Source-linked AI summary
CLES, Code Liegeois d'Evolution Stellaire
R. Scuflaire, S. Theado, J. Montalban, A. Miglio, P. -O. Bourge, M. Godart, A. Thoul, A. Noels
TL;DR
Clés addresses the need for precise, flexible stellar models for asteroseismology, where detailed model physics affects oscillation predictions. It provides a customizable evolution code with configurable physical inputs and ongoing feature development, but its current physics limits helium-burning applications and documentation remains incomplete.
Problem
Asteroseismology requires stellar-evolution models precise enough to capture details affecting oscillation frequencies and mode stability.
Method
Clés implements a customizable stellar-evolution code with selectable physical inputs, including opacity treatments and nuclear-reaction modeling.
Results
The development effort has produced multiple feature-specific versions, with plans to consolidate the most significant developments into a unique version 19.
Takeaways & Limitations
Clés provides a versatile framework that users can tailor to their modeling needs while incorporating ongoing physical and technical developments.
Takeaways & Limitations
The current version is not intended for helium-burning phases, and its documentation is limited beyond the user manual.
Abstract
from arXiv · showhide
Cles is an evolution code recently developed to produce stellar models meeting the specific requirements of studies in asteroseismology. It offers the users a lot of choices in the input physics they want in their models and its versatility allows them to tailor the code to their needs and implement easily new features. We describe the features implemented in the current version of the code and the techniques used to solve the equations of stellar structure and evolution. A brief account is given of the use of the program and of a solar calibration realized with it.
1 Introduction
Clés was created to produce precise stellar-evolution models for asteroseismology, where oscillation frequencies and mode stability are sensitive to modeling details. Its active development emphasizes customization and added physical features, although the current version is not intended for helium-burning phases.
- Clés was developed because asteroseismic frequencies and mode stability are highly sensitive to model details that were less important for ordinary stellar evolution.
- The current implementation is written in FORTRAN 77 for GNU/Linux, with GNU Fortran extensions and supporting Bash and Tcl scripts.
- Because implemented physics remains limited, the present version is not intended to model helium-burning evolutionary phases.
2 Structure and evolution equations
Clés solves stellar structure and composition evolution using standard structure equations, boundary conditions, nuclear reactions, diffusion, and instantaneous convective mixing. Its initialization supports user-selected composition inputs and atmosphere-matched outer conditions.
- The structure equations describe hydrostatic balance, mass conservation, energy generation, and the temperature gradient, with radiative and convective treatments differing through ∇.
- The luminosity equation includes nuclear energy production and εg, whose time-dependent contribution governs evolution when nuclear sources are insignificant.
- The energy term accounts for chemical-composition changes through chemical potentials, rather than retaining only the −TdS/dt contribution.
- Outer boundary conditions are imposed by smoothly joining the interior solution to a precomputed atmosphere model as the diffusion approximation breaks down.
- Abundance evolution combines nuclear-reaction contributions and diffusion, while convective and overshooting zones are imposed to be chemically homogeneous.
- Initial models begin on the Hayashi track with homogeneous composition, user-defined hydrogen and metal fractions, and selectable metal mixtures and isotopic abundances.
3 Input physics
Clés combines tabulated thermodynamics, merged opacity data, nuclear reaction networks, and multiple treatments of convection, diffusion, and mixing. Several physics limitations remain, including neglected conductive opacity effects, absent semi-convection, and restricted helium-burning applicability.
- 3.1 Equation of state: Clés interpolates precomputed EOS tables and derives thermodynamic quantities while supporting CEFF, OPAL 2001, and OPAL 2005 implementations.
- 3.2 Opacity: The standard opacity setup smoothly merges OPAL data with low-temperature Alexander–Ferguson opacities, while tools support additional metal mixtures and opacity tables.The blend uses a cubic transition function across logT ∈ [3.9,4.15].
- 3.3 Nuclear reactions: The nuclear network follows deuterium and lithium burning thoroughly, uses specified reaction-rate prescriptions, and includes the main helium-burning reactions without yet accurately supporting that phase.
- 3.5 Convection: Convection supports Ledoux and Schwarzschild criteria, mixing-length, Henyey, and FST prescriptions, user-selected overshooting, and instantaneous chemical mixing.
- 3.5 Convection: The current physics omits semi-convection, permits numerical diffusion at convective boundaries, neglects conductive opacity effects, and is not intended for helium-burning phases.
4 Discretization
Clés advances stellar models on a Lagrangian grid by separately updating diffusion and then jointly treating nuclear burning and mixing. Its discretization includes stability treatments for stiff processes and continuity-preserving handling of receding convective zones.
- 4.1 Structure: The code uses a Lagrangian grid whose points follow material elements, while shell masses between grid points provide the fundamental grid quantities.
- 4.2 Chemical evolution: Chemical composition is updated in two stages: diffusion is computed first, followed by simultaneous nuclear burning and mixing.The authors identify this sequencing as inherited from the code’s development history.
- 4.2 Chemical evolution: Stiff diffusion equations use updated values in the discrete evolution equations to maintain numerical stability when outer-layer diffusion times are very short.
- 4.2 Chemical evolution: Nuclear species with lifetimes much shorter than the timestep are treated with the same stiff-system strategy used for diffusion.
- 4.2 Chemical evolution: A dedicated algorithm maintains a continuous chemical profile when a convective zone recedes by more than one spatial interval during a timestep.
5 Implementation
Clés uses a partially simultaneous timestep strategy, iterating composition and structure updates to convergence with Newton–Raphson methods. Adaptive grids and timestep controls regulate spatial and temporal changes, but diffusion can become the effective timestep limiter.
- 5.1 Evolution strategy: Each timestep alternates composition updating and structure solving until convergence, placing Clés in the partially simultaneous category.
- 5.2 Numerical solution: Newton–Raphson solves both nonlinear composition and structure equations, with damped corrections and smaller timesteps used when convergence becomes difficult.
- 5.3 Grid and timestep control: The adaptive grid controls neighboring variations in r, m, P, and T using default limits of 5×10^-3R, 5×10^-3M, 5×10^-2P, and 10^-2.
- 5.3 Grid and timestep control: A 2 M⊙ model typically uses 700 grid points initially, reaches 1150 at the zero-age main sequence, and retains roughly that number thereafter.
- 5.3 Grid and timestep control: Diffusion sequences have timesteps effectively controlled by convergence requirements of the diffusion algorithm.
- 5.3 Grid and timestep control: Without user intervention, a 2 M⊙ sequence requires 125 pre-main-sequence steps, 75 main-sequence steps, and 20 additional steps during second gravitational contraction.
6 The use of Cl´es
Clés supports progressively advanced use through command files, user-generated tables, runtime customization, and direct modification of modular code components. Default parameters allow basic operation while preserving extensive tailoring options.
- 6.1 Basic use: Basic users configure Clés through command files specifying quantities such as stellar mass, composition, EOS, opacity, and convection parameters.Unspecified parameters receive default values.
- 6.2 Extended use: Users can supply new tables, including opacity tables for different metal mixtures, with dedicated tools converting external data to Clés format.
- 6.3 Interactive use: The customizable clesuser subroutine runs before each timestep and lets users inspect or modify the latest model or computation parameters.
- 6.4 Code customization: Clés’ modular structure facilitates implementing research-specific features directly in users’ copies of the code.
7 Calibration of solar models
Clés calibrates solar models by adjusting three initial or convection parameters to reproduce observed solar properties at the solar age, then compares models using different opacity tables with helioseismic diagnostics.
- Table 1 additionally reports the normalized convective-envelope-base radius and surface helium abundance alongside calibrated solar-model parameters.Helioseismic reference values are 0.713 ± 0.001 for rcz and 0.245±0.005 for YS.
- Solar calibration adjusts α, X0, and Z0 to reproduce the observed luminosity, radius, and photospheric Z/X at 4.57 10^9 yr.The calibration uses a finer spatial and temporal discretization than the standard calculation.
- Two solar models use OPAL or OP opacity tables, while sharing the same convection, metal mixture, nuclear-rate, and equation-of-state inputs.Both opacity choices are complemented at low temperature with Ferguson et al. opacities.
- The calibrated models are evaluated through relative differences in squared sound speed between each model and the Sun.
8 Discussion
Clés development proceeds through collaborative implementation of desirable features, with the authors aiming to consolidate major developments into a unique version 19. They identify documentation as a remaining priority because the approach depends on close collaboration at one site.
- Developers and users have implemented desirable features from standard version 18, and the authors aim to consolidate the most significant developments in version 19.They also hope to repeat this development cycle for later versions.
- The collaborative development strategy worked because developers were working closely together on the same site.
- Documentation is inadequate beyond a user manual, so writing good documentation is identified as the second development priority.