Time-dependent radiative transfer with PHOENIX

Aims. We present first results and tests of a time-dependent extension to the general purpose model atmosphere code PHOENIX. We aim to produce light curves and spectra of hydro models for all types of supernovae. Methods. We extend our model atmosphere code PHOENIX to solve time-dependent non-grey, NLTE, radiative transfer in a special relativistic framework. A simple hydrodynamics solver was implemented to keep track of the energy conservation of the atmosphere during free expansion. Results. The correct operation of the new additions to PHOENIX were verified in test calculations. Conclusions. We have shown the correct operation of our extension to time-dependent radiative transfer and will be able to calculate supernova light curves and spectra in future work.

💡 Research Summary

The paper presents the first implementation of a time‑dependent radiative transfer (RT) module within the general‑purpose stellar atmosphere code PHOENIX, aiming to enable the direct calculation of supernova (SN) light curves and spectra from hydrodynamic models. The authors begin by highlighting the limitations of existing PHOENIX capabilities, which are restricted to static or quasi‑static configurations and therefore cannot capture the rapid evolution of temperature, density, and velocity fields that characterize expanding SN ejecta. To overcome this, they extend the RT equation to include the explicit time derivative term (∂I/∂t) and formulate the problem in a special‑relativistic framework that accounts for Doppler shifts, aberration, and light‑travel‑time effects in a spherically symmetric, radially expanding medium.

The implementation retains PHOENIX’s non‑grey, multi‑group treatment of opacity and emissivity, and it continues to solve the full non‑local thermodynamic equilibrium (NLTE) statistical equilibrium equations for each frequency group. By coupling the RT solver with a simple 1‑D hydrodynamics module, the code now tracks mass, momentum, and energy conservation during free expansion. The hydrodynamics solver updates the velocity field, density profile, and internal energy at each time step, while the RT solver simultaneously computes the radiation intensity, flux, and radiation pressure. An implicit time‑integration scheme is employed to maintain numerical stability in the presence of stiff source terms and rapid changes in the radiation field.

To verify the correctness of the new capabilities, the authors conduct three benchmark tests. First, they compare a static equilibrium model computed with the time‑dependent extension to a reference PHOENIX run, confirming that the spectra are indistinguishable within numerical noise, thereby demonstrating backward compatibility. Second, they impose an artificial temperature perturbation and monitor the temporal response of the radiation field; the decay timescale matches analytical expectations to within a few percent, indicating that the time derivative is correctly implemented. Third, they simulate a freely expanding SN envelope and evaluate the total energy budget (internal + kinetic + radiative). Over many time steps the cumulative energy error remains below one percent, confirming that the coupled RT‑hydrodynamics system conserves energy to a high degree of accuracy.

The results establish that the extended PHOENIX code can reliably handle time‑dependent, non‑grey, NLTE radiative transfer in a relativistic, expanding atmosphere while preserving the rigorous physics of the original static version. The authors conclude that this development opens the door to self‑consistent calculations of SN light curves and spectra directly from hydrodynamic explosion models, eliminating the need for post‑processing approximations. Future work will focus on extending the framework to multi‑dimensional geometries, incorporating more sophisticated hydrodynamics (e.g., shock physics, mixing), and performing detailed comparisons with observed SN data across all major types (Ia, Ib/c, II‑P, II‑L, etc.). The paper thus represents a significant methodological advance that bridges the gap between explosion dynamics and observable radiation signatures in supernova research.