or small-volume applications (Chan et al., 18 Aug 2025)

6. Applications, Validation, and Performance

CHIMES has been extensively validated against analytic solutions and public astrophysical codes (e.g., CLOUDY), and benchmarked on key astrophysical problems:

• Reproducing equilibrium abundance and cooling curves to $$\frac{d n_i}{dt} = \sum_j k_{j \to i}(T, J) n_j - \sum_k k_{i \to k}(T, J) n_i$$020% accuracy compared to CLOUDY (Richings et al., 2014)
• Capturing the HI→H₂ transition, molecular line emission, and ISM multi-phase structure in isolated galaxies, matching Milky Way and external survey observations (Thompson et al., 2024, Richings et al., 2022)
• Idealized tests in SPARCS confirm accuracy to 10% in ionization fronts and equilibrium temperatures, robustly scaling to large core counts with parallel efficiency above 85–90% (Chan et al., 18 Aug 2025)
• Hybrid schemes recover ISM phase diagrams, cold/warm ISM pressure, and the position of the molecular transition, with errors and phase boundaries controlled by network completeness, especially inclusion of atomic oxygen (Ploeckinger et al., 18 Jun 2025)

Including the CHIMES module typically increases wall-clock run time by factors of 2–10 depending on species tracked and coupling to radiative transfer. Memory costs are modest, tracking $$\frac{d n_i}{dt} = \sum_j k_{j \to i}(T, J) n_j - \sum_k k_{i \to k}(T, J) n_i$$1160 species and $$\frac{d n_i}{dt} = \sum_j k_{j \to i}(T, J) n_j - \sum_k k_{i \to k}(T, J) n_i$$22000 reaction rates per computational cell.

7. Limitations, Developments, and Context

While CHIMES is one of the most complete non-equilibrium ISM chemistry modules available, several limitations and caveats are frequently noted:

• Non-equilibrium effects are most prominent during large, rapid changes (e.g., shocks, strong feedback, bursty star formation), and less significant in high-mass, slowly evolving systems (Thompson et al., 2024)
• Reduced chemical networks accelerate computation but can over- or under-predict molecular formation (e.g., omission of O leads to overproduction of H₂ by up to two orders of magnitude near the HI–H₂ transition (Ploeckinger et al., 18 Jun 2025))
• Empirical depletion and dust models carry intrinsic uncertainties; some observables (e.g., [CII], [OIII] emission) are sensitive to these prescriptions (Richings et al., 2022)
• Multivariate fits of observables (e.g., for $$\frac{d n_i}{dt} = \sum_j k_{j \to i}(T, J) n_j - \sum_k k_{i \to k}(T, J) n_i$$3) can require recalibration against simulation suites and may not generalize across parameter space (Thompson et al., 2024)

Despite these, CHIMES enables on-the-fly, physically motivated, and scalable non-equilibrium chemistry and cooling that underpins current-generation galaxy formation, radiative transfer, and ISM structure studies.

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References:

• (Richings et al., 2014) Richings, Schaye & Oppenheimer, "Non-equilibrium chemistry and cooling in the diffuse interstellar medium – I. Optically thin regime"
• (Thompson et al., 2024) FIRE-2+CHIMES implementation, galaxy-scale CO and H₂
• (Richings et al., 2022) Local stellar radiation and dust depletion in CHIMES–FIRE simulations
• (Ploeckinger et al., 18 Jun 2025) Hybrid-CHIMES, cosmological and multi-phase ISM cooling
• (Chan et al., 18 Aug 2025) SPARCS, radiation-hydrodynamics coupling with CHIMES in SWIFT