GENEC Stellar Evolution Models

• GENEC models are 1D stellar evolution frameworks that integrate nuclear reaction networks, convection criteria, and rotation-induced mixing to simulate the evolution of massive stars.
• They employ specialized numerical schemes, including the Henyey relaxation method and operator-split techniques, to accurately resolve burning stages and mixing processes.
• The models cover a broad range of masses and metallicities, enabling predictions of remnant properties, stellar feedback, and nucleosynthetic yields for chemical evolution studies.

GENEC models refer to the evolutionary calculations conducted with the Geneva stellar evolution code (GENEC), one of the most widely utilized 1D stellar evolution frameworks for modeling the structure, rotation, mixing, mass loss, and terminal fates of stars, particularly in the massive star regime. GENEC implements a comprehensive set of microphysics—nuclear reaction networks, opacities, mass-loss prescriptions, convective boundary mixing, and rotational instabilities—thereby enabling detailed studies of individual stars, binary systems, and complete grids across a broad range of masses and metallicities. The code’s flexible treatment of key physical ingredients, especially rotational mixing and mass loss, underpins its use in mapping the lifecycles and end products of massive stars and in interpreting their roles in stellar feedback, chemical evolution, and the formation of compact remnants.

1. Fundamental Physics and Numerical Schemes

GENEC solves the 1D stellar structure and evolution equations via a Lagrangian Henyey relaxation method, treating, in a sequential manner, hydrostatic structure, nuclear burning, and mixing. Composition changes are tracked via an operator-split approach, permitting integration with nuclear reaction networks of varying complexity: from modestly sized α-chain networks for late burning to extended 43-isotope networks or beyond (as in GeValNet25/48), crucial for tracking light element depletion, s-process nucleosynthesis, and advanced burning stages (Frischknecht et al., 2010, Griffiths et al., 6 Aug 2024, Dumont et al., 14 Jul 2025).

Convection is typically handled using the Schwarzschild or Ledoux criterion, with core overshooting implemented as an instantaneous (penetrative) extension of the convective zone by a fraction α_ov of the local pressure scale height, i.e.,

$d_\mathrm{ov} = \alpha_\mathrm{ov} \, H_P.$

GENEC also includes treatments of semi-convection, thermohaline mixing, and, optionally, extra turbulent diffusion as parameterized in some external models (Rosu et al., 2020). Meridional circulation and rotation-induced mixing are solved using both advective and diffusive formalisms, and, where relevant, additional instabilities such as the Tayler–Spruit dynamo or the magneto-rotational instability (MRI) are implemented as effective diffusion coefficients (Griffiths et al., 2022, Nandal et al., 2023).

Mass-loss rates are prescribed according to stage-specific, empirically or theoretically motivated formulae: Vink et al. (2001) for OB stars, Nugis & Lamers (2000) or hydrodynamic calibrations for the Wolf–Rayet phase, m-CAK theory for optically thin winds, and Eddington factor–dependent prescriptions for transitions to optically thick winds at

$$\Gamma_\text{e} = \frac{L_* \kappa_\text{e}}{4 \pi c G M_*}$$

(Romagnolo et al., 2023, Gormaz-Matamala et al., 19 Jul 2024).

2. Rotational Mixing, Angular Momentum Transport, and Magnetic Instabilities

Rotation in GENEC is implemented under the “shellular” approximation: angular velocity is assumed to be nearly constant along isobars, justified when horizontal transport is much faster than vertical. The angular momentum transport equation reads

$$\rho \frac{d}{dt}[r^2 \Omega]_{M_r} = \frac{1}{5r^2} \frac{\partial}{\partial r}[\rho r^4 \Omega U(r)] + \frac{8}{5r^2} \frac{\partial}{\partial r}[\rho D_\text{shear} r^4 \frac{\partial \Omega}{\partial r}]$$

where

• $U(r)$ is the meridional circulation velocity,
• $D_\text{shear}$ is the vertical shear diffusion coefficient.

Chemical transport is solved using a sum of shear and “effective” diffusion,

$D_\text{eff} = \frac{|r U(r)|^2}{30 D_\text{h}},$

where $D_\text{h}$ is the horizontal turbulence diffusion, calculated with various prescriptions (e.g., Zahn 1992, Maeder 1997, Talon & Zahn 1997, Mathis 2004) (Frischknecht et al., 2010, Nandal et al., 2023).

Magnetic transport processes, notably the Tayler–Spruit dynamo, can be activated to provide a large effective viscosity

$$\nu_\text{mag} \approx r^2 \Omega \left(\frac{K}{r^2 N_T}\right)^{1/2} \left| \frac{\partial \ln \Omega}{\partial \ln r} \right|^2$$

which erases differential rotation, leading to near solid-body rotation, especially during the main sequence evolution (Griffiths et al., 2022, Nandal et al., 2023). The MRI is introduced when the criterion

$$-q > \frac{\left[\frac{\eta}{\kappa}N^2_T + f_\mu N^2_\mu\right]}{2\Omega^2}$$

is satisfied, with the MRI’s transport modeled via an effective viscosity $\nu_\text{mag,MRI} = \alpha |q| \Omega r^2$ (Griffiths et al., 2022).

3. Nuclear Physics, Reaction Networks, and Sensitivity to Rates

GNNEC has adopted updated nuclear reaction rates for all key burning stages, particularly those affecting the CNO cycles, the 12C(α,γ)16O process, and advanced fusions (12C+12C, 12C+16O, 16O+16O). The code supports the direct incorporation of experimentally measured or theoretically predicted rates, with analytic REACLIB fits for all major channels (Monpribat et al., 2021, Dumont et al., 14 Jul 2025). Changes in rates—for example, the transition from older Kunz et al. (2002) to newer deBoer et al. (2017) for 12C(α,γ)—predominantly affect the critical 12C/16O ratio at He-depletion, the lifetime and structure of C- and O-burning stages, and thus the compactness and remnant type. Fusion hindrance models (HIN/RES) or quantum mechanical TDHF rates can alter burning lifetimes by ±10–50%, core compactness, and final nucleosynthetic yields by up to an order of magnitude for certain isotopes (Monpribat et al., 2021, Dumont et al., 14 Jul 2025).

GENEC is also equipped to trace the evolution of fragile surface elements (Li, Be, B) with extended networks, and to follow neutron capture nucleosynthesis, for example, in studies of the weak s-process via the 22Ne($\alpha$,n)25Mg neutron source (Frischknecht et al., 2010, Bennett et al., 2010).

4. Grid Coverage: Parameter Ranges and Predictive Remnant Mapping

GENEC models span a vast parameter space: initial masses from $\sim$1.7, through typical massive star regimes (9–40 $M_\odot$), to extremely high values (up to 500 $M_\odot$ and more for VMS and supermassive star studies) (Sibony et al., 9 Jul 2024, Nandal et al., 9 Jun 2025, Hirschi et al., 28 Aug 2025). Metallicity grids cover from extremely metal-poor ($Z=10^{-5}$, approaching Pop III conditions) to supersolar $Z=0.02$ (Sibony et al., 9 Jul 2024, Romagnolo et al., 2023, Hirschi et al., 28 Aug 2025). Initial rotation is typically parameterized by $v_\text{ini}/v_\text{crit}$; standard grids use $v_\text{ini}/v_\text{crit}=0$ and 0.4, but specialized studies extend to $v_\text{ini}/v_\text{crit}=0.01-0.10$ for supermassive stars (Nandal et al., 9 Jun 2025).

Fate mapping relies on CO core mass and envelope composition at the end of core He-burning:

• $M_\text{CO} \lesssim 6\,M_\odot$: neutron star
• $6<M_\text{CO}<12\,M_\odot$: fallback OSN/BH
• $12<M_\text{CO}<40\,M_\odot$: direct BH
• $40<M_\text{CO}<60\,M_\odot$: PPISN
• $60<M_\text{CO}<130\,M_\odot$: PISN (no remnant)
• $M_\text{CO}>130\,M_\odot$: direct BH Supernova spectral types are tied to hydrogen and helium envelope masses; thresholds are adopted (e.g., $M_\text{H}^\text{env}>2\,M_\odot$: Type IIP; $M_\text{He}^\text{env}<0.5\,M_\odot$: Type Ic) (Hirschi et al., 28 Aug 2025).

5. Applications: Stellar Feedback, Yields, and Transient Phenomena

GENEC is leveraged to:

• Constrain rotational and magnetic mixing using light and CNO elemental surface abundances (Frischknecht et al., 2010, Keszthelyi et al., 2021, Nandal et al., 2023)
• Quantify the effect of updated wind and WR mass-loss prescriptions, particularly for the prediction of maximum BH masses, WR and WNh star formation, and the occupancy of observed loci in the HR diagram (Romagnolo et al., 2023, Gormaz-Matamala et al., 19 Jul 2024)
• Model grids at $Z=10^{-5}$, revealing the enhanced primary nitrogen production in EMP stars and implying their role in early-universe chemical evolution (Sibony et al., 9 Jul 2024)
• Trace the progenitor structures leading to pair-instability supernovae, SLSNe, and fast-evolving transients, and examine uncertainties in predicted light curves due to envelope structure and radiative transfer (Kozyreva et al., 2016, Josiek et al., 11 Apr 2025)
• Analyze the boundary between “explodability” regimes: the presence and width of the pair-instability gap, and the metallicity (and rotation) dependence of maximum BH mass and remnant mass functions (Romagnolo et al., 2023, Sibony et al., 9 Jul 2024, Hirschi et al., 28 Aug 2025)
• Provide initial conditions for multi-dimensional hydrodynamic (SN explosion) and radiative transfer (spectral) codes, with emphasis on realistic pre-supernova core and envelope profiles, including improvements in the EoS and the treatment of electron capture and opacities (Griffiths et al., 6 Aug 2024)

6. Uncertainties, Inter-Model Comparisons, and Observational Validation

Uncertainties in GENEC predictions arise from:

• The treatment of rotational and magnetic mixing (especially the value and scaling of $D_\text{shear}$, $D_\text{h}$, and possible turbulent diffusion)
• The adopted mass-loss prescriptions and the metallicity scaling, particularly near the Eddington limit and the WR threshold
• The sensitivity of burning phases and core structures to nuclear reaction rates, notably 12C(α,γ)16O and heavy-ion fusions
• The ambiguity in mass–loss transitions (between OB and thick WR-type winds), the connection to envelope inflation, and the correction for wind-altered effective temperatures in spectroscopic models (Gormaz-Matamala et al., 19 Jul 2024, Josiek et al., 11 Apr 2025)
• The treatment of mixing at convective boundaries (e.g., instantaneous vs. diffusive overshoot), which affects core masses and evolutionary tracks Direct intercomparisons with KEPLER and MESA demonstrate $\lesssim$30% agreement in nucleosynthetic yields and core sizes when using matching input physics (Jones et al., 2014, Griffiths et al., 6 Aug 2024), while discrepancies in convective shell structure or rotation profiles may affect remnant masses and transient properties.

Validation comes through:

• Surface abundances (CNO, LiBeB) in OB stars and asteroseismic rotation rates (Frischknecht et al., 2010, Keszthelyi et al., 2021, Nandal et al., 2023)
• Core mass and compactness parameters from SN progenitor modeling (Griffiths et al., 6 Aug 2024)
• Observed HRD positions, supernova type fractions, BH mass distributions, and the characteristics of WR/WNh stars and SLSN hosts (Gormaz-Matamala et al., 19 Jul 2024, Romagnolo et al., 2023, Hirschi et al., 28 Aug 2025)

7. Data Dissemination and Grid Utility

GENEC model grids are made available as comprehensive electronic tables, sampled at hundreds of points per model, each marked for consistent evolutionary phases across mass and $Z$ (Sibony et al., 9 Jul 2024). These allow robust interpolation for population synthesis, rapid calculation of SN and remnant rates under different IMFs ($dN/dM \propto M^{-\alpha}$, with $\alpha=2.35$ or other slopes), and are used widely in galactic-scale chemical evolution, cosmological feedback, and gravitational wave event rate modeling.

To summarize, GENEC models provide a rigorous and flexible backbone for modeling the evolutionary trajectories and endpoint properties of massive stars across the cosmic metallicity and mass spectrum. Their implementations of rotation, mixing, and the latest nuclear and atmospheric physics underpin predictive calculations relevant to the origin of compact remnants, nucleosynthesis, and stellar feedback. Continued updates—especially in late-stage microphysics and convection/mixing theory—remain essential for improving the reliability of predictions in stellar and extragalactic astrophysics.