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A higher-than-predicted measurement of iron opacity at solar interior temperatures

Abstract

Nearly a century ago it was recognized1 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 models2,3,4,5. A particular problem arose2,3,6,7,8 when refined photosphere spectral analysis9,10 led to reductions of 30–50 per cent in the inferred amounts of carbon, nitrogen and oxygen in the Sun. Standard solar models11 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 predicted2,3,6,7,8, because increased opacity compensates for the decreased element abundances. Iron accounts for a quarter of the total opacity2,12 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) × 1022 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.

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Figure 1: Experiment diagram and example transmission image.
Figure 2: Measured iron opacity spectra at four Te/ne values compared with calculations.
Figure 3: Comparisons of iron opacity spectra with multiple models at the solar radiation/convection zone boundary temperature.
Figure 4: Measured iron opacity impact on solar mixture Rosseland mean.

References

  1. Eddington, A. S. The Internal Constitution of the Stars (Cambridge Univ. Press, 1926)

    MATH  Google Scholar 

  2. Basu, S. & Antia, H. M. Helioseismology and solar abundances. Phys. Rep. 457, 217–283 (2008)

    ADS  CAS  Article  Google Scholar 

  3. Basu, S., Grevesse, N., Mathis, S. & Turck-Chièze, S. Understanding the internal chemical composition and physical processes of the solar interior. Space Sci. Rev. http://dx.doi.org/10.1007/s11214-014-0035-9 (2014)

  4. Christensen-Dalsgaard, J. in Proc. IAU Symp. No. 258, The Ages of Stars (2008) (eds Mamajek, E. E., Soderblom, D. R. & Wyse, R. F. G. ) 431–442 (International Astronomical Union, 2009)

  5. Delahaye, F. & Pinsonneault, M. Comparison of radiative accelerations obtained with atomic data from OP and OPAL. Astrophys. J. 625, 563–574 (2005)

    ADS  Article  Google Scholar 

  6. Bahcall, J. N., Serenelli, A. M. & Pinsonneault, M. How accurately can we calculate the depth of the solar convective zone? Astrophys. J. 614, 464–471 (2004)

    ADS  CAS  Article  Google Scholar 

  7. Turck-Chièze, S. et al. Surprising Sun: a new step towards a complete picture? Phys. Rev. Lett. 93, 211102 (2004)

    ADS  Article  Google Scholar 

  8. Serenelli, A. M., Basu, S., Ferguson, J. W. & Asplund, M. New solar composition: the problem with solar models revisited. Astrophys. J. 705, L123–L127 (2009)

    ADS  CAS  Article  Google Scholar 

  9. Asplund, M., Grevesse, N., Sauval, J. A. & Scott, P. The chemical composition of the Sun. Annu. Rev. Astron. Astrophys. 47, 481–522 (2009)

    ADS  CAS  Article  Google Scholar 

  10. Caffau, E. et al. Solar chemical abundances determined with a CO5BOLD 3D model atmosphere. Sol. Phys. 268, 255–269 (2011)

    ADS  CAS  Article  Google Scholar 

  11. Bahcall, J. N. et al. Standard solar models and the uncertainties in predicted capture rates of solar neutrinos. Rev. Mod. Phys. 54, 767–799 (1982)

    ADS  CAS  Article  Google Scholar 

  12. Blancard, C., Cosse & Faussurier, G. Solar mixture opacity calculations using detailed configuration and level accounting treatments. Astrophys. J. 745, 10 (2012)

    ADS  Article  Google Scholar 

  13. Nahar, S. N., Pradhan, A. K., Chen, G.-X. & Eissner, W. Highly excited core resonances in photoionization of Fe XVII: implications for plasma opacities. Phys. Rev. A 83, 053417 (2011)

    ADS  Article  Google Scholar 

  14. Rosseland, S. Note on the absorption of radiation within a star. Mon. Not. R. Astron. Soc. 84, 525–528 (1924)

    ADS  Article  Google Scholar 

  15. Perry, T. S. et al. Absorption experiments on x-ray-heated mid-Z constrained samples. Phys. Rev. E 54, 5617–5631 (1996)

    ADS  CAS  Article  Google Scholar 

  16. Bailey, J. E. et al. Experimental investigation of opacity models for stellar interior, inertial fusion, and high energy density plasmas. Phys. Plasmas 16, 058101 (2009)

    ADS  Article  Google Scholar 

  17. Bailey, J. E. et al. Iron-plasma transmission measurements at temperatures above 150 eV. Phys. Rev. Lett. 99, 265002 (2007)

    ADS  CAS  Article  Google Scholar 

  18. Rochau, G. A. et al. ZAPP: the Z Astrophysical Plasma Properties collaboration. Phys. Plasmas 21, 056308 (2014)

    ADS  Article  Google Scholar 

  19. Davidson, S. J. et al. Investigation of the opacity of hot, dense aluminum in the region of its K edge. Appl. Phys. Lett. 52, 847–849 (1988)

    ADS  CAS  Article  Google Scholar 

  20. Foster, J. M. et al. L-shell absorption spectrum of an open-M-shell germanium plasma: comparison of experimental data with a detailed configuration-accounting calculation. Phys. Rev. Lett. 67, 3255–3258 (1991)

    ADS  CAS  Article  Google Scholar 

  21. Nash, T. J., Rochau, G. A. & Bailey, J. E. Design of dynamic Hohlraum opacity samples to increase measured sample density on Z. Rev. Sci. Instrum. 81, 10E518 (2010)

    CAS  Article  Google Scholar 

  22. Nagayama, T. et al. Control and diagnosis of temperature, density, and uniformity in x-ray heated iron/magnesium samples for opacity measurements. Phys. Plasmas 21, 056502 (2014)

    ADS  Article  Google Scholar 

  23. Hansen, S., Bauche, J., Bauche-Arnoult, C. & Gu, M. Hybrid atomic models for spectroscopic plasma diagnostics. High Energy Density Phys. 3, 109–114 (2007)

    ADS  CAS  Article  Google Scholar 

  24. Iglesias, C. A. & Rogers, F. J. Opacities for the solar radiative interior. Astrophys. J. 371, 408–417 (1991)

    ADS  CAS  Article  Google Scholar 

  25. Seaton, M. J., Yu, Y., Mihalas, D. & Pradhan, A. K. Opacities for stellar envelopes. Mon. Not. R. Astron. Soc. 266, 805–828 (1994)

    ADS  CAS  Article  Google Scholar 

  26. Badnell, N. R. et al. Updated opacities from the opacity project. Mon. Not. R. Astron. Soc. 360, 458–464 (2005)

    ADS  CAS  Article  Google Scholar 

  27. Colgan, J. et al. Light element opacities from ATOMIC. High Energy Density Phys. 9, 369–374 (2013)

    ADS  CAS  Article  Google Scholar 

  28. Porcherot, Q., Pain, J.-C., Gilleron, F. & Blenski, T. A consistent approach for mixed detailed and statistical calculation of opacities in hot plasmas. High Energy Density Phys. 7, 234–239 (2011)

    ADS  CAS  Article  Google Scholar 

  29. Bailey, J. E. et al. Dynamic hohlraum radiation hydrodynamics. Phys. Plasmas 13, 056301 (2006)

    ADS  Article  Google Scholar 

  30. Bailey, J. E. et al. Diagnosis of x-ray heated Mg/Fe opacity research plasmas. Rev. Sci. Instrum. 79, 113104 (2008)

    ADS  CAS  Article  Google Scholar 

  31. Jeynes, C., Barradas, N. P. & Szilágyi, E. Accurate determination of quantity of material in thin films by Rutherford backscattering spectrometery. Anal. Chem. 84, 6061–6069 (2012)

    CAS  Article  Google Scholar 

  32. Loisel, G. et al. A methodology for calibrating wavelength dependent spectral resolution for crystal spectrometers. Rev. Sci. Instrum. 83, 10E133 (2012)

    CAS  Article  Google Scholar 

  33. Henke, B. L. et al. Low-energy x-ray response of photographic films. II. Experimental characterization. J. Opt. Soc. Am. B 1, 828–849 (1984)

    ADS  CAS  Article  Google Scholar 

  34. Nagayama, T. et al. Parallax diagnostics of radiation source geometric dilution for iron opacity experiments. Rev. Sci. Instrum. 85, 11D603 (2014)

    CAS  Article  Google Scholar 

  35. MacFarlane, J. J. et al. in Proc. Int. Symp. on Inertial Fusion Science and Applications (Monterey, California, 2003) 457–464 (American Nuclear Society, 2003)

  36. Henke, B. L., Gullikson, G. M. & Davis, J. C. X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92. At. Data Nucl. Data Tables 54, 181–342 (1993)

    ADS  CAS  Article  Google Scholar 

  37. del Grande, N. K. L Shell photoabsorption spectroscopy for solid metals: Ti, V, Cr, Fe, Ni, Cu. Phys. Scr. 41, 110–114 (1990)

    ADS  CAS  Article  Google Scholar 

  38. Zheng, L., Cui, M.-Q., Zhu, J. & Zhao, Y.-D. Determination of the photoabsorption cross-sections of Al and Fe films in the soft x-ray region using synchrotron radiation. High Energy Phys. Nuclear Phys. 28, 1121–1125 (2004)

    CAS  Google Scholar 

  39. Cowan, R. D. The Theory of Atomic Structure and Spectra (Univ. California Press, 1981)

    Google Scholar 

  40. MacFarlane, J. J., Golovkin, I. E. & Woodruff, P. R. HELIOS-CR—a 1-D radiation-magnetohydrodynamics code with inline atomic kinetics modeling. J. Quant. Spectrosc. Radiat. Transf. 99, 381–397 (2006)

    ADS  CAS  Article  Google Scholar 

  41. Nagayama, T. et al. Investigation of iron opacity experiment plasma gradients with synthetic data analyses. Rev. Sci. Instrum. 83, 10E128 (2012)

    CAS  Article  Google Scholar 

Download references

Acknowledgements

Sandia is a multiprogramme laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000. The Los Alamos National Laboratory is operated by Los Alamos National Security, LLC, for the NNSA of the US DOE under contract number DE-AC5206NA25396. J.E.B. acknowledges support from a DOE High Energy Density Laboratory Plasmas grant. A.K.P. and C.O. also acknowledge support from a DOE High Energy Density Laboratory Plasmas grant. We appreciate the efforts of the entire Z facility team. We thank S. Turck-Chièze, H. Morris, and M. Pinsonneault for discussions. We also thank R. W. Lee for critiquing the manuscript. We appreciate support for the experiments provided by R. J. Leeper, J. L. Porter, M. K. Matzen and M. Herrmann.

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Authors and Affiliations

Authors

Contributions

These measurements were conceived and planned by J.E.B. and G.A.R. J.E.B. was the primary author of the manuscript, with important contributions from T.N. Experiments were conducted by J.E.B., G.A.R. and G.P.L. The Z-facility data were analysed by T.N., J.E.B. and G.P.L., with assistance from G.A.R., C.A.I., B.G.W., I.G., J.J. M. and R.C.M. OPAS calculations were performed by C.B., G.F. and Ph.C. ATOMIC calculations were performed by J.C., with assistance from C.F., D.P.K. and M.S. SCRAM calculations were provided by S.B.H. SCO calculations were performed by J.-C.P. and F.G. OP calculations were performed by C.O., with assistance from A.K.P. and S.N.N. All authors discussed the results, commented on the manuscript, and contributed to the interpretation.

Corresponding author

Correspondence to J. E. Bailey.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Schematic diagram of four sample configurations used in Z opacity experiments.

The FeMg layer (red line) is completely encapsulated by the CH (blue) in order to avoid exposure to atmosphere during the experiment preparation. One sample type employed a Be tamper (yellow) to provide additional tamping while greatly reducing both the attenuation and emission in comparison with CH. Te and ne both increase as the tamper mass increases. The tamper thicknesses and the resulting average Te and ne values22 are listed below each sample type. Experiments were also conducted using the same tamper construction, but without the FeMg layer, to provide calibrations of the opacity measurement accuracy.

Extended Data Figure 2 Data illustrating the transmission determination method.

The five experiments shown here were conducted with a CH + Be tamper. a, The seven measurements of the unattenuated spectral intensity I from five experiments using the CCP4a and CCP10a spectrometers are denoted with black lines. The mean spectral intensity <I> (red) is used to determine transmission, [σ/I]abs represents the absolute percentage unattenuated spectrum 1σ uncertainty (green), and [σ/I]rel represents the relative percentage 1σ uncertainty as a function of wavelength (blue). A similar collection of data are obtained from the seven CCP4b and CCP10b spectrometer measurements. (arb, arbitrary units.) b, The attenuated (red) and unattenuated (blue) spectral intensities used to determine the transmission on experiment Z2624. These data were recorded with the CCP4a and CCP10a crystals and a similar data set (not shown) was recorded with the CCP4b and CCP10b crystals. c, The transmissions T measured on Z2624 agree within the 1σ uncertainties. d, The optical depth (τ, red) inferred by taking the natural log of the mean transmission measured on Z2624 includes contributions from both Fe and Mg. The optical depth corresponding to the iron contribution only (black) is inferred by subtracting the Mg contribution calculated with PrismSPECT35 (blue) from the FeMg mixture measurement. e, The mean opacities κ inferred from the three Be-tamped iron opacity measurements (solid), along with 1σ fractional absolute uncertainties (dashed). f, These measurements are combined to infer the overall mean opacity (<κ>, red) and associated 1σ fractional uncertainty (blue) for these conditions. The error bars in b, c, and e represent the 1σ uncertainty.

Extended Data Figure 3 The measured Z iron opacity exceeds the room-temperature value for wavelengths where models predict the opacity is dominated by photoionization.

a, The measured iron opacity from the Be-tamped result is larger than the room-temperature value36,37 for wavelengths shorter than approximately 9 Å. The error bars correspond to 1σ uncertainties. b, The SCRAM opacity model predicts that the ratio of the bound–free (BF) opacity contribution with the total opacity (blue) is larger than the ratio of the bound–bound (BB) opacity contribution with the total (red) for wavelengths less than approximately 9.5 Å.

Extended Data Figure 4 Beer–Lambert–Bouguer scaling test for Be-tamped iron opacity data.

The transmission should scale according to T2  = T1Nx2/Nx1, where Nx1 and Nx2 are areal densities associated with transmissions T1 and T2. The thick iron sample transmission Tthick (NX ≈ 1.91 × 1018 atoms per cm2) is shown in red (left axis). The average transmission for the two experiments using a thin iron sample (NX ≈ 0.98 × 1018 atoms per cm2) was scaled by the ratio of the areal densities (Tscaled; blue). The error bars represent 1σ uncertainties. A quantitative evaluation is provided by taking the ratio of the transmission difference with the summed 1σ uncertainties (black; right axis). Values below unity (dashed black) satisfy the scaling test.

Extended Data Figure 5 Evaluation of changes in the model–data comparisons at the error bounds determined for the plasma conditions.

The measured iron opacity at Te = 2.11 × 106 K and ne = 3.1 × 1022 cm−3 is denoted with a black line, with error bars corresponding to the 1σ uncertainty. SCRAM23 calculations are shown at the nominal conditions in blue, at the minimum Te, maximum ne in red and at the maximum Te, minimum ne in green. The minimum Te, maximum ne values lead to the lowest ionization and the maximum Te, minimum ne values lead to the highest ionization.

Extended Data Table 1 Sample specifications for Z opacity experiments

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Bailey, J., Nagayama, T., Loisel, G. et al. A higher-than-predicted measurement of iron opacity at solar interior temperatures. Nature 517, 56–59 (2015). https://doi.org/10.1038/nature14048

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