Nearly a century ago it was recognized that radiation absorption by stellar matter controls the internal temperature profiles within stars. Laboratory opacity measurements, however, have never been performed at stellar interior conditions, introducing uncertainties in stellar models. A particular problem arose when refined photosphere spectral analysis led to reductions of 30-50 per cent in the inferred amounts of carbon, nitrogen and oxygen in the Sun. Standard solar models using the revised element abundances disagree with helioseismic observations that determine the internal solar structure using acoustic oscillations. This could be resolved if the true mean opacity for the solar interior matter were roughly 15 per cent higher than predicted, because increased opacity compensates for the decreased element abundances. Iron accounts for a quarter of the total opacity at the solar radiation/convection zone boundary. Here we report measurements of wavelength-resolved iron opacity at electron temperatures of 1.9-2.3 million kelvin and electron densities of (0.7-4.0) × 10(22) per cubic centimetre, conditions very similar to those in the solar region that affects the discrepancy the most: the radiation/convection zone boundary. The measured wavelength-dependent opacity is 30-400 per cent higher than predicted. This represents roughly half the change in the mean opacity needed to resolve the solar discrepancy, even though iron is only one of many elements that contribute to opacity.

Absorption and emission spectra of plasmas with multicharged-ions contain transition arrays with a huge number of coalescent electricdipole (E1) lines, which are well suited for treatment by the unresolved transition array and derivative methods. But, some transition arrays show detailed features whose description requires diagonalization of the Hamiltonian matrix. We developed a hybrid opacity code, called SCORCG, which combines statistical approaches with fine-structure calculations consistently. Data required for the computation of detailed transition arrays (atomic configurations and atomic radial integrals) are calculated by the super-configuration code SCO (SuperConfiguration Opacity), which provides an accurate description of the plasma screening effects on the wave-functions. Level energies as well as position and strength of spectral lines are computed by an adapted RCG routine of R. D. Cowan. The resulting code provides opacities for hot plasmas and can handle mid-Z elements. The code is also a powerful tool for the interpretation of recent laser and Z -pinch experimental spectra, as well as for validation of statistical methods.

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Understanding stellar interiors, inertial confinement fusion, and Z pinches depends on opacity models for mid-Z plasmas in the 100-300 eV temperature range. These models are complex and experimental validation is crucial. In this paper we describe the diagnosis of the first experiments to measure iron plasma opacity at a temperature high enough to produce the charge states and electron configurations that exist in the solar interior. The dynamic Hohlraum x-ray source at Sandia National Laboratories' Z facility was used to both heat and backlight Mg/Fe CH tamped foils. The backlighter equivalent brightness temperature was estimated to be T(r) approximately 314 eV+/-8% using time-resolved x-ray power and imaging diagnostics. This high brightness is significant because it overwhelms the sample self-emission. The sample transmission in the 7-15.5 A range was measured using two convex potassium acid phthalate crystal spectrometers that view the backlighter through the sample. The average spectral resolution over this range was estimated to be lambda/deltalambda approximately 700 by comparing theoretical crystal resolution calculations with measurements at 7.126, 8.340, and 12.254 A. The electron density was determined to be n(e)=6.9+/-1.7 x 10(21) cm(-3) using the Stark-broadened Mg Hebeta, Hegamma, and Hedelta lines. The temperature inferred from the H-like to He-like Mg line ratios was T(e)=156+/-6 eV. Comparisons with three different spectral synthesis models all have normalized chi(2) that is close to unity, indicating quantitative consistency in the inferred plasma conditions. This supports the reliability of the results and implies the experiments are suitable for testing iron opacity models.

In multiply-charged ion plasmas, a significant number of electrons may occupy high-energy orbitals. These "Rydberg" electrons, when they act as spectators, are responsible for a number of satellites of X-ray absorption or emission lines, yielding a broadening of the red wing of the resonance lines. The contribution of such satellite lines may be important, because of the high degeneracy of the relevant excited configurations which give these large Boltzmann weights. However, it is in general difficult to take these configurations into account since they are likely to give rise to a large number of lines. We propose to model the perturbation induced by the spectators in a way similar to the PartiallyResolved-Transition-Array approach recently published by C. Iglesias. It consists in a partial detailedline-accounting calculation in which the effect of the Rydberg spectators is included through a shift and width, expressed in terms of the canonical partition functions, which are key-ingredients of the SuperTransition-Arrays model. The resulting method can a priori be used in any detailed-configuration/lineaccounting opacity code.

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 517, 56 (2015)]. Hightemperature (>180 eV) chromium and nickel opacities are measured with 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 short-wavelength quasi-continuum opacity was observed only from iron and only at temperature above 180 eV. Thus, either opacity theories are missing physics that has non-monotonic dependence on the number of bound electrons, or there is an experimental flaw unique to the iron measurement at temperatures above 180 eV.

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We found that in transition arrays of complex atomic spectra, the strengths of electric-dipolar lines obey Benford's law, which means that their significant digits follow a logarithmic distribution favoring the smallest values. This indicates that atomic processes result from the superposition of uncorrelated probability laws and that the occurence of digits reflects the constraints induced by the selection rules. Furthermore, Benford'law can be a useful test of theoretical spectroscopic models. Its applicability to the statistics of electric-dipolar lines can be understood in the framework of Random Matrix Theory and is consistent with the Porter-Thomas law.