Atmospheric Model for Asymptotic Giant Branch Stars

Authors: Daniel Kitzmann, Joachim Stock

Overview

This is a self-consistent model for the stationary, spherically symmetric, dust-driven wind of a carbon-rich asymptotic giant branch (AGB) star. Carbon that is not locked into CO condenses into amorphous-carbon grains in the cool, extended atmosphere; the radiative acceleration on these grains, once it exceeds gravity, drives a slow, massive outflow. The model solves the coupled radiation–chemistry–dust–hydrodynamics problem for the steady-state structure and the mass-loss rate.

The code couples:

• a spherical, frequency-dependent radiative transfer solver (Rybicki–Hummer variable-Eddington-factor moment method);
• a radiative-equilibrium temperature determination (Unsöld–Lucy correction and a full-linearisation Newton corrector);
• equilibrium gas-phase chemistry (FastChem);
• carbon-dust nucleation and growth following Gail & Sedlmayr (moment method with self-consistent, differential carbon depletion);
• stationary wind hydrodynamics (Melia Φ transform with a mass-loss eigenvalue, plus an optional Henyey global-Newton structure solver),

iterated to a self-consistent stationary outflow.

Requirements

• A C++17 compiler (GCC or Clang) with OpenMP.
• CMake ≥ 3.10.
• Network access at configure time — the build automatically fetches its dependencies.

The following are downloaded and built by CMake (FetchContent / ExternalProject), so no manual installation is needed:

Dependency	Version	Purpose
FastChem	4.0.2	equilibrium gas-phase chemistry
LX-MIE	pinned	Mie theory for the dust opacities
Eigen	3.4.0	linear algebra (Henyey solver)
toml++	3.4.0	parsing the config.toml
CppAD	20250000.3	automatic differentiation (Henyey Jacobian)

In addition the model needs, at run time:

• an opacity database of cross sections (HELIOS-K format), and
• a dust refractive-index file (e.g. amorphous carbon).

Note: Do not add -march=native to the build flags — FastChem's bundled Eigen breaks under it. The Release flags are deliberately limited to -O3 -DNDEBUG -funroll-loops (and -ffast-math is omitted) to keep the radiative-transfer results bit-reproducible.

Building

Standard out-of-source CMake build:

mkdir build
cd build
cmake ..
make -j

The first cmake .. clones and builds the dependencies; subsequent builds reuse them. The executable is written into the source directory as agb_wind.

A built-in self-test validates the Henyey structure solver (automatic- differentiation Jacobian, Newton/eigenvalue solve, grey bootstrap) without running a full model:

./agb_wind --selftest

Running

Pass the path to a model folder containing a config.toml:

./agb_wind IRC10216/

All input and output paths in the configuration are interpreted relative to the model folder. Parallelism is controlled through OMP_NUM_THREADS; results are bit-reproducible run-to-run for a fixed thread count.

A typical model folder:

IRC10216/
├── config.toml                 # model configuration (required)
├── fastchem_parameters.dat     # FastChem element-abundance file
├── atmosphere_converged.dat    # starting structure (or use "grey")
├── atmosphere.dat              # output: converged structure
├── spectrum.dat                # output: emergent spectrum
├── dust.dat                    # output: dust distribution
└── hydro.dat                   # output: wind structure

Configuration

The model is configured by a single TOML file, config.toml, in the model folder. It is organised into blocks — [star], [model], [spectral_grid], [radiative_transfer], [temperature], [hydrodynamics], [grid], [dust], [movable_grid], [opacity], [output] — each with sensible built-in defaults. A complete, annotated example ships in IRC10216/config.toml, and every key is documented in the full documentation.

The starting model is either a path to an existing structure file or the literal string "grey", which builds a hydrostatic Lucy grey structure on a logarithmic radial grid with no input file.

Output

Depending on the [output] block, the model writes:

• the converged atmospheric structure (radius, density, pressure, gas/dust temperature, velocity);
• the emergent spectrum (wavelength vs. flux);
• the dust distribution (degree of condensation, grain number density and radius, nucleation rate, growth timescale, moments K0…K3);
• the wind structure (velocity, sound speed, radiative acceleration α, the Melia Φ variable).

File formats are documented in the documentation.

Documentation

Extensive documentation — covering both the configuration/usage and the theory/modelling of every module — is maintained as a Sphinx project on the docs branch of the companion agb_docs repository. Build it with:

cd doc_src
make html        # output in ../doc_built/html

(requires pip install sphinx furo).

References

• Kitzmann, D., diploma thesis — the spherical variable-Eddington-factor radiative-transfer scheme and the full-linearisation temperature correction.
• Gail, H.-P. & Sedlmayr, E. — dust nucleation and the moment method.
• Winters, J. M., PhD thesis — the coupled stationary-wind scheme and the differential carbon depletion.
• Melia, F. (1988) — the Φ transform removing the sonic-point singularity.
• Dominik, C. (1990) — the Henyey-type relaxation of the wind structure.

Status

Research software under active development. The default configuration — Melia Φ shooting solver with an eigenvalue mass-loss rate, Taylor radiative-transfer discretisation, and the two-phase Unsöld–Lucy → linearisation temperature corrector — converges the IRC+10216 model and reproduces its observed mass-loss rate.