Diagnostics for the solar chromosphere using neutral carbon Rydberg lines

Diagnostics for the solar chromosphere are relatively few compared to other parts of the atmosphere. Despite this, hundreds of Rydberg lines emitted by neutrals in this region have been observed at UV wavelengths. Here, we investigate their diagnostic potential by modelling the lines emitted by neutral carbon using recent atomic data. We use the radiative transfer code Lightweaver to explore how they form and how they respond to temperature, density and micro-turbulent velocity perturbations in the atmosphere. To simplify the modelling, we investigate lines emitted from levels with principal quantum number $n\geq10$, which are expected to be in Saha-Boltzmann equilibrium with the ground state of the singly-charged ion. Optical depth effects are apparent in the lines and their response to atmospheric perturbations suggest that they will be useful in reconstructions of the atmosphere using inversions. The study opens the way for using many such lines emitted by multiple elements over a range of heights, a large number of which will be observed by the forthcoming Solar-C EUV High-throughput Spectroscopic Telescope (EUVST).

💡 Research Summary

This paper investigates the diagnostic potential of neutral‑carbon (C I) Rydberg lines in the solar chromosphere, focusing on transitions from highly excited levels with principal quantum numbers n ≥ 10. Hundreds of such lines have been observed in the far‑UV, but their use as chromospheric diagnostics has been limited because modelling them traditionally requires large, non‑LTE atomic models that include both neutral and singly‑ionised carbon and all the collisional and radiative processes linking them. The authors exploit the fact that, at chromospheric densities, the populations of the high‑n Rydberg levels are expected to be in Saha‑Boltzmann (SB) equilibrium with the ground state of C II. Consequently, the level populations can be expressed analytically in terms of the C II ion fraction, electron temperature, and electron density, bypassing the need for a full non‑LTE treatment of the Rydberg manifold.

The methodology combines the latest atomic data for C I Rydberg states (energies and Einstein A‑coefficients from Storey et al. 2023) with the 1‑D radiative‑transfer code Lightweaver (Osborne & Milic 2021). The calculation proceeds in two steps. First, a comprehensive non‑LTE model including H, He, C, O, Mg, Al, Si, S, and Fe is solved to obtain the ionisation balance and the populations of long‑lived lower levels. Second, the C I and C II ground and metastable levels are frozen, and the Rydberg levels are populated using the SB formula (Eq. 1). This hybrid approach dramatically reduces computational cost while retaining a physically realistic description of line formation.

The authors compute emergent intensities, contribution functions, and response functions for temperature, electron density, and micro‑turbulent velocity perturbations. Optical‑depth effects are evident, especially for the series converging near 1240 Å, where partial redistribution (PRD) of Lyman‑α and Lyman‑β photons influences the line wings. Response‑function analysis shows that a ±2 % temperature perturbation or a ±2 % density perturbation produces measurable changes in line strength, with higher‑n lines being more temperature‑sensitive. Micro‑turbulence (±100 m s⁻¹) mainly broadens the profiles with modest impact on core intensity.

Synthetic spectra are compared with SOHO/SUMER observations (Curdt et al. 2001) covering 680–1611 Å. In the 1100–1240 Å range the modeled line intensities and shapes agree very well with the observed spectrum, confirming that the SB‑populated Rydberg levels capture the essential physics. At longer wavelengths (> 1450 Å) the synthetic lines are 2–3 times weaker than observed, suggesting either an underestimation of the C II ion fraction in the model atmosphere or contamination by unidentified molecular or blended lines.

The study emphasizes that Rydberg lines from multiple elements (C, O, Si, S) form over a range of heights, offering a dense set of diagnostics spanning the lower chromosphere to the temperature minimum. With the upcoming Solar‑C EUV High‑throughput Spectroscopic Telescope (EUVST) poised to deliver high‑resolution, high‑throughput UV spectra, hundreds of such lines will become routinely observable. The demonstrated sensitivity of C I Rydberg lines to temperature, density, and velocity perturbations makes them promising candidates for multi‑line inversions, potentially enabling three‑dimensional reconstructions of chromospheric structure.

In conclusion, the paper shows that neutral‑carbon Rydberg lines, despite exhibiting optical‑depth and PRD effects, can be modelled efficiently using SB equilibrium for the high‑n levels. Their strong response to key atmospheric parameters, combined with the imminent observational capabilities of EUVST, opens a new avenue for chromospheric diagnostics and will provide valuable constraints for state‑of‑the‑art magnetohydrodynamic simulations of the solar atmosphere.