Density-dependent ionization equilibria for carbon with kappa distributions

¹ Astronomical Institute of the Czech Academy of Sciences, Fričova 298, Ondřejov, Czech Republic
² DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

Received: 4 July 2024
Accepted: 13 September 2024

Abstract

Context. Recent atomic models for the solar transition region have shown the importance of electron density, photoionization, and charge transfer on the ionization equilibria and line intensities of several elements and ions, especially from the Li- and Na-like ion sequences.

Aims. Non-Maxwellian electron distributions have been proposed as one solution that may account for the discrepancies. We have studied the interplay of the new atomic models with the effects of energetic particles, which have been shown to alter ionization equilibria considerably.

Methods. Level-resolved ionization and recombination rates were calculated for non-Maxwellian kappa distributions and included in a collisional-radiative model for carbon. The effect of photoionization and density suppression of dielectronic recombination for kappa distributions were also included in the models, and the models were run at a variety of densities and pressures.

Results. We find that the level-resolved collisional ionization rates increase with electron density, while the radiative and dielectronic recombination rates decrease. Their overall effect on the ionization equilibrium is to shift the formation of the lower charge states to a lower temperature and increase their peak abundance, especially for C IV. These shifts are not as significant as the effects of the non-extensive shape parameter given by the thermodynamic kappa index, κ. With decreasing κ; that is, with increasing departure from a Maxwellian distribution, ion formation moves to a much lower temperature, ion formation takes place over a wider temperature range, and peak abundances decrease. The effect of level-resolved rates and density suppression on the ion balances diminishes as κ decreases. Photoionization is shown to be significant only at relatively low densities and high κ.

Conclusions. Density effects are an important factor to consider in higher-density plasma and improve on the coronal approximation, even where there are significant departures from Maxwellian energy distributions. However, the changes they make to ion formation are not as significant as when there are electron distributions with very low κ-values.