Gas-phase chemistry (FastChem)

Module: src/chemistry/ — agb::FastChemChemistry, wrapping FastChem 4.0.2.

The equilibrium gas-phase chemical composition is computed with FastChem, a fast equilibrium chemistry solver. At each radial grid point, given the gas temperature and pressure (and the elemental abundances, with the prescribed C/O ratio), FastChem returns the number densities of all gas-phase species, the mean molecular weight, and the total element and hydrogen number densities.

Interface

agb::FastChemChemistry::calcChemicalComposition() takes the temperature and pressure profiles and a per-layer degree of carbon condensation and fills:

  • number_densities[i][species] — per-layer species number densities;

  • mean_molecular_weight — used in the equation of state and the isothermal sound speed;

  • total_element_density and total_h_density — reference densities used to normalise the dust moments and the condensable-carbon budget.

The species the rest of the model needs (the carbon molecules \(\mathrm{C}, \mathrm{C_2}, \mathrm{C_2H}, \mathrm{C_2H_2}\) that feed dust formation, plus the opacity carriers) are indexed through fastchem_species_indices / fastchem_element_indices and the chem_species.h identifiers.

Carbon depletion coupling

The C/O ratio sets the condensable carbon abundance \(\varepsilon_C-\varepsilon_O\) (all oxygen is assumed locked into the very stable CO molecule). Only this excess carbon is available to form amorphous-carbon dust.

In the current scheme the gas-phase chemistry is evaluated at the full (un-depleted) element abundances; the carbon actually consumed by dust is not fed back into a separate FastChem call. Instead the Gail & Sedlmayr moment sweep depletes the growth species differentially as it integrates outward (see Dust formation (Gail & Sedlmayr)). This avoids a fragile outer chemistry↔dust fixed point — the moment method is memoryless, so an outer Picard on the degree of condensation can oscillate.

Note

The degree_of_condensation_c argument to calcChemicalComposition() exists so that a future, more detailed coupling (re-equilibrating the free C ↔ C₂ ↔ C₂H₂ subsystem at the depleted carbon abundance — “B2” in the development notes) can be enabled cheaply. In the default path it is passed as zero.

Equation of state

After the composition is known, agb::Atmosphere::equationOfState() closes the thermodynamics (pressure ↔ density ↔ mean molecular weight), and the isothermal sound speed used by the hydrodynamics follows from

\[c_T = \sqrt{\frac{k_B\,T_\mathrm{gas}}{\mu\,m_p}} ,\]

with \(\mu\) the mean molecular weight per particle.