Opacity Calculations Research Articles

Radiative Pressure on Fractal Dust Grains in Oxygen-rich AGB Stars

There is still considerable debate on the exact composition of grains formed in the outflows of O-rich, asymptotic giant branch stars. Estimates of the expected condensation distances based on radiative transfer calculations show that iron-free silicates can condense close to the star but typically lack the opacity to drive an outflow unless they are large enough that radiation pressure due to scattering on the grains becomes significant. Iron-containing silicates have a much higher absorption opacity, but due to this stronger absorption, their expected condensation location is well beyond the expected dust formation zone. Recent measurements of the efficiency of SiO condensational growth have shown that this rate is low. The result of this low growth efficiency is that nucleation may persist for longer, giving a larger number of smaller primary particles, leading to an increased likelihood of particle aggregation in these outflows. In this work, we examine how the radiation pressure changes with the possible aggregation of these primary particles into fractal aggregates. Opacity calculations are made using optical properties of both forsterite and astronomical silicate for aggregates containing up to 256 primary particles and for fractal dimensions of 1.8 and 2.8. For primary particles of radius less than ∼0.1 μm, aggregation leads to an enhancement of the radiation pressure over an equivalent cloud of isolated primary particles.

Solar Opacity Calculations: Recent Theoretical Advances Prompted by Laser and Z-Pinch Experiments

Solar Opacity Calculations: Recent Theoretical Advances Prompted by Laser and Z-Pinch Experiments

A Thermodynamic Criterion for the Formation of Circumplanetary Disks

The formation of circumplanetary disks is central to our understanding of giant planet formation, influencing their growth rate during the post-runaway phase and observability while embedded in protoplanetary disks. We use three-dimensional global multifluid radiation hydrodynamics simulations with the FARGO3D code to define the thermodynamic conditions that enable circumplanetary disk formation around Jovian planets on wide orbits. Our simulations include stellar irradiation, viscous heating, static mesh refinement, and active calculation of opacity based on multifluid dust dynamics. We find a necessary condition for the formation of circumplanetary disks in terms of a mean cooling time: When the cooling time is at least 1 order of magnitude shorter than the orbital timescale, the specific angular momentum of the gas is nearly Keplerian at scales of one-third of the Hill radius. We show that the inclusion of multifluid dust dynamics favors rotational support because dust settling produces an anisotropic opacity distribution that favors rapid cooling. In all our models with radiation hydrodynamics, specific angular momentum decreases as time evolves, in agreement with the formation of an inner isentropic envelope due to compressional heating. The isentropic envelope can extend up to one-third of the Hill radius and shows negligible rotational support. Thus, our results imply that young gas giant planets may host spherical isentropic envelopes, rather than circumplanetary disks.

Matrix methods for opacity calculations

Atomic structure calculations are the first step in an opacity calculation. They provide the self-consistent electronic potential and electron wavefunctions that are needed to evaluate the Slater integrals and dipole matrix elements. In this paper, we show that simple matrix methods can be used to perform Hartree–Fock–Slater or LDA calculations on standard atomic structure grids, including relativistic corrections, yielding bound and continuum wavefunctions that can be used, in conjunction with statistical broadening techniques, to obtain realistic average-atom opacities.

CAI formation in the early Solar System

Calcium-aluminium-rich inclusions (CAIs) are the oldest dated solid materials in the Solar System, and are found as light-coloured crystalline ingredients in carbonaceous chondrite meteorites. Their formation time is commonly associated with age zero of the Solar System. Nevertheless, the physical and chemical processes that once led to the formation of these submillimetre- to centimetre-sized mineral particles in the early solar nebula are still a matter of debate. In this paper, we propose a pathway to form such inclusions during the earliest phases of disc evolution. We combine 1D viscous disc evolutionary models with 2D radiative transfer, equilibrium condensation, and new dust opacity calculations. We show that the viscous heating associated with the high accretion rates in the earliest evolutionary phases causes the midplane inside of about 0.5 au to heat up to limiting temperatures of about 1500–1700 K, but no further. These high temperatures force all refractory material components of the inherited interstellar dust grains to sublimate – except for a few Al-Ca-Ti oxides, such as Al2O3, Ca2Al2SiO7, and CaTiO3. This is a recurring and very stable result in all our simulations, because these minerals form a natural thermostat. Once the Mg-Fe silicates are gone, the dust becomes more transparent and the heat is more efficiently transported to the disc surface, which prevents further warming. This thermostat mechanism keeps these minerals above their annealing temperature for hundreds of thousands of years, allowing them to form large pure crystalline particles. These particles are dragged out by the viscously spreading disc, and once they reach a distance of about 0.5 au, the silicates recondense on the surface of the Ca-Al-rich particles, adding an amorphous silicate matrix. We estimate that this mechanism of CAI production works during the first 50 000 yr of disc evolution. These particles then continue to move outward and populate the entire disc up to radii of about 50 au, before the accretion rate eventually subsides, the disc cools, and the particles start to drift inwards.

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.

A note on efficiently generating ionic configurations for opacity calculations

When calculating the spectral opacity of hot dense plasmas one often encounters the need to generate a list of detailed ionic configurations of bound states for each ion stage in the plasma. We present here a non-recursive algorithm for the efficient construction of such a list of states.

Atomic data and expansion opacity calculations in two representative 4d transition elements, niobium and silver, of interest for kilonovae studies

Aims. Neutron star (NS) mergers are thought to be a source of heavy trans-iron element production. The latter can be detected in the spectra of the ejected materials, from which bright electromagnetic radiation is emitted. This latter is due to the radioactive decay of the produced heavy r-process nuclei and is known as kilonova. Because of their complex atomic structures – characterized by configurations involving unfilled nd or nf subshells – the heavy elements of the kilonova ejecta often give rise to numerous absorption lines generating significant opacities. The determination of the latter, which are of paramount importance for the analysis of kilonova light curves, requires knowledge of the radiative parameters of the spectral lines belonging to the ions expected to be present in the kilonova ejecta. The aim of the present work is to provide new atomic opacity data for two representative 4d elements, niobium (Nb) and silver (Ag), in their first four charge states, namely for Nb I–IV and Ag I–IV. Methods. Large-scale calculations based on the pseudo-relativistic Hartree-Fock (HFR) method were performed to obtain the atomic structure and radiative parameters while the expansion formalism was used to estimate the opacities. Results. Wavelengths and oscillator strengths were computed for several million spectral lines in Nb I–IV and Ag I–IV ions. The reliability of these parameters was estimated by comparison with the few previously published experimental and theoretical results. The newly obtained atomic data were then used to calculate expansion opacities for typical kilonova conditions expected one day after NS merger, a density of ρ = 10−13 g cm−3, and temperatures ranging from T = 5000 K to T =15 000 K.

Monte Carlo Radiation Transport for Astrophysical Transients Powered by Circumstellar Interaction

In this paper, we introduce SuperLite, an open-source Monte Carlo radiation transport code designed to produce synthetic spectra for astrophysical transient phenomena affected by circumstellar interaction. SuperLite utilizes Monte Carlo methods for semi-implicit, semirelativistic radiation transport in high-velocity shocked outflows, employing multigroup structured opacity calculations. The code enables rapid post-processing of hydrodynamic profiles to generate high-quality spectra that can be compared with observations of transient events, including superluminous supernovae, pulsational pair-instability supernovae, and other peculiar transients. We present the methods employed in SuperLite and compare the code’s performance to that of other radiative transport codes, such as SuperNu and CMFGEN. We show that SuperLite has successfully passed standard Monte Carlo radiation transport tests and can reproduce spectra of typical supernovae of Type Ia, Type IIP, and Type IIn.

On the importance of using realistic partition functions in kilonova opacity calculations

On the importance of using realistic partition functions in kilonova opacity calculations

Synthetic photometry for carbon-rich giants

Context. The properties and the evolution of asymptotic giant branch (AGB) stars are strongly influenced by their mass loss through a stellar wind. This, in turn, is believed to be caused by radiation pressure due to the absorption and scattering of the stellar radiation by the dust grains formed in the atmosphere. The optical properties of dust are often estimated using the small particle limit (SPL) approximation, and it has been used frequently in modelling AGB stellar winds when performing radiation-hydrodynamics (RHD) simulations. Aims. We aim to investigate the effects of replacing the SPL approximation by detailed Mie calculations of the size-dependent opacities for grains of amorphous carbon forming in C-rich AGB star atmospheres. Methods. We performed RHD simulations for a large grid of carbon star atmosphere+wind models with different effective temperatures, luminosities, stellar masses, carbon excesses, and pulsation properties. Also, a posteriori radiative transfer calculations for many radial structures (snapshots) of these models were done, resulting in spectra and filter magnitudes. Results. We find that, when giving up the SPL approximation, the wind models become more strongly variable and more dominated by gusts, although the average mass-loss rates and outflow speeds do not change significantly; the increased radiative pressure on the dust throughout its formation zone does, however, result in smaller grains and lower condensation fractions (and thus higher gas-to-dust ratios). The photometric K magnitudes are generally brighter, but at V the effects of using size-dependent dust opacities are more complex: brighter for low mass-loss rates and dimmer for massive stellar winds. Conclusions. Given the large effects on spectra and photometric properties, it is necessary to use the detailed dust optical data instead of the simple SPL approximation in stellar atmosphere+wind modelling where dust is formed.

Opacity calculations for aluminum, hydrogen, and gold using FLYCHK with improved free-free opacity formalism

Opacity is an essential property for understanding the fundamental properties of high-energy-density (HED) and astrophysical plasmas. FLYCHK, a collisional-radiative code, has been used to calculate the opacities of HED plasmas under various conditions because of its simplicity and availability. However, the opacity calculations of FLYCHK have limitations in a strongly coupled region, partly because of the problem of a free-free opacity formalism. In this study, we improved the free-free opacity calculation model of FLYCHK and generated opacities of various materials, including high-Z materials (Al, H, and Au). The FLYCHK opacities were in good agreement over a wide range of conditions with those obtained using the Los Alamos opacity code ATOMIC and the detailed level accounting model.

Expansion and line-binned opacities of samarium ions for the analysis of early kilonova emission from neutron star mergers

ABSTRACTOpacity calculations performed within the expansion and the line-binned formalisms are reported for Sm V–X ions in this paper. These were determined by means of new large-scale atomic structure and radiative rate computations carried out using the pseudo-relativistic Hartree-Fock (HFR) method from which energy levels, wavelengths, and oscillator strengths were deduced for more than 100 millions of spectral lines in the considered samarium ions. In the absence of any experimental data, the reliability of HFR results was roughly estimated by comparison with those obtained with an independent theoretical approach, namely the fully relativistic multiconfiguration Dirac-Hartree-Fock method, in Sm VI and Sm VII. The opacities were estimated for typical conditions corresponding to early phases of kilonovae following neutron star mergers, i.e. for a density ρ = 10−10 g cm−3, a time after the merger t = 0.1 day and temperatures ranging from 25 000 to 70 000 K. In addition, the atomic calculations allowed us to establish the ground level for each of the Sm ions considered (still unknown until now), as well as reliable partition functions that are crucial for the determination of the ionization balance by solving the Saha equation and for accurate opacity calculations.

New Ga IV, Ga V, Ge IV and Ge V line widths for white dwarf spectra analysis; quantum mechanical results

Abstract We provide in the present paper new Stark broadening parameters for the four ions Ga IV, Ga V, Ge IV and Ge V. The calculations have been performed using our quantum mechanical method. To the best of our knowledge, the only available Stark broadening results are those of the Ge IV ion, where the semi classical perturbation and the modified semi empirical methods have been used. For the three other ions, no data have been found. In 2020 and for the first time, about five hundred lines of trans-iron elements including Gallium (Ga) and Germanium (Ge) have been identified in the ultraviolet spectrum of a DAO-type white dwarf BD-22°3467. Other precedent observations showed the existence of Ga IV-V lines in two white dwarfs (G191-B2B and RE 0503-289), and those of Ge IV and Ge V in the UV spectrum of RE 0503-289. Theoretical evaluations and measurements of atomic and Stark broadening data are a prerequisite for stellar-atmosphere modeling, which is a tool for the determination of the photospheric Gallium and Germanium abundance in white dwarfs. Since there is no Stark broadening data for the three ions Ga IV, Ga V and Ge V, our calculations come to fill this gap, and the obtained results can be used for the abundance determination of elements, the calculation of stellar opacity, the interpretation and modelling of stellar spectra, and the estimation of the relative transfer through stellar plasmas,... etc. They will be also implemented into the database of Stark broadening parameters STARK-B.

Modeling density effects on electronic configurations in warm dense plasmas

We present a method to calculate the shift of the K edge in warm dense aluminum. We use the average-atom model and show how to build the energy of an electronic configuration with integer subshell populations and by taking into account the interaction of the bound electrons with the free electrons. We successfully compare our calculation of the spectral opacity with the Henke table for aluminum at solid density and 300 K. We found a redshift of the K edge along the principal Hugoniot consistent with experimental data. We also compute the 2s and 2p edges. We obtain L edge redshifts similar to the K edge redshift.

Photoionization and Opacity

Opacity determines radiation transport through material media. In a plasma source, the primary contributors to atomic opacity are bound–bound line transitions and bound-free photoionization into the continuum. We review the theoretical methodology for state-of-the-art photoionization calculations based on the R-matrix method as employed in the Opacity Project, the Iron Project, and solution of the heretofore unsolved problem of plasma broadening of autoionizing resonances due to electron impact, Stark (electric microfields), Doppler (thermal), and core-excitations. R-matrix opacity calculations entail huge amount of atomic data and calculations of unprecedented complexity. It is shown that in high-energy-density (HED) plasmas, photoionization cross sections become 3-D energy–temperature–density-dependent owing to considerable attenuation of autoionizing resonance profiles. Hence, differential oscillator strengths and monochromatic opacities are redistributed in energy. Consequently, Rosseland and Planck mean opacities are affected significantly.

Quantum mechanical line widths of ionized oxygen, silicon, and aluminium; comparisons with recent experimental results

ABSTRACT We present in this paper new quantum Half Widths at Half intensity Maximum (HWHM) for 101 spectral lines of the following ions: O II (35 lines), O III (20 lines), Si II (9 lines), Si III (12 lines), and Al III (25 lines). The present quantum results are compared to new experimental ones. No previous quantum calculations have been performed for these ions. The relatively high differences found between the new and previous measurements and the available theoretical calculations encourage us to conduct these quantum calculations. Our quantum method has been used many years ago and has given good results compared to other approaches, so it can be a useful tool to check the new experimental results or to understand the disagreement found for some lines. Furthermore, the obtained results can be used for the abundance determination of elements, the calculation of stellar opacity, the interpretation and modelling of stellar spectra, and the estimation of the relative transfer through stellar plasmas, etc. Part of the present results will be also implemented to the data base of Stark broadening parameters STARK-B.

A Non-Intrusive Particle Temperature Extraction Methodology Using Infrared and Visible-Image Sequences for High-Temperature Particle Plumes

Abstract The direct measurement of particle temperatures in particle-laden flows presents a unique challenge to thermometry due to the flow's transient and stochastic nature. Previous attempts to measure the bulk particle temperature of a dilute particle plume or particle curtain using intrusive and non-intrusive methods have been mildly successful. In this work, a non-intrusive method using a high-speed infrared (IR) camera and a visible-light camera to yield an indirect particle temperature measurement technique is developed and tested. The image sequences obtained from the IR camera allow for the calculation of the apparent particle temperature, while the visible-light image sets allow for the calculation of the plume opacity as a function of flow discharge position. To extract the true particle temperature, a post-processing algorithm based on Planck's radiation theory was developed. The results were validated through a series of lab-scale tests at the University of New Mexico using a test rig capable of generating particle curtains at various temperatures. The temperature profiles extracted from the methodology presented were compared to the temperature data measured during experimental measurements yielding agreement of the bulk particle temperature of the plume within 10% error. The methods described here will be developed further to estimate the heat losses from the falling particle receiver at Sandia National Laboratories.

Transfer learning as a method to reproduce high-fidelity non-local thermodynamic equilibrium opacities in simulations

Simulations of high-energy density physics often need non-local thermodynamic equilibrium opacity data. These data, however, are expensive to produce at relatively low fidelity. It is even more so at high fidelity such that the opacity calculations can contribute 95 % of the total computation time. This proportion can even reach large proportions. Neural networks can be used to replace the standard calculations of low-fidelity data, and the neural networks can be trained to reproduce artificial, high-fidelity opacity spectra. In this work, it is demonstrated that a novel neural network architecture trained to reproduce high-fidelity krypton spectra through transfer learning can be used in simulations. Further, it is demonstrated that this can be done while achieving a relative per cent error of the peak radiative temperature of the hohlraum of approximately 1 % to 4 % while achieving a 19.4 $\times$ speed up.

A superconfiguration calculation of opacity with consistent bound and continuum electron treatments using green’s functions

One of the challenges in calculating the opacity of dense plasmas is the difficulty in consistently modeling electrons bound to nuclei and those that exist within the continuum of free states in electronic structure models. We address this issue by adapting the green’s function approach, originally developed for use in average atom calculations, to the determination of superconfiguration (SC) electronic structure. The spectra created using these SCs indicate that a consistent treatment of continuum electronic structure is important for phenomena involving electrons near ionization thresholds, such as the pressure ionization of bound states and the opacity due to transitions near bound-free edges. Though important for dense plasmas, the detailed incorporation of continuum electrons into structure calculations does not have significant impact on the recent discrepancies between the predicted and measured opacity of hot, dense iron (Bailey et al 2015 Nature 517 56). We find that the inclusion of plasma effects through an ion-sphere model along with our treatment of continuum electronic states gives a description of pressure ionization in hot, dense aluminum that is in better agreement with experiment than methods that rely on perturbative descriptions of the plasma environment (Hoarty et al 2013 Phys. Rev. Lett. 110 265003).