[Paper Review] Line formation in the magnetized solar chromosphere

Thore Espedal Moe|arXiv (Cornell University)|Oct 17, 2023

Solar and Space Plasma Dynamics28 references4 citations

TL;DR

This study investigates how spatial resolution in 3D radiative MHD simulations affects inferences of solar atmospheric parameters from synthetic spectra. Using simulations at 6, 12, and 23 km grid spacing, it shows that higher resolution reveals finer structures and more extreme velocities/magnetic fields even after degradation; sub-resolution effects induce systematic errors in inversions that diminish with finer resolution, suggesting that numerical resolution should be at least half the target observational resolution to minimize bias.

ABSTRACT

The theme of this thesis has been the use of forward modeling to study the formation of spectral lines in the solar atmosphere, with a particular focus on the chromospheric Ca II 854.2 nm line which is important for magnetic field diagnostics. Starting from state-of-the-art numerical simulations, modern radiative transfer codes have been used to calculate synthetic spectra, including the effects of Zeeman polarization. Combining the physical state of the model atmospheres with the resulting synthetic spectra has allowed us to investigate how these correlate, thereby guiding the interpretation of real observations. We have used simulations of differing resolutions to estimate the effect of spatially unresolved processes on inferences of atmospheric quantities from spectra. Furthermore, we have examined the use of clustering techniques to classify the shapes of the spectral profiles generated from simulations, and studied how these shapes correlate with the simulations’ atmospheric structure. We have also employed these clustering methods to characterize, contrast and compare the spectra from simulations with the spectra from real observations.

Motivation & Objective

• To assess how differences in numerical resolution in 3D rMHD simulations impact inferred line-of-sight velocities and magnetic fields when spectra are degraded to common observational resolution.
• To investigate whether sub-resolution structures in high-resolution simulations leave systematic imprints on degraded spectra that affect inversion results.
• To evaluate the performance of the STiC inversion code on spectra degraded from simulations with varying spatial resolution.
• To determine the optimal numerical resolution for minimizing sub-resolution effects in synthetic observations of the solar chromosphere and photosphere.
• To provide guidance on resolution requirements in simulations to ensure reliable inferences when compared to real observations.

Proposed method

• Simulations were generated using the Bifrost code at horizontal grid spacings of 6 km, 12 km, and 23 km, starting from identical initial conditions and snapshots taken at the same elapsed time.
• Synthetic spectra for the Fe I 617.33 nm line (LTE) and Ca II 854.209 nm line (non-LTE) were produced using the RH 1.5D code.
• Spectra from the highest-resolution simulation (6 km) were spatially degraded via Gaussian convolution to match the 23 km resolution, enabling direct comparison across resolutions.
• Simple inference methods—center-of-gravity and weak-field approximation—were applied to degraded spectra to estimate line-of-sight velocities and magnetic fields.
• The STiC inversion code was applied to the degraded spectra to retrieve atmospheric parameters, including line-of-sight velocity, magnetic field strength, and temperature.
• Results were compared pixel-by-pixel across resolutions, with statistical distributions analyzed at different optical depth (log τ₅₀₀₀) levels.

Experimental results

Research questions

• RQ1 How do synthetic spectra from simulations with different spatial resolutions compare after spatial degradation to a common resolution?
• RQ2 To what extent do sub-resolution structures in high-resolution simulations bias inferred line-of-sight velocities and magnetic fields when spectra are degraded?
• RQ3 How do the retrieved atmospheric parameters from the STiC inversion code vary with the original simulation resolution, despite identical observational degradation?
• RQ4 What is the quantitative impact of progressively finer sub-resolution structures on inversion errors, and does this effect diminish with increasing resolution?
• RQ5 What is the optimal numerical resolution for simulations to minimize systematic errors in inferred atmospheric parameters when compared to real observations?

Key findings

• Even after spatial degradation to the same resolution, higher-resolution simulations (6 km) reveal more fine-grained structures and more extreme line-of-sight velocities and magnetic fields than lower-resolution simulations (23 km).
• Sub-resolution effects in high-resolution simulations leave systematic imprints on degraded spectra, leading to biased inversion results, with the magnitude of error increasing with the amount of unresolved structure.
• The impact of sub-resolution effects on inversion errors diminishes with progressively finer resolution, indicating a trend of diminishing returns beyond a certain threshold.
• The STiC inversion results show that simulations with 12 km grid spacing already capture most of the relevant dynamics and magnetic structure, reducing the need for even finer grids.
• A numerical grid size of approximately half the target observational resolution (e.g., 12 km for 100 km resolution) is recommended to minimize sub-resolution biases in inferred atmospheric parameters.
• The study suggests that a 23 km grid spacing in simulations is roughly equivalent to an observational resolution of 100 km pix⁻¹, and that 12 km resolution significantly reduces leakage of unresolved structure into inferred quantities.