Interface of equation of state, atomic data, and opacities in the solar problem

Abstract

The dependence of the Rosseland Mean Opacity (RMO) on the equation-of-state and the number of included atomic levels of iron ions prevalent at the solar radiative/convection boundary is investigated. The ”chemical picture” Mihalas-Hummer-Däppen MHD-EOS, and its variant QMHD-EOS, are studied at two representative temperature-density sets at the base of the convection zone (BCZ) and the Sandia Z experiment: (2 × 106K, 1023/cc) and (2.11 × 106K, 3.16 × 1022/cc), respectively. It is found that whereas the new atomic datasets from accurate R-matrix calculations for opacities (RMOP) are vastly overcomplete, involving hundreds to over a thousand levels of each of the three Fe ions considered — Fe xvii , Fe xviii , Fe xix — the EOS constrains contributions to RMOs by relatively fewer levels. The RMOP iron opacity spectrum is quite different from the Opacity Project distorted wave model and shows considerably more plasma broadening effects. This work points to possible improvements needed in the EOS for opacities in high-energy-density (HED) plasma sources.

R-matrix calculations for opacities: I. Methodology and computations

“…Previous works have discussed the inexplicable differences of orders of magnitude in occupation probabilities between OP and OPAL [36]. The EOS issue therefore remains open for future study [4].…”

“…The most important consequence, and likely source of missing opacity, is the intrinsic autoionizing broadening and the extrinsic plasma broadening thereof. The much wider spread of resonances in the continuum than lines raises the opacity significantly [4,25,26].…”

“…Opacity increases due to the prevalence of lower stages of ionization, as more bound electrons are active in absorption of radiation via larger number of bound-bound and bound-free transitions than at higher temperatures below the BCZ. Table 2 shows the ionization states of the dominant elements that determine opacity at the BCZ: O, Ne and Fe [4,19]. Almost 90% oxygen is in H-like or fully ionized [4], and 86% of neon is in H-like and He-like ionization states.…”

“…Table 2 shows the ionization states of the dominant elements that determine opacity at the BCZ: O, Ne and Fe [4,19]. Almost 90% oxygen is in H-like or fully ionized [4], and 86% of neon is in H-like and He-like ionization states. But one and two electron K-shell ionization states do not contribute as much to opacity, as lower ones such as the partially filled Lshell Fe ions with percentage contributions given in table 2.…”

“…absorption and scattering of photons by atoms at all frequencies of radiation prevalent in a given environment. Methods for calculating opacities are well-established, and essentially involve the atomic physics of bound-bound and bound-free transition probabilities incorporated within an equation-ofstate (EOS) of the plasma [1][2][3][4]. However, in practice complexities arise owing to several physical factors that influence the accurate determination of opacity, and are addressed in this series of papers.…”