# Modelling ion populations in astrophysical plasmas: carbon in the solar transition region

## TL;DR

This paper improves ion population modeling in the solar transition region by incorporating updated atomic data and processes, leading to more accurate predictions of spectral line intensities in the quiet Sun.

## Contribution

It introduces a new model for carbon ion populations using recent atomic rates and photo-ionising radiances, surpassing previous coronal approximation methods.

## Key findings

- Enhanced accuracy in predicted line intensities for carbon ions.
- Significant differences from earlier coronal approximation models.
- Better agreement with observed solar transition region spectra.

## Abstract

The aim of this work is to improve the modelling of ion populations in higher density, lower temperature astrophysical plasmas, of the type commonly found in lower solar and stellar atmospheres. Ion population models for these regions frequently employ the coronal approximation, which assumes conditions more suitable to the upper solar atmosphere, where high temperatures and lower densities prevail. Using the coronal approximation for modelling the solar transition region gives theoretical lines intensities for the Li-like and Na-like isoelectronic sequences which can be factors of 2-5 times lower than observed. The works of Burgess & Summers (1969) and Nussbaumer & Storey (1975) showed the important part ions in excited levels play when included in the modelling. Their models, however, used approximations for the atomic rates to determine the ion balance. Presented here is the first stage in updating these earlier models of carbon by using rates from up-to-date atomic calculations and more recent photo-ionising radiances for the quiet Sun. Where such atomic rates are not readily available, in the case of electron-impact direct ionisation and excitation--auto-ionisation, new calculations have been made and compared to theoretical and experimental studies. The effects each atomic process has on the ion populations as density changes is demonstrated, and final results from the modelling are compared to the earlier works. Lastly, the new results for ion populations are used to predict line intensities for the solar transition region in the quiet Sun, and these are compared with predictions from coronal-approximation modelling and with observations. Significant improvements in the predicted line intensities are seen in comparison to those obtained from zero-density modelling of carbon.