New Measurement Resolves Key Astrophysical Fe XVII Oscillator Strength Problem

One of the most enduring and intensively studied problems of x-ray astronomy is the disagreement of state-of-the art theory and observations for the intensity ratio of two Fe XVII transitions of crucial value for plasma diagnostics, dubbed $3C$ and $3D$. We unravel this conundrum at the PETRA III synchrotron facility by increasing the resolving power 2.5 times and the signal-to-noise ratio thousandfold compared with our previous work. The Lorentzian wings had hitherto been indistinguishable from the background and were thus not modeled, resulting in a biased line-strength estimation. The present experimental oscillator-strength ratio $R_{\exp }=f_{3C}/f_{3D}=3.51(2{)}_{\mathrm{stat}}(7{)}_{\mathrm{sys}}$ agrees with our state-of-the-art calculation of $R_{\mathrm{th}}=3.55(2)$, as well as with some previous theoretical predictions. To further rule out any uncertainties associated with the measured ratio, we also determined the individual natural linewidths and oscillator strengths of $3C$ and $3D$ transitions, which also agree well with the theory. This finally resolves the decades-old mystery of Fe XVII oscillator strengths.

Figure 1

Fluorescence yield of the soft x-ray transitions $3C$ and $3D$ of Fe XVII as well as $B$ and $C$ of Fe XVI as a function of the exciting-photon energy. Fitted Voigt profiles (orange) show residuals (bottom panel) due to a nonperfectly Gaussian distribution of the monochromator spectral bandwidth. Inset (right): $3C$ comparison between present and previous [55] works. Inset (left): resolved $C$ and $3D$ from this work compared to unresolved in LCLS measurements (green [24]) and Capella observations (red [76]).

Figure 2

Left: Synthetic Voigt profiles for $C$ (purple) and $3D$ (red). Predicted natural linewidths are convolved with a Gaussian component. At similar line intensities, the overlapping product is only 1% of the total $3D$ intensity, which suppresses feeding of the $3D$ lower state in Fe XVII from the upper level of $C$ in Fe XVI through an autoionization decay branch of $\approx 60\%$. Right: Synthetic $3C$ Voigt profile without (blue) and with a strong background (green) as in Ref. [55] for comparison. A Gaussian model (orange) fitted to this curve can hardly separate the Lorentzian wings from the background and recovers only 94% of the true intensity. There, a Voigt fit to the data from Ref. [55] also does not work well at the wings due to the low SNR.

Figure 3

Present experimental $3C/3D$ oscillator-strength ratio compared with predictions, including our own, shown in an inset. Theoretical approaches [28, 29, 35, 37, 38, 39, 40, 41, 51, 54, 55, 82, 83, 84, 85, 86, 87] are marked as follows: Distorted wave (magenta hexagons), multiconfiguration Dirac-Fock (teal diamonds), $R$ matrix (blue triangles), many-body perturbation theory (orange crosses), and configuration interaction (black circles). Blue band: observed line ratios in astrophysical sources [12, 19, 26, 88, 89, 90], with color shades coding the distribution of values weighted by their reported accuracies. Purple band: spread of tokamak results [46]. Black diamonds: previous EBIT results [24, 33, 47, 55]. Navy blue squares: spectral plasma models and databases [82, 91, 92, 93]. The data behind the figure are given in the Supplemental Material [66].