Systematic Study of $L$-Shell Opacity at Stellar Interior Temperatures

The first systematic study of opacity dependence on atomic number at stellar interior temperatures is used to evaluate discrepancies between measured and modeled iron opacity [J. E. Bailey et al., Nature (London) 517, 56 (2015)]. High-temperature ($>180\mathrm{eV}$) chromium and nickel opacities are measured with $\pm 6\%–10\%$ uncertainty, using the same methods employed in the previous iron experiments. The 10%–20% experiment reproducibility demonstrates experiment reliability. The overall model-data disagreements are smaller than for iron. However, the systematic study reveals shortcomings in models for density effects, excited states, and open $L$-shell configurations. The 30%–45% underestimate in the modeled quasicontinuum opacity at short wavelengths was observed only from iron and only at temperature above 180 eV. Thus, either opacity theories are missing physics that has nonmonotonic dependence on the number of bound electrons or there is an experimental flaw unique to the iron measurement at temperatures above 180 eV.

Figure 1

(a) Opacity-experiment setup. (b) Target side view. (c) Dominant electron configurations of Cr, Fe, and Ni at achieved conditions. Vacancies in the shells are indicated by open circles.

Figure 2

Reproducibility in measured opacities for (a) Cr and (b) Ni. Each color corresponds to independent experiments with their sample areal densities ($\text{g}/{\mathrm{cm}}^2$) embedded in the figure.

Figure 3

Comparison of OP opacity (red line) and measured opacity (black line) approximately at 180 eV and $3\times {10}^{22}{\mathrm{cm}}^{-3}$ for (a) Cr, (b) Fe, and (c) Ni. Fe data and calculation are adopted from Fig. 3 of BNLR15. Opacities over 9.1–9.3 Å depend on the accuracy of Mg He-$\alpha$ removal and are not shown here. Wavelength upper limit is determined by the onset of strong lines from $n=2\to 3$ transitions, which are still under investigation.

Figure 4

Enlarged comparison of measured (black line) and modeled (colored lines) opacities for (a) Cr, (b) Fe, and (c) Ni over the window and $2p\text{−}4d$ bound-bound lines. While only two models are compared in each plot for clarity, the level of disagreement is similar for all models. The opacity-window (black arrows) disagreement is not observed for Ni, potentially due to closed $L$-shell configuration.

Figure 5

(a) Reproducibility in Ne-like Ni $2p\text{−}4d$ line shapes. (b) Model-dependent variation of calculated Ne-like Ni $2p\text{−}4d$ line opacity (without instrument-broadening effects). (c) Comparisons of measured (black line) and modeled (colored lines) line shapes (with instrumental transmission resolution, see text). Only the broadest one shows good agreement; other models require 60%–90% extra broadening.

Figure 6

Comparison of measured (black line) and modeled (colored lines) quasicontinuum opacities for (a) Cr, (b) Fe, and (c) Ni, revealing notable discrepancy only from Fe. Models: ATOMIC (green line), OPAS (purple line), SCO-RCG (cyan line), SCRAM (orange line), and TOPAZ (gray line).