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A Primer on Mean Opacities in the Radiative Transfer Equation

The radiative transfer equation is used in many applications, including the simulation of nuclear weapons. Opacity is a term that is often used in conjunction with the radiative transfer equation along with mean opacities. For someone new to the subject, there may be confusion over various parts of the radiative transfer equation or why opacities and mean opacities are so important to solving certain problems. This report aims to give a brief introduction to the radiative transfer equation as well as an explanation to why opacities and mean opacities are important. We also derive the Planck and Rosseland mean opacities, which are the most common mean opacities used in applications. At the end of the report are references that can be used to learn more about the subject.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Progress toward NIF opacity measurements

The opacities of iron and other mid-Z elements help to regulate the transport of energy in the sun. Recent experiments on the Sandia National Laboratories Z machine have shown large discrepancies between the measured and calculated opacities of iron at certain solar conditions. To replicate these opacity measurements a platform is being developed on the National Ignition Facility to measure the opacities of iron and other elements at the same conditions as in the Z experiments. The NIF platform consists of a hohlraum to heat the opacity sample to the desired conditions, a separate backlighter to radiograph the sample, and a spectrometer to give the spectrally resolved opacity. Not only must the opacity be measured but the temperature and density of the sample must also be accurately determined. This platform has now produced its first iron transmission measurements. Overall, these measurements will be presented along with plans for future measurements and details on how the measurements will be improved.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Role of opacity at the 9 keV back lighter energy used in measuring the equation of state of boron at pressures up to a Gbar

Many experiments have been conducted at the National Ignition Facility to measure the equation of state Hugoniot of plastic, boron, and diamond at extreme pressures up to a Gbar. The “Gbar” design employs a strong spherically converging shock launched through a solid ball of material using a hohlraum radiation drive. The shock front conditions are characterized using X-ray radiography, typically at energies near 9 keV. Here we examine how the opacity of boron at 9 keV changes at high pressures and temperatures. Understanding this is vital to unfolding the density in the shock front as pressures exceed 100 Mbar. We compare opacity calculations from a number of methods including the legacy XSN opacity tables, super transition array (STA), average atom (AVAT), and detailed configuration accounting (DCA) methods. We examine how the changing opacity is correlated with the K-shell occupation calculated using the opacity methods as well as other electronic structure methods such as MECCA, Purgatorio, and an all-electron Kohn-Sham density functional theory calculation that uses optimized all-electron norm-conserving Vanderbilt pseudopotentials (ONCV). We also examine the relative contribution of free-free opacity to the overall opacity, which is dominated by bound-free absorption.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Opacity: A window into High Energy Density Plasma Physics

Opacity is a fundamental property of matter and knowledge of it is required to understand the transport of radiation through a material. Exact knowledge of opacity is crucial in many fields such as astrophysics, which recently produced a white paper on the current state of astrophysical opacities [1], plasma physics, including inertial confinement fusion (ICF) and magnetic confinement fusion, high energy density physics (HEDP), the semiconductor industry [2] and stockpile stewardship. In industry, the accurate knowledge of the opacity of tin is important for extreme ultraviolet (EUV) lithography and the development of processors with smaller components. In astrophysics, Cepheid variable stars are used as “standard candles” for determining the distance to objects. Opacities of these stars are required to understand the relationship between their periodicity, luminosity and distance. Our sun is the most studied star and provides the basis of our understanding for other stars. Yet in significant ways the sun is poorly understood. In recent years, there has been a debate over the abundances of heavy elements (Z > 2) in the solar interior. Current solar atmosphere models [3] find a significantly lower abundance for C, N, and O compared to models used roughly a decade ago. Although solar evolution models have matured, a discrepancy still exists between spectroscopic solar models (which require opacities) with updated abundances, and solar properties inferred from helioseismology and neutrinos [4]. Despite its necessity, opacity is not solved, and is an open and active area of research needed for improving our understanding of plasma physics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

National Opacity Program - Tri-Lab Assessment of Measurements and Models (Milestone 7720)

Opacity-on-NIF has obtained opacity data under conditions similar to those achieved by the entirely different Opacity-on-Z platform. From low- and high-Z elements at different anchor points, rigorously compare the opacity data between the laboratories and to multiple opacity theory models. Compare and assess the data acquisition and processing methods for obtaining opacities and for measuring/inferring sample conditions. Explain, or develop hypotheses for, any discrepancies. Map progress to the National Opacity Strategy and define future directions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Milestone 7720: National Opacity Program - Tri-Lab Assessment of Measurements and Models

Opacity-on-NIF has obtained opacity data under conditions similar to those achieved by the entirely different Opacity-on-Z platform. From low- and high-Z elements at different anchor points, rigorously compare the opacity data between the laboratories and to multiple opacity theory models. Compare and assess the data acquisition and processing methods for obtaining opacities and for measuring/inferring sample conditions. Explain, or develop hypotheses for, any discrepancies. Map progress to the National Opacity Strategy and define future directions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Measurement of atmospheric opacity at 278 GHz at McMurdo Station, Antarctica in austral spring seasons, 1986 and 1987

A quasi-continuous record is presented of atmospheric opacity measured at 278 GHz (1.1 mm wavelength) from the McMurdo Station (Antarctica) during austral spring seasons of 1986 (August 30 - October 30) and 1987 (September 4 - October 13) with measurements taken every 20 minutes (except during storms or other periods of high opacity). All data are reduced to represent opacity in the zenith direction. It was found that, during much of September, the two successive years differed considerably in tropospheric opacity. In 1986, water vapor and attendant opacity were generally lower, due to low tropospheric temperatures. Measured opacities were found to be higher than would be expected from the empirical relationships representing opacity as a function of water vapor column density at mm-wavelengths, as proposed by Rice and Ade (1979), Zammit and Ade (1981), and Liebe (1985).

De Zafra, R. L.↗

Impact of in situ nuclear networks and atomic opacities on neutron star merger ejecta dynamics, nucleosynthesis, and kilonovae

Context. Binary neutron star merger (BNSM) ejecta are key sites of rapid neutron capture (r-process) nucleosynthesis and they produce kilonovae powered by the radioactive decay of freshly synthesized nuclei. Modeling their evolution requires multi-physics simulations involving hydrodynamics, nuclear reactions, and radiative processes. The impact of nuclear burning and atomic opacity is poorly understood and often treated with simplified prescriptions. Aims. We systematically investigate different treatments of nuclear heating, particle thermalization, and atomic opacities in radiation-hydrodynamics simulations of BNSM ejecta and kilonova light curves. Methods. Ejecta profiles from long-term numerical-relativity simulations of asymmetric neutron star binaries with a massive neutron star remnant were evolved to ∼30 days using a 2D ray-by-ray approach. We compared simplified heating-rate and thermalization prescriptions with in situ Nuclear reaction Network (NN) calculations that track nuclear energy deposition and include a composition-dependent thermalization scheme. We also contrasted various gray opacity models with a frequency-dependent treatment based on atomic calculations. Results. Coupling NN and hydrodynamics significantly affects nucleosynthesis and kilonova emission. Assuming homologous expansion alters abundance evolution and produces a narrower, less populated second r-process peak and a third peak shifted to higher mass numbers. The back-reaction of nuclear heating affects the temperature evolution enough to delay and redden the early (t∼ hours) kilonova peaks. A constant thermalization efficiency underestimates and reddens the early emission while overestimating the late-time luminosity compared to the composition-dependent treatment. Analytical opacity prescriptions yield a more extended, colder photosphere, resulting in dimmer, redder kilonovae at early times (t≲ hour), while the delayed recession of the photosphere prolongs the red emission at t ≳ 5 days. Conclusions. Coupling hydrodynamics to an in situ NN is crucial for reliable nucleosynthesis and kilonova predictions. Resolving the first several hundred milliseconds of the hydrodynamics is essential for robust nucleosynthesis calculations. Composition-dependent thermalization and frequency-dependent, atomic-physics-based opacities are needed to accurately capture the temperature evolution of the ejecta and the brightness and color evolution of the kilonova. Calibrated analytic nuclear-power fits with simplified thermalization and opacity prescriptions can still reproduce the density and temperature evolution of the ejecta.

74 ATOMIC AND MOLECULAR PHYSICS↗

Oxygen Opacity Measurements at High-Energy-Density Conditions

We present the first benchmark measurements of oxygen opacity at high-energy-density, crucial for understanding stellar interiors. A 3–5−μm thick SiO 2 sample was heated using a Z facility x-ray source, and opacity was measured in the 5–19.5 Å range with multiple spectrometers. The electron temperature and density inferred from Si 𝐾-shell spectra were 148 ± 4 eV and 8.6 ±1.4 × 10 21 cm −3 , respectively. Six experiments showed opacity reproducibility within ±15% and 5%–25% opacity uncertainty. Measured oxygen opacity and seven different opacity models exhibit extraordinary overall agreement. Discrepancies near the H-like photon ionization threshold and in certain spectral lines suggest the need for model refinements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simultaneous compression and opacity data from time-series radiography with a Lagrangian marker

Time-resolved radiography can be used to obtain absolute shock Hugoniot states by simultaneously measuring at least two mechanical parameters of the shock, and this technique is particularly suitable for one-dimensional converging shocks where a single experiment probes a range of pressures as the converging shock strengthens. However, at sufficiently high pressures, the shocked material becomes hot enough that the x-ray opacity falls significantly. Additionally, if the system includes a Lagrangian marker such that the mass within the marker is known, this additional information can be used to constrain the opacity as well as the Hugoniot state. In the limit that the opacity changes only on shock heating, and not significantly on subsequent isentropic compression, the opacity of the shocked material can be determined uniquely. More generally, it is necessary to assume the form of the variation of opacity with isentropic compression or to introduce multiple marker layers. Alternatively, assuming either the equation of state or the opacity, the presence of a marker layer in such experiments enables the non-assumed property to be deduced more accurately than from the radiographic density reconstruction alone. An example analysis is shown for measurements of a converging shock wave in polystyrene at the National Ignition Facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Quantitative comparison of opacities calculated using the R -matrix and distorted-wave methods: Fe xvii

ABSTRACT We present here a detailed calculation of opacities for Fe xvii at the physical conditions corresponding to the base of the Solar convection zone. Many ingredients are involved in the calculation of opacities. We review the impact of each ingredient on the final monochromatic and mean opacities (Rosseland and Planck). The necessary atomic data were calculated with the R-matrix and the distorted-wave (DW) methods. We study the effect of broadening, of resolution, of the extent of configuration sets and of configuration interaction to understand the differences between several theoretical predictions as well as the existing large disagreement with measurements. New Dirac R-matrix calculations including all configurations up to the n = 4, 5, and 6 complexes have been performed as well as corresponding Breit–Pauli DW calculations. The DW calculations have been extended to include autoionizing initial levels. A quantitative contrast is made between comparable DW and R-matrix models. We have reached self-convergence with n = 6 R-matrix and DW calculations. Populations in autoionizing initial levels contribute significantly to the opacities and should not be neglected. The R-matrix and DW results are consistent under the similar treatment of resonance broadening. The comparison with the experiment shows a persistent difference in the continuum while the filling of the windows shows some improvement. This study defines our path to the next generation of opacities and opacity tables for stellar modelling.

Delahaye, F.↗

Opacities of singly and doubly ionized neodymium and uranium for kilonova emission modeling

ABSTRACT Even though the electromagnetic counterpart AT2017gfo to the binary neutron star merger GW170817 is powered by the radioactive decay of r-process nuclei, only few tentative identifications of light r-process elements have been made so far. One of the major limitations for the identification of heavy nuclei is incomplete or missing atomic data. While substantial progress has been made on lanthanide atomic data over the last few years, for actinides there has been less emphasis, with the first complete set of opacity data only recently published. We perform atomic structure calculations of neodymium (Z = 60) as well as the corresponding actinide uranium (Z = 92). Using two different codes [flexible atomic code (fac) and hartree–fock-relativistic (hfr)] for the calculation of the atomic data, we investigate the accuracy of the calculated data (energy levels and electric dipole transitions) and their effect on kilonova opacities. For the fac calculations, we optimize the local central potential and the number of included configurations and use a dedicated calibration technique to improve the agreement between theoretical and available experimental atomic energy levels (AELs). For ions with vast amounts of experimental data available, the presented opacities agree quite well with previous estimations. On the other hand, the optimization and calibration method cannot be used for ions with only few available AELs. For these cases, where no experimental nor benchmarked calculations are available, a large spread in the opacities estimated from the atomic data obtained with the various atomic structure codes is observed. We find that the opacity of uranium is almost double the neodymium opacity.

Flörs, A. (ORCID:0000000320242819)↗

A statistical method for treating molecular line opacities

A method for treating atomic and molecular line opacities in cool stellar atmospheres by a statistical opacity sampling is investigated. Under the usual assumptions of plane-parallel geometry, radiative equilibrium, hydrostatic equilibrium, and LTE, each radiative quantity is computed monochromatically at each chosen frequency and depth without any averaging of the opacity. The number of frequencies needed to allow an accurate integration of the energy flux over a given spectral interval is investigated as a function of depth, including opacity for both CN and C2. This method is extended to the calculation of a model atmosphere of a star, and the effect of the number and placement of frequency points is studied. The method is applied to treating molecular lines of CO, C2, and CN in a cool carbon star. Significant advantages of the opacity sampling method are its flexibility, which permits computation of models having arbitrary variations of chemical composition and of opacity with wavelength and depth, and generalizability to include departures from LTE.

Sneden, C.↗

The effect of Livermore OPAL opacities on the evolutionary masses of RR Lyrae stars

We have investigated the effect of the new Livermore OPAL opacities on the evolution of horizontal-branch (HB) stars. This work was motivated by the recent stellar pulsation calculations using the new Livermore opacities, which suggest that the masses of double-mode RR Lyrae stars are 0.1-0.2 solar mass larger than those based on earlier opacities. Unlike the pulsation calculations, we find that the effect of opacity change on the evolution of HB stars is not significant. In particular, the effect of the mean masses of RR Lyrae stars is very small, showing a decrease of only 0.01-0.02 solar mass compared to the models based on old Cox-Stewart opacities. Consequently, with the new Livermore OPAL opacities, both the stellar pulsation and evolution models now predict approximately the same masses for the RR Lyrae stars. Our evolutionary models suggest that the mean masses of the RR Lyrae stars are about 0.76 and about 0.71 solar mass for M15 (Oosterhoff group II) and M3 (group I), respectively. If (alpha/Fe) = 0.4, these values are decreased by about 0.03 solar mass. Variations of the mean masses of RR Lyrae stars with HB morphology and metallicity are also presented.

Yi, Sukyoung↗

Momentum deposition on Wolf-Rayet winds: Nonisotropic diffusion with effective gray opacity

We derive the velocity and mass-loss rate of a steady state Wolf-Rayet (WR) wind, using a nonisotropic diffusion approximation applied to the transfer between strongly overlapping spectral lines. Following the approach of Friend & Castor (1983), the line list is assumed to approximate a statistically parameterized Poisson distribution in frequency, so that photon transport is controlled by an angle-dependent, effectively gray opacity. We show the nonisotropic diffusion approximation yields good agreement with more accurate numerical treatments of the radiative transfer, while providing analytic insight into wind driving by multiple scattering. We illustrate, in particular, that multiple radiative momentum deposition does not require that potons be repeatedly reflected across substantial distances within the spherical envelope, but indeed is greatest when photons undergo a nearly local diffusion, e.g., through scattering by many lines closely spaced in frequency. Our results reiterate the view that the so-called 'momentum problem' of Wolf-Rayet winds is better characterized as an 'opacity problem' of simply identfying enough lines. One way of increasing the number of thick lines in Wolf-Rayet winds is to transfer opacity from saturated to unsaturated lines, yielding a steeper opacity distribution than that found in OB winds. We discuss the implications of this perspective for extending our approach to W-R wind models that incorporate a more fundamental treatment of the ionization and excitation processes that determine the line opacity. In particular, we argue that developing statistical descriptions of the lines to allow an improved effective opacity for the line ensemble would offer several advantages for deriving such more fundamental W-R wind models.

Gayley, Kenneth G.↗

Building access and community standards for opacity data at the onset of next-generation atmosphere observations

The characterization of a diverse set of exoplanet atmosphere observations, ranging from hot gas giants to small temperate rocky worlds, will be one of the legacies of upcoming facilities such as the James Webb Space Telescope (JWST). Our understanding and interpretation of such observations will hinge on our ability to link observations with atmospheric theoretical studies that critically rely on fundamental molecular and atomic opacities. Computing such opacities is a highly non-trivial and inaccessible process which requires several terabytes of available disk space, hours of CPU time per pressure-temperature combination, and requires users to carefully aggregate line lists data from various sources, which limits access and intercomparison of opacity data in the exoplanet community. Here we present MAESTRO (Molecules and Atoms in Exoplanet Science: Tools and Resources for Opacities) an opacity database that can be accessed by the community via a web interface and python API. MAESTRO was built with community input to create a version-controlled opacity database that is easily queryable, includes informative metadata to ensure reproducibility, and exports relevant citations for inclusion in publications. Scheduled for community release in 2022, MAESTRO will prove to be an invaluable community resource in the era of JWST and beyond.

Natasha Batalha↗

Atomic structure considerations for the low-temperature opacity of Xenon

Here, we have begun a preliminary investigation into the opacity of Xe at low temperatures (<50 eV). The emissivity and opacity of Xe is a crucial factor in determining the utility of Xe in EUV lithography, with numerous industrial applications. To this end, we have been exploring the accuracy of some approximations used in opacity models for the relevant ion stages of Xe (6 times ionized through 20 times ionized). Due to the complexity of Xe atomic structure, one needs to use full configuration-interaction to properly describe the strong mixing in the various n=4 sub-shells that give rise to the Δn=0 and Δn=1 transitions that dominate the opacity spectrum at low temperatures. Since calculations that include full configuration-interaction for large numbers of configurations quickly become computationally prohibitive, we have explored hybrid calculations, in which full configuration-interaction is retained for the most important transitions, while intermediate coupling is employed for all other transitions. After verifying atomic structure properties, local-thermodynamic-equilibrium (LTE) opacities are generated using the ATOMIC code at selected temperatures and densities and compared to various experimental results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Overview of oxygen opacity experiments at the National Ignition Facility and investigation of potential systematic errors

Experiments to measure oxygen opacity at stellar interior conditions have been performed at the National Ignition Facility in a Discovery Science campaign. These experiments utilize the Opacity-on-NIF platform with a sample comprised of O, Mg, and Si. The spectral data from the Opacity Spectrometer cover the 1000–2000 eV photon energy range showing bound-free continuum absorption from O and line absorption from Mg and Si. DANTE and the Gated X-ray Detector are employed to measure the sample plasma’s temperature and density, respectively. Initial data show lower transmission than expected by theoretical models, raising questions of whether potential background or data uniformity concerns could produce systematic errors in the inferred transmission. Here, we investigate three concerns thought to be important for the oxygen opacity data, including instrumental scattered background, sample self-emission non-uniformity, and backlight continuum non-uniformity. Additionally, we show the effect of a recently developed method to account for 2nd order crystal reflection. The total effect of these concerns on one experiment is found to be small compared to the observed difference between the inferred transmission and a model calculation at the inferred temperature and density. Thus, we conclude that these potential sources of systematic error cannot account for the observed difference, increasing the likelihood of a real effect due to the high temperature and density conditions. However, because this is only a single experiment, we cannot make a firm conclusion. More experiments measuring the opacity and necessary calibrations are needed to assess the reproducibility and uncertainty of this result.

79 ASTRONOMY AND ASTROPHYSICS↗