Type IIP thermal balance

Species treatment

H I is the only NLTE species. Its level populations are solved from the NLTE rate equations, and the H ionization balance uses the H I continuum rates. Elements without continuum rates, such as helium when only H I is listed under continuum_interaction.species, follow the C-TARDIS treatment:

  • Ionization uses the nebular approximation of Mazzali & Lucy (1993) at the radiation temperature and dilution factor of the current iteration and at each trial electron temperature. Charge conservation sets the electron density.

  • Excitation is dilute LTE at the radiation temperature and dilution factor of the current iteration.

Collision strengths for levels missing from the atomic level data are ignored with a warning, so a model with helium needs no extra atomic data.

Level-population solve

The Type IIP workflow solves NLTE level populations for each thermal-balance trial. When the direct root does not yield a physical population that closes the normalized level equations to 1e-10, it retries from the fixed initial population using logarithmic population ratios. These ratios keep trial fractions positive and normalized.

If the equations remain open, the level solver retries with an empirical 1e-4 floor on each starting fraction and then renormalizes. This permits excited levels depleted by the previous thermal state to recover. The solver keeps the candidate with the smallest normalized physical equation residual, regardless of the optimizer’s reported success status.

Thermal-balance solve

The thermal optimizer can evaluate an approximate physical level state during its search. If its joint-shell candidate fails to converge, the workflow retries each shell with an open electron or fractional-heating residual, starting from that candidate. A stalled local solve is retried from the same shell’s pre-optimization state. The workflow then rebuilds the full plasma state. The accepted state must pass the final level, electron, charge, and heating convergence checks; otherwise the workflow raises an error.

The local objective retains the joint optimizer’s fixed level-population guess. The final rebuild uses the resulting population as its guess, so a change to a different nonlinear level branch can still fail final convergence.