3D Radiative Transfer of Lyman-series Lines with SKIRT

The paper presents the extension of the Monte Carlo radiative transfer (MC-RT) code SKIRT to include Lyman-series lines of H-like ions, enabling self-consistent modelling of resonance scattering, radiative recombination, and polarisation of these lines in X-ray photo-ionised plasmas. The implementation covers Lyman-series transitions up to n = 10 for ions with atomic numbers Z = 1–30, including fine-structure splitting and linear polarisation in resonance scattering. Two channels for the production of Lyman-series lines are considered: resonance scattering (RS) and radiative recombination (RR). The microphysics, including cross-sections, branching ratios, and redistribution functions, are validated against analytical solutions and compared with the 1D RT code Cloudy based on the two-stream solver. The code successfully reproduces RT effects such as line-profile distortion due to frequency diffusion, the Lyman decrement, and the formation of P Cygni profiles in velocity fields. In 3D geometries, the simulations demonstrate that anisotropic illumination and velocity fields significantly modify the Lyman series line ratios and profiles, all of which are observable with XRISM. The extended version of SKIRT provides a powerful framework for interpreting X-ray line spectra and polarisation from photo-ionised plasmas, particularly suited for constraining the geometry and velocity structure in the vicinity of compact objects in the XRISM and IXPE era.

Improvements to AI systems:

1. Physics-constrained generative models for X-ray spectra: Train a diffusion or normalizing-flow model on SKIRT’s synthetic Lyman-series spectra (including polarization) across 3D geometries and velocity fields. The improved AI can generate realistic, physically consistent X-ray line profiles and polarization maps for arbitrary compact-object environments, enabling rapid mock observations for XRISM/IXPE mission planning.

2. Neural emulator for MC-RT simulations: Replace the computationally expensive SKIRT runs with a graph neural network or transformer that takes ion abundance, density, temperature, and velocity field as input, and outputs line ratios, line-profile distortions, and polarization fractions. The improved AI can predict outcomes of radiative transfer in photo-ionized plasmas in milliseconds, enabling Bayesian inference of source geometry from observed spectra without iterative MC runs.

3. Inverse solver for velocity-field and geometry reconstruction: Build an invertible neural network (e.g., a conditional normalizing flow) trained on SKIRT’s 3D outputs to map observed Lyman-series line ratios and P Cygni profiles back to the underlying 3D velocity field, illumination anisotropy, and column density. The improved AI can directly infer the spatial structure of accretion flows or outflows around black holes/neutron stars from XRISM data, including uncertainty quantification.

4. Polarization-aware spectral classifier: Develop a multi-task deep learning model that jointly classifies emission mechanisms (resonance scattering vs. radiative recombination) and estimates fine-structure splitting contributions from observed polarization-angle and line-shape features. The improved AI can automatically disentangle RS and RR contributions in IXPE polarization data, revealing the dominant excitation process in the plasma.

5. Data-driven closure for two-stream solvers: Use SKIRT’s validated microphysics (cross-sections, redistribution functions) to train a recurrent neural network that corrects the approximate two-stream solver in Cloudy. The improved AI can upgrade fast 1D codes to match 3D MC accuracy for Lyman-series lines, enabling high-throughput spectral fitting of large X-ray surveys.

6. Generative surrogate for frequency diffusion effects: Train a neural operator that learns the mapping from initial photon frequency and scattering angle to the final frequency redistribution (including partial redistribution). The improved AI can accelerate MC-RT by replacing the per-scattering physics with a fast, differentiable surrogate, enabling real-time interactive exploration of parameter spaces for observatory proposals.

Context. High-resolution X-ray spectroscopy and polarimetry provided by XRISM and IXPE offer new diagnostics of the geometry and kinematics of photo-ionised plasmas around compact objects. Interpreting reprocessed X-ray emission in such systems requires full three-dimensional radiative transfer (3D RT) including photon-ion interactions. Aims. We extend the Monte Carlo (MC) RT code SKIRT by implementing the Lyman-series lines of H-like ions, enabling self-consistent modelling of resonance scattering, radiative recombination, and polarisation of these lines in X-ray photo-ionised plasmas. Methods. We implemented Lyman-series transitions (up to n=10) for ions with Z= 1--30, including fine-structure splitting and linear polarisation in resonance scattering. Two channels for the production of the Lyman-series lines (resonance scattering and radiative recombination) are considered. Results. The implementation reproduces analytical expectations and shows good agreement with Cloudy. The SKIRT simulations naturally capture RT effects such as P Cygni profiles and line-profile distortion in optically thick media, which are inaccessible to the conventional 1D RT codes commonly used in X-rays. In 3D geometries, we find that anisotropic illumination and velocity fields significantly modify the Lyman series line ratios and profiles, all of which are observable with XRISM. Conclusions. The extended version of SKIRT provides a powerful framework for interpreting X-ray line spectra and polarisation from photo-ionised plasmas. It is particularly suited for constraining the geometry and velocity structure in the vicinity of compact objects in the XRISM and IXPE era.