Sequential spectral line analysis for accurate density and temperature diagnosis of laboratory opacity measurements

The accuracy of iron opacity calculated in stellar interiors has been questioned since the discovery of the "solar problem" and the discrepancies between the measured and modeled iron opacity reported in 2015. Experimental opacity benchmarks require accurate temperature and density measurements, which were inferred by analyzing tracer magnesium spectra in those experiments. Could the observed discrepancy be explained by insufficient accuracy in the inferred temperature, density, and their uncertainties? Previous analyses may have yielded biased results due to three limitations: (1) simultaneous multi-line fitting, (2) approximations in line-shape models, and (3) exclusion of certain spectral lines due to insufficient background characterization. Notably, the first issue is a common concern for many inversion methods, including Bayesian inferences. We present a refined analysis method that overcomes these limitations, applied to three categories of iron opacity experiments (Anchor 1, 2, and 3). In particular, the sequential fitting method yields unbiased results with more realistic uncertainties by accounting for line inconsistencies in the parameter uncertainties. The average electron temperature and density values are 162 ± 6 eV and (7.0 ± 1.9) × 1021 cm-3 for six Anchor 1 experiments, 189 ± 7 eV and (3.4 ± 0.3) × 1022 cm-3 for 21 Anchor 2 experiments, and 201 ± 6 eV and (4.8 ± 1.1) × 1022 cm-3 for nine Anchor 3 experiments. These results show ∼4% temperature and ∼20% density reproducibility over a decade, which also aligns with the inferred parameter uncertainties. The resulting temperature and density uncertainties lead to a quasi-continuum iron opacity variation of ±4%-7% for wavelengths below 9.5 Å, which is insufficient to explain the significant model-data discrepancies reported in 2015.