1.5D investigation of the Hanle effect in the Ca I 4227 line using partial frequency redistribution. Comparison of synthetic Stokes profiles in Bifrost and MURaM-ChE rMHD models

The paper investigates the formation of synthetic Stokes profiles of the Ca i 4227 Å line in two different 3D radiative magnetohydrodynamic (rMHD) simulations of the solar chromosphere: Bifrost and MURaM-ChE. The authors extract 1D vertical columns from snapshots of these simulations and solve the 1.5D non-local thermodynamic equilibrium (non-LTE) polarized radiative transfer equation (PRTE) including partial frequency redistribution (PFR) and the Hanle effect.

Intensity profiles: The emergent, spatially averaged intensity profiles from both simulations coincide at the line core, but the line wings in MURaM-ChE show higher intensity. The line core forms at greater heights in MURaM-ChE (most probable height of 969 km) than in Bifrost (789 km). The line wings form slightly higher in Bifrost, and the most probable mean temperature at wing formation heights is 6013 K in Bifrost versus 6133 K in MURaM-ChE, explaining the higher wing intensity in MURaM-ChE.

Nonmagnetic polarization: In the absence of magnetic fields, the emergent, spatially averaged ⟨Q⟩/⟨I⟩ profiles show a characteristic triple-peak structure with PFR. The peak value at line center is 2.68% for Bifrost and 1.82% for MURaM-ChE. In the core minima region, the maximum amplitude is 0.55% in Bifrost and 0.30% in MURaM-ChE. In the line wings, MURaM-ChE produces a maximum of 1.06% compared to 0.74% in Bifrost. The most probable polarization formation heights at line wing, core minima, and line center are respectively 164 km (181 km), 240 km (291 km), and 1060 km (1180 km) for Bifrost (MURaM-ChE). The differences in heights of polarization formation cause respective differences in ⟨Q⟩/⟨I⟩ amplitudes of 0.32%, 0.25%, and 0.86%.

Magnetic field effects: When depth-dependent magnetic fields from the 3D rMHD simulations are included, the spatially averaged profiles indicate stronger Hanle depolarization of ⟨Q⟩/⟨I⟩ in the Bifrost snapshot. The magnitude of depolarization is 1.643% in Bifrost compared to 0.401% in MURaM-ChE. The most probable heights of polarization formation in the magnetic case are 1028 km for Bifrost and 1207 km for MURaM-ChE. The most probable magnetic field strengths at these heights are 9.5 G in Bifrost and 5.8 G in MURaM-ChE, with Bifrost showing a broader distribution spanning 0–100 G.

Conclusions: The differing thermal and magnetic structures at the corresponding line formation heights in the two simulations lead to distinct Stokes profiles. The Hanle depolarization signatures indicate that the line-core formation region in the MURaM-ChE snapshot is less strongly magnetized than in the Bifrost snapshot. The authors note that a meaningful comparison with observations requires the inclusion of plasma bulk velocity fields and a more realistic treatment of scattering using angle-dependent PFR and 3D PRTE.

Improvements to AI Systems:

1. Physics-Informed Neural Emulator for Non-LTE Polarized Radiative Transfer: Train a neural network to directly map 3D rMHD simulation parameters (temperature, density, velocity, magnetic field vector) to emergent Stokes profiles (I, Q, U, V) for the Ca i 4227 Å line, bypassing the computationally expensive 1.5D PRTE solver. The improved AI system can predict synthetic spectra in milliseconds instead of hours, enabling real-time parameter inference from observed solar spectropolarimetric data.

2. Uncertainty-Aware Surrogate Model for Hanle Depolarization: Develop a Bayesian deep learning model that predicts the magnitude of Hanle depolarization (e.g., ⟨Q⟩/⟨I⟩ reduction) given the 3D magnetic field topology and line formation height distributions. The AI system can output both the expected depolarization and its uncertainty, allowing astronomers to robustly constrain magnetic field strengths in the chromosphere from unresolved observations, even when the field is sub-resolution.

3. Automated Line Formation Height Estimator: Create a transformer-based model that takes a Stokes profile and predicts the most probable formation height distribution (e.g., 789 km vs. 969 km for line core) and the corresponding thermodynamic state (e.g., temperature at wing formation). This AI system can invert observed spectra to diagnose which atmospheric model (Bifrost vs. MURaM-ChE) is more consistent with the data, and flag discrepancies due to missing physics (e.g., bulk velocities, angle-dependent PFR).

4. Domain-Adversarial Model for Simulation-Observation Gap: Use a generative adversarial network (GAN) with a domain-adversarial loss to learn a mapping from simulated Stokes profiles (from either Bifrost or MURaM-ChE) to real observed profiles, while preserving the physics of Hanle depolarization. The improved AI system can correct for systematic biases in simulations (e.g., missing velocity fields or 3D radiative transfer effects) and produce synthetic observations that are directly comparable to telescope data, enabling validation of rMHD codes.

5. Multi-Task Deep Learning for Magnetic Field Inference: Build a multi-output neural network that simultaneously predicts (a) the line-core formation height, (b) the most probable magnetic field strength at that height, and (c) the spatial distribution of field strengths (e.g., broad 0–100 G vs. narrow 5–10 G). This AI system can separate thermal and magnetic contributions to the Stokes profiles, allowing for a more precise determination of chromospheric magnetism from the Ca i 4227 Å line alone, without needing full Stokes inversions.

6. Active Learning for Simulation Selection: Implement an active learning framework that queries the most informative synthetic profiles (e.g., those with large differences between Bifrost and MURaM-ChE predictions) to iteratively refine a classifier that distinguishes between atmospheric models. The AI system can then recommend which simulation snapshot to use for future observational comparisons, reducing computational cost by focusing on regions where models diverge most.

7. Physics-Constrained Diffusion Model for Super-Resolution of Stokes Profiles: Train a diffusion model conditioned on low-resolution (spatially averaged) Stokes profiles to generate high-resolution, spatially resolved profiles that are consistent with the Hanle effect and PFR physics. The improved AI system can upscale observed data to infer sub-resolution magnetic structures, revealing the broad field distribution seen in Bifrost but not in MURaM-ChE.

Modeling scattering polarization in the Ca I 4227 line is important for diagnosing chromospheric magnetic fields. We investigate the relative influence of formation heights and magnetic fields, through the Hanle effect, on spatially averaged synthetic Stokes profiles using realistic solar atmospheres. We employ 1D vertical columns from 3D radiative magnetohydrodynamic simulations of the solar chromosphere performed with the Bifrost and MURaM-ChE codes, and solve the 1.5D non-local thermodynamic equilibrium polarized radiative transfer equation including partial frequency redistribution and the Hanle effect. The intensity profiles from both simulations agree at line center, while MURaM-ChE exhibits enhanced wing intensity due to deeper, hotter formation regions. The polarization signals form at greater heights in MURaM-ChE than in Bifrost. In the non-magnetic case, Bifrost produces stronger line-core polarization, whereas MURaM-ChE shows enhanced wing polarization. Including the magnetic fields from the simulations results in stronger Hanle depolarization of <Q>/<I> in Bifrost. The distinct thermal and magnetic structures at the corresponding formation heights therefore produce significantly different polarization profiles. In particular, the Hanle signatures suggest that the line-core formation region in MURaM-ChE is less strongly magnetized than that in Bifrost.