Diagnostics for the solar chromosphere using neutral carbon Rydberg lines

TL;DR

This paper investigates neutral-carbon Rydberg lines in the solar chromosphere as potential diagnostics, leveraging SB equilibrium for high-n levels with respect to the ground state of C$^+$ ($N_u/N_p$ as $N_u/N_p = (g_u/(2 g_p)) \sqrt{ (h^2/(2 \pi m_e k T_e))^3 } \exp( I_{up}/(k T_e) ) N_e$). A two-step forward-modeling approach within the 1D Lightweaver NLTE framework is used, combining SB-populated Rydberg levels with detailed line and continuum treatment and a PRD-inclusive hydrogen Lyman series, calibrated against SUMER data. The results show good agreement with observed lines at shorter wavelengths, reveal opacity-driven differences across Rydberg series, and map emission to heights from the temperature minimum up to about 1000–1800 km depending on the line, with clear sensitivity to C$^+$ ion fractions and continuum formation. The study demonstrates the diagnostic potential of hundreds of Rydberg lines for multi-height chromospheric inversions and highlights the upcoming EUVST mission as a key platform to exploit these lines for solar atmospheric diagnostics.

Abstract

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).

Figures (7)

• Figure 1: Schematic illustration of the formation mechanism of Ci Rydberg lines, including the series limits at UV wavelengths.
• Figure 2: Comparison of Ci Rydberg line intensities from the radiative transfer calculation with observations and with the relative intensities from the optically thin calculations of storey2023c1. The other main lines contributing to the spectrum that have been identified and are not being modelled here are indicated by black labels. The '/2' in the labels denotes a second order line in SUMER. All intensities are in erg s$^{-1}$ cm$^{-2}$ sr$^{-1}$ Å$^{-1}$.
• Figure 3: Contribution functions for all three Rydberg series. The $\tau=1$ layer (black dotted line) is also shown.
• Figure 4: The left plots show the source and Planck functions with height at line centres 1114.46 Å (upper plots) and 1256.50 Å (lower plots), the middle plots show the source functions with respect to wavelength and height, and the right plots show the contribution functions. The $\tau=1$ layer is shown on the contribution function plots by black dotted lines. Brighter colours indicate greater values of the source and contribution functions. Both sets of lines are emitted from upper levels with $2s^2\,2p\,10d,11s$ configurations.
• Figure 5: Response functions for the lines emitted by the $2s^2\,2p\,10d,11s$ levels, following temperature, electron density and micro-turbulent velocity perturbations.