Radiative Opacity Research Articles

Theoretical investigations on the radiative opacity of Sn plasmas with an open 4d orbital using a detailed-level accounting model

Theoretical investigations on the radiative opacity of Sn plasmas with an open 4<i>d</i> orbital using a detailed-level accounting model

The wide spectral range characteristics and dynamic evolution of laser-produced tin plasmas

The energy levels and transitions of highly charged Sn ions are key data for analyzing emission spectra, radiative opacity, and conversion efficiency of laser-produced Sn plasmas. Temporally–resolved spectra in the 6–45-nm range were acquired via high-precision, spatio–temporally resolved techniques. In addition, the Cowan code, based on Hartree–Fock multi-configurational interactions, was used to perform structural calculations for Sn4+–Sn13+ ion spectra. Emission spectra in the 11–18-nm range were primarily attributed to Sn8+–Sn12+ ions, with transitions involving principal quantum numbers Δn=0 and Δn=1. Whereas, emission spectra in the 6–11-nm and 18–45-nm ranges were mainly attributed to Sn9+–Sn13+and Sn4+– Sn9+ions, with transitions involving principal quantum numbers Δn=1,2. Furthermore, Segmented simulations were conducted based on the assumptions of a normalized Boltzmann distribution among the excited states and a steady-state collisional-radiative model to explain the characteristics of the radiation spectra and variations in state parameters variations during laser-produced plasma expansion from the core to the outer periphery. A specific analysis was conducted on the temporal evolution of the electron temperature and density, while the charge state of the plasma was analyzed over the 6–18-nm range. Based on the spectral diagnostics, this work focused on the impact of non-uniformity in the expansion of the Sn plasma.

An Expanded Set of Los Alamos OPLIB Tables in MESA: Type-1 Rosseland-mean Opacities and Solar Models

We present a set of 1194 Type-1 Rosseland-mean opacity tables for four different metallicity mixtures. These new Los Alamos OPLIB atomic radiative opacity tables are an order of magnitude larger in number than any previous opacity table release, and span regimes where previous opacity tables have not existed. For example, the new set of opacity tables expands the metallicity range to Z = 10−6 to Z = 0.2, which allows improved accuracy of opacities at low and high metallicity, increases the table density in the metallicity range Z = 10−4 to Z = 0.1 to enhance the accuracy of opacities drawn from interpolations across neighboring metallicities, and adds entries for hydrogen mass fractions between X = 0 and X = 0.1 including X = 10−2, 10−3, 10−4, 10−5, 10−6 that can improve stellar models of hydrogen deficient stars. We implement these new OPLIB radiative opacity tables in MESA and find that calibrated solar models agree broadly with previously published helioseismic and solar neutrino results. We find differences between using the new 1194 OPLIB opacity tables and the 126 OPAL opacity tables range from ≈20% to 80% across individual chemical mixtures, up to ≈8% and ≈15% at the bottom and top of the solar convection zone respectively, and ≈7% in the solar core. We also find differences between standard solar models using different opacity table sources that are on par with altering the initial abundance mixture. We conclude that this new, open-access set of OPLIB opacity tables does not solve the solar modeling problem, and suggest the investigation of physical mechanisms other than the atomic radiative opacity.

In-depth analysis of solar models with high-metallicity abundances and updated opacity tables

Context. As a result of the high-quality constraints available for the Sun, we are able to carry out detailed combined analyses using neutrino, spectroscopic, and helioseismic observations. These studies lay the ground for future improvements of the key physical components of solar and stellar models because ingredients such as the equation of state, the radiative opacities, or the prescriptions for macroscopic transport processes of chemicals are then used to study other stars in the Universe. Aims. We study the existing degeneracies in solar models using the recent high-metallicity spectroscopic abundances by comparing them to helioseismic and neutrino data and discuss the effect on their properties of changes in the micro and macro physical ingredients. Methods. We carried out a detailed study of solar models computed with a high-metallicity composition from the literature based on averaged 3D models that were claimed to resolve the solar modelling problem. We compared these models to helioseismic and neutrino constraints. Results. The properties of the solar models are significantly affected by the use of the recent OPLIB opacity tables and the inclusion of macroscopic transport. The properties of the standard solar models computed using the OPAL opacities are similar to those for which the OP opacities were used. We show that a modification of the temperature gradient just below the base of the convective zone is required to remove the discrepancies in solar models, particularly in the presence of macroscopic mixing. This can be simulated by a localised increase in the opacity of a few percent. Conclusions. We conclude that the existing degeneracies and issues in solar modelling are not removed by using an increase in the solar metallicity, in contradiction to what has been suggested in the recent literature. Therefore, standard solar models cannot be used as an argument for a high-metallicity composition. While further work is required to improve solar models, we note that direct helioseismic inversions indicate a low metallicity in the convective envelope, in agreement with spectroscopic analyses based on full 3D models.

On the computation of moments in the Super-Transition-Arrays model for radiative opacity calculations

In the Super-Transition-Array statistical method for the computation of radiative opacity of hot dense matter, the moments of the absorption or emission features involve partition functions with reduced degeneracies, occurring through the calculation of averages of products of subshell populations. In the present work, we discuss several aspects of the computation of such peculiar partition functions, insisting on the precautions that must be taken in order to avoid numerical difficulties. In a previous work, we derived a formula for supershell partition functions, which takes the form of a functional of the distribution of energies within the supershell and allows for fast and accurate computations, truncating the number of terms in the expansion. The latter involves coefficients for which we obtained a recursion relation and an explicit formula. We show that such an expansion can be combined with the recurrence relation for shifted partition functions. We also propose, neglecting the effect of fine structure as a first step, a positive-definite formula for the Super-Transition-Array moments of any order, providing an insight into the asymmetry and sharpness of the latter. The corresponding formulas are free of alternating sums. Several ways to speed up the calculations are also presented.

Benford’s law in atomic spectra and opacity databases

The intriguing law of anomalous numbers, also named Benford’s law, states that the significant digits of data follow a logarithmic distribution favoring the smallest values. In this work, we test the compliance with this law of the atomic databases developed at the National Institute of Standards and Technology (NIST) focusing on line energies, oscillator strengths, Einstein coefficients and radiative opacities. The considered databases are the Atomic Spectra Database (ASD) and the NIST-LANL (Los Alamos National Laboratory) Lanthanide/Actinide Opacity Database. The present study is not limited to the first digit and the case of multipole lines is also considered. The fact that the law is verified with a high accuracy means that the occurrence of digits reflects the constraints induced, in a given angular-momentum coupling, by the selection rules for atomic processes. As a consequence, Benford’s law may be of great interest to detect inconsistencies in atomic databases.

Radiation burnthrough measurements to infer opacity at conditions close to the solar radiative zone–convective zone boundary

Recent measurements at the Sandia National Laboratory of the x-ray transmission of iron plasma have inferred opacities much higher than predicted by theory, which casts doubt on modeling of iron x-ray radiative opacity at conditions close to the solar convective zone-radiative zone boundary. An increased radiative opacity of the solar mixture, in particular iron, is a possible explanation for the disagreement in the position of the solar convection zone-radiative zone boundary as measured by helioseismology and predicted by modeling using the most recent photosphere analysis of the elemental composition. Here, we present data from radiation burnthrough experiments, which do not support a large increase in the opacity of iron at conditions close to the base of the solar convection zone and provide a constraint on the possible values of both the mean opacity and the opacity in the x-ray range of the Sandia experiments. The data agree with opacity values from current state-of-the-art opacity modeling using the CASSANDRA opacity code.

Ideas and Tools for Error Detection in Opacity Databases

In this article, we propose several ideas and tools in order to check the reliability of radiative opacity and atomic physics databases. We first emphasize that it can be useful to verify that mathematical inequalities, which impose lower and upper bounds on the Rosseland and/or Planck mean opacities, are satisfied, either for pure elements or mixtures. In the second part, we discuss the intriguing law of anomalous numbers, also named Benford’s law, which enables one to detect errors in line-strength collections, required in order to perform fine-structure calculations. Finally, we point out and illustrate the importance of quantifying the uncertainties due to interpolations in the density-temperature opacity (or more generally atomic-data) tables and performing convergence checks, which are crucial in the accuracy-completeness compromise inherent in opacity computations.

Updated High-temperature Opacities for the Dartmouth Stellar Evolution Program and Their Effect on the Jao Gap Location

The Jao Gap, a 17% decrease in stellar density at M G ∼ 10 identified in both Gaia Data Release 2 and Early Data Release 3, presents a new method to probe the interior structure of stars near the fully convective transition mass. The Gap is believed to originate from convective-kissing instability wherein asymmetric production of 3He causes the core convective zone of a star to periodically expand and contract and consequently causes the star luminosities to vary. Modeling of the Gap has revealed a sensitivity in its magnitude to a population metallicity primarily through opacity. Thus far, models of the Jao Gap have relied on OPAL high-temperature radiative opacities. Here we present updated synthetic population models tracing the Gap location modeled with the Dartmouth stellar evolution code using the OPLIB high-temperature radiative opacities. Use of these updated opacities changes the predicted location of the Jao Gap by ∼0.05 mag as compared to models that use the OPAL opacities. This difference is likely too small to be detectable in empirical data.

Theoretical investigation on extreme ultraviolet radiative opacity and emissivity of Sn plasmas at local-thermodynamic equilibrium

Sn is the material for an extreme ultraviolet (EUV) light source working at 13.5 nm, therefore the radiative properties of Sn plasma are of great importance in designing light source. The radiative opacity and emissivity of Sn plasma at local thermodynamic equilibrium are investigated by using a detailed-level-accounting model. In order to obtain precise atomic data, a multi-configuration Dirac-Fock method is used to calculate energy levels and oscillator strengths of &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}${\rm{Sn}}^{6+}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M3.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;-&lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}${\rm{Sn}}^{14+}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M4.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. The electronic correlation effects of &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$4{\rm d}^m\text{-}4{\rm f}^m$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M5.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M5.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;(&lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$m=1, 2, 3, 4$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M6.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M6.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;) and &lt;inline-formula&gt;&lt;tex-math id="M7"&gt;\begin{document}$ 4\mathrm{p}^n\text{-}4\mathrm{d}^n $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M7.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M7.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;(&lt;inline-formula&gt;&lt;tex-math id="M8"&gt;\begin{document}$n=1, 2, 3$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M8.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M8.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;) are mainly considered, which dominate the radiation near 13.5 nm. The number of fine-structure levels reaches about 200000 for each ionization stage in the present large-scale configuration interaction calculations. For the large oscillator strengths (&gt; 0.01), the length form is in accord with the velocity form and their relative difference is about 20%–30%. The calculated transmission spectra of Sn plasma at 30 eV and 0.01 g/cm&lt;sup&gt;3&lt;/sup&gt; are compared with the experimental result, respectively, showing that they have both good consistency. The radiative opacity and emissivity of Sn plasma at the temperature in a range of 16–30 eV and density in a scope of of 0.0001–0.1 g/cm&lt;sup&gt;3&lt;/sup&gt; are investigated systematically. The effects of the plasma temperature and plasma density on radiation characteristics are studied. The results show that the radiative properties near 13.5 nm are broadened with the increase of density at a specific temperature, while it is narrowed with the increase of temperature for a specific density. The present investigation should be helpful in designing and studying EUV light source in the future.

First-principles study of L-shell iron and chromium opacity at stellar interior temperatures.

Recently developed free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter has been applied for studying L-shell opacity of iron and chromium at T=182eV. We use Mermin-Kohn-Sham density functional theory with a ground-state and a fully-temperature-dependent generalized gradient approximation exchange-correlation (XC) functionals. It is demonstrated that the role of XC at such a high-T is negligible due to the total free energy of interacting systems being dominated by the noninteracting free-energy term, in agreement with estimations for the homogeneous electron gas. Our DFT predictions are compared with the radiative emissivity and opacity of the dense plasma model, with the real-space Green's function method, and with experimental measurements. Good agreement is found between all three theoretical methods, and in the bound-continuum region for Cr when compared with the experiment, while the discrepancy between direct DFT calculations and the experiment for Fe remains essentially the same as for plasma-physics models.

Dissecting the microphysics behind the metallicity-dependence of massive stars radii

ABSTRACT Understanding the radii of massive stars throughout their evolution is important to answering numerous questions about stellar physics, from binary interactions on the main sequence to the pre-supernova radii. One important factor determining a star’s radius is the fraction of its mass in elements heavier than Helium (metallicity, Z). However, the metallicity enters stellar evolution through several distinct microphysical processes, and which dominates can change throughout stellar evolution and with the overall magnitude of Z. We perform a series of numerical experiments with 15 $\, \mathrm{M}_{\odot }$mesa models computed doubling separately the metallicity entering the radiative opacity, the equation of state, and the nuclear reaction network to isolate the impact of each on stellar radii. We explore separately models centred around two metallicity values: one near solar Z = 0.02 and another sub-solar Z ∼ 10−3, and consider several key epochs from the end of the main sequence to core carbon depletion. We find that the metallicity entering the opacity dominates at most epochs for the solar metallicity models, contributing to on average ∼60–90 per cent of the total change in stellar radius. Nuclear reactions have a larger impact (∼50–70 per cent) during most epochs in the subsolar Z models. The methodology introduced here can be employed more generally to propagate known microphysics errors into uncertainties on macrophysical observables including stellar radii.

Apparent change of the 3C/3D line intensity ratio in neonlike ions.

The resonance 3C ([(2p5)1/23d3/2]J=1 → [2p6]J=0) to intercombination 3D ([(2p5)3/23d5/2]J=1 → [2p6]J=0) line intensity ratio of neonlike ions has been studied. The measured line intensity ratio for neonlike Xe44+ ions shows an apparent change, which is reproduced by the calculations using the relativistic configuration interaction plus many-body perturbation theory. It is clearly elucidated that the change in the 3C/3D line intensity ratio is caused by strong configuration mixing between the upper levels of the 3D and 3F ([(2p5)1/23s]J=1 → [2p6]J=0) lines. The present measurement allows us to discuss the 3C/3D line intensity ratio for the highest-Z ions hitherto, which suggests that the experiment-theory discrepancy in the 3C/3D line intensity ratio of neonlike ions diminishes with increasing atomic number Z and further trends to vanish at higher-Z ions. Furthermore, the present study provides benefits to better understand configuration mixing effect in the radiative opacity of hot plasmas.

New calibrated models for the tip of the red giant branch luminosity and a thorough analysis of theoretical uncertainties

ABSTRACT The luminosity of the tip of the red giant branch (TRGB) is instrumental for the construction of the distance ladder, and its accurate modelling is key for determining the local Hubble parameter. In this work, we present an extensive quantitative analysis of the TRGB luminosity, accounting for virtually all input physics that affect it, namely: chemical composition, opacity, diffusion, nuclear reaction rates, electron screening, neutrinos, convection efficiency, boundary conditions, and mass-loss, amongst others. Our analysis is based on a newly produced grid of ∼3 × 106 TRGB models, evolved from pre-main sequence up to the helium ignition at the TRGB, and covering a wide range of metallicity (Z = 0.0001–0.02) and initial mass (M = 0.8–1.4 M⊙). Through a Monte Carlo analysis, we study the systematic variation of the TRGB luminosity due to the combined effect of all above input physics, and show that a maximum theoretical uncertainty of about $1.6 {{\ \rm per\ cent}}$ is still present on the current generation of models, dominated by systematics of radiative opacity. Results are also provided in several photometric bands. As a by-product of our analysis, we demonstrate robust evidence for the linear response of the tip luminosity to individual changes of input physics, which can significantly simplify future analyses. A comparison of our results with other stellar evolution codes shows excellent agreement. Our full grid of models is available upon reasonable requests, while a partial grid is available online on Zenodo.

Adaptive Algorithm for the Generation of Superconfigurations in Hot-Plasma Opacity Calculations

In hot plasmas, such as the ones encountered in astrophysics or laser-fusion studies, the number of ionic excited states may become huge, and the relevant electron configurations cannot always be handled individually. The Super Transition Array approach enables one to calculate the massic photo-absorption cross-section (or radiative opacity) in a statistical manner consisting of grouping configurations close in energy into superconfigurations. One of the main issues of the method, beyond its spectral resolution, is the determination of the most relevant configurations that contribute to opacity. In this work, we discuss different aspects of the generation of superconfigurations in a hot plasma and propose a new adaptive algorithm.

Evolution of Highly Magnetic White Dwarfs by Field Decay and Cooling: Theory and Simulations

Abstract We investigate the luminosity suppression and its effect on the mass–radius relation and cooling evolution of highly magnetized white dwarfs. Based on the effect of magnetic field relative to gravitational energy, we suitably modify our treatment of the radiative opacity, magnetostatic equilibrium, and degenerate core equation of state to obtain the structural properties of these stars. Although the Chandrasekhar mass limit is retained in the absence of magnetic field and irrespective of the luminosity, strong central fields of about 1014 G can yield super-Chandrasekhar white dwarfs with masses ∼2.0 M ⊙. Smaller white dwarfs tend to remain super-Chandrasekhar for sufficiently strong central fields even when their luminosity is significantly suppressed to 10−16 L ⊙. Nevertheless, owing to the cooling evolution and simultaneous field decay over 10 Gyr, the limiting masses of small magnetized white dwarfs can fall to 1.5 M ⊙ over time. However, the majority of these systems still remain practically hidden throughout their cooling evolution because of their high fields and correspondingly low luminosities. Utilizing the stellar evolution code stars, we obtain close agreement with the analytical mass limit estimates, which suggests that our analytical formalism is physically motivated. Our results argue that super-Chandrasekhar white dwarfs born as a result of strong-field effects may not remain so forever. This explains their apparent scarcity, in addition to making them hard to detect because of their suppressed luminosities.

A systematic study on 2p → 3d radiative opacity of lowly charged Cu plasmas

The L-shell radiative opacity of lowly charged Cu plasmas is investigated using a detailed level accounting method. The transmission spectra are compared with a recent experiment at ∼16 eV and 0.005 g/cm3, and good agreement is observed. For a systematic study, radiative opacities caused by 2p → 3d transitions at temperatures of 10–35 eV and densities of 0.001–0.1 g/cm3 are calculated. The dominant ionization stages are lowly charged ones with an open M-shell at such plasma conditions. The result shows that charge state distribution and radiative opacities are very sensitive to temperature. The two strongest absorption peaks of 2p3/2 → 3d5/2 and 2p1/2 → 3d3/2 caused by relativistic orbital splitting are well separated at temperatures lower than 25 eV, whereas they are mixed together to form a broadband structure at higher temperatures.

Development of radiative opacity code OPIND for high energy density plasma and its application in radiation hydrodynamics

We developed the program OPIND to generate opacity data for use in radiation hydrodynamics simulations. This is an extension of our earlier work on opacity of elemental plasma based on average atom model [1]. In this work, we extended the capability of OPIND to treat mixture plasmas which employs the ideal gas mixing rule to obtain partial densities. Screened hydrogenic model was employed to obtain radiative properties and hence total opacity. Extensive validation for average ionization and Rosseland mean opacity of C, Al, Fe, Ge, Xe and Au plasmas were performed. OPIND was then employed to study the opacity of CH and Au-Gd mixture plasmas. The role of pressure ionization on CH opacity as well as opacity enhancement in Au-Gd plasma due to the presence of Gd were investigated. Further validation of OPIND was done by performing 1D radiation hydrodynamics simulations to study the ablation in Al slab subjected to radiation temperature drives. We studied the shock trajectory, mass ablation rate and evolution of thermodynamic parameters during shock propagation in Al slab. The scaling law for radiation temperature as a function of shock speed for strong shocks was also verified. We observed good agreement of data generated in our simulations with reported experimental and simulation data. Equation of state data were generated using the SBCRIS library developed by us.

Optimized recursion relation for the computation of partition functions in the superconfiguration approach

Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion relation for the calculation of such partition functions. In this paper, we propose an optimization of the latter method and explain how to implement it in practice. The formalism relies on the evaluation of elementary symmetric polynomials, which opens the way to further improvements.

Comparing Radiative Transfer Codes and Opacity Samplings for Solar Irradiance Reconstructions

Some techniques developed to reproduce solar irradiance variations make use of synthetic radiative fluxes of quiet and magnetic features. The synthesis of radiative fluxes of astronomical objects is likely to be affected by uncertainties resulting from approximations and specific input employed for the synthesis. In this work we compare spectra obtained with three radiative transfer codes with the purpose of investigating differences in reproducing solar irradiance variations. Specifically, we compare spectral synthesis produced in non-local thermodynamic equilibrium obtained with COSI and RH using 1-D atmosphere models. We also compare local thermodynamic equilibrium syntheses emerging from 3-D MURaM simulations of the solar atmosphere obtained with two sets of opacity tables generated with the ATLAS9 package and with the RH code, and test the effects of opacity sampling on the emergent spectra. We find that, although the different codes and methodologies employed to synthesize the spectrum reproduce overall the observed solar spectrum with a similar degree of accuracy, subtle differences in quiet Sun spectra may translate into larger differences in the computation of the contrasts of magnetic features, which, in turn, critically affect the estimates of solar variability.