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

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. These assumptions include all ion charge-states being in the ground state, and steady-state equilibrium where there is sufficient time for ionisation and recombination to take place. 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. As density increases metastable levels become populated and ionisation rates increase, whereas dielectronic recombination through the highly-excited levels becomes suppressed. Photo-ionisation was also shown by Nussbaumer & Storey to have an effect on the charge-state distribution of carbon in these regions. 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 using the Flexible Atomic Code and Autostructure, 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.

Modelling low charge ions in the solar atmosphere

“…Concerning free electron processes in the lower atmosphere, Dufresne & Del Zanna (2019) and Dufresne et al (2020) show for carbon and oxygen that suppression of dielectronic recombination (DR) and ionisation and recombination from metastable levels notably alter ion formation. The latter effect is relatively stronger than the former in altering the charge state distribution for the first few charge states.…”

“…The present work is part of a series of papers with the aim of building on those pioneering works, in order to answer the questions raised above, and to provide modelling suitable for the transition region. Dufresne & Del Zanna (2019) and Dufresne et al (2020) develop the coronal approximation of carbon and oxygen by adding the effects modelled by Burgess & Summers (1969) and Nussbaumer & Storey (1975). It is shown that, by including the effects of density on the electron collisional processes, predicted intensities are in better agreement with observations for the lines emitted below 100 000 K, when compared to coronal approximation modelling.…”

Atomic Data for Plasma Spectroscopy: The CHIANTI Database, Improvements and Challenges

“…As it turns out that CI from (populated) excited states is very important for the calculation of the charge state distribution, an effort is ongoing to calculate DI with FAC, and EA with the available R-matrix CE rates. Rates for the carbon and oxygen ions have been produced [55,56], and further work is ongoing.…”

“…One way to estimate the DR suppression is therefore to use the recent DR project rates and apply the variation with density found by [67]. This approximation has been adopted by [55,56] using directly the effective rates of [67], and by [68] using the empirical formulae of [69] which aim to reproduce the same effective rates. The [69] formulae will be introduced in CHIANTI version 10 to improve the modeling of high density plasma (on a side note, earlier empirical formulae by [70] were affected by a few problems).…”

“…A first step towards a proper modeling of the ion populations (neglecting the autoionizing levels) is the level-resolved collisional-radiative modeling developed for the carbon ions by [55]. All the J-resolved states in the six ionization stages, plus the bare nuclei have been included in a single matrix formulation, and level populations of all the ions obtained at once.…”