Iron Opacity Research Articles

Systematic Study of L-Shell Opacity at Stellar Interior Temperatures.

The first systematic study of opacity dependence on atomic number at stellar interior temperatures is used to evaluate discrepancies between measured and modeled iron opacity [J. E. Bailey etal., Nature (London) 517, 56 (2015)NATUAS0028-083610.1038/nature14048]. High-temperature (>180 eV) chromium and nickel opacities are measured with ±6%-10% uncertainty, using the same methods employed in the previous iron experiments. The 10%-20% experiment reproducibility demonstrates experiment reliability. The overall model-data disagreements are smaller than for iron. However, the systematic study reveals shortcomings in models for density effects, excited states, and open L-shell configurations. The 30%-45% underestimate in the modeled quasicontinuum opacity at short wavelengths was observed only from iron and only at temperature above 180eV. Thus, either opacity theories are missing physics that has nonmonotonic dependence on the number of bound electrons or there is an experimental flaw unique to the iron measurement at temperatures above 180eV.

A proposal to measure iron opacity at conditions close to the solar convective zone-radiative zone boundary

A major problem in stellar modelling is the discrepancy between solar models and helioseismology data in the position of the convective zone-radiative zone boundary in the sun. This could be explained by a large uncertainty in the calculated opacity data and recent experimental data on iron using the Sandia National Laboratory Z facility have shown large differences, up to a factor of 4, between measurement and prediction at plasma conditions close to the convective zone-radiative zone boundary. This paper describes a proposal for a radiative burn-through experiment to be fielded on NIF to observe if a radiation wave transit through a Fe2O3 sample is consistent with the factor of 2–4 change in the iron opacity seen in the Z experiments. A target design and the diagnostic method are described. A detailed radiation-hydrodynamic model has been used to generate synthetic results and explore the sensitivities and experimental accuracy needed for the proposed measurement.

The Wolf–Rayet Stellar Response To The Iron Opacity Bump: Envelope Inflation, Winds, and Microturbulence

Abstract Early-type Wolf–Rayet (WR) stellar models harbor a super-Eddington layer in their outer envelopes due to a prominent iron opacity bump. In the past few decades, one-dimensional hydrostatic and time-steady hydrodynamic models have suggested a variety of WR responses to a super-Eddington force including envelope inflation and optically thick winds. In this paper, I study these responses using semianalytical estimates and WR models from both MESA and Ro & Matzner; four conclusions are present. First, early-type WR stars do not harbor inflated envelopes because they have either strong winds or insufficient luminosities. Second, the condition for an opacity bump to harbor a sonic point is expressible as a minimum mass-loss rate, . In agreement with Grassitelli et al. and Ro, the majority of galactic early-type WR stars can harbor sonic points at the iron opacity bump. However, about half of those in the Large Magellanic Cloud cannot given typical wind parameters. Third, WR winds driven by the iron opacity bump must have mass-loss rates that exceed a global minimum of 10−5.8–10−6 yr . Lastly, the observed early-type WR distribution follows a simple mass-loss relation derived here if the radiation-to-gas pressure ratio is approximately p r /p g ≃ 145 in the wind; a value consistent with studies by Gräfener et al. and Nakauchi & Saio.

Mean-force scattering potential for calculating optical properties of dense plasmas

We assess the relative importance of ionic structure on the opacity of dense plasmas by using the potential of mean force as a scattering potential within the Kubo-Greenwood formalism. We compare results from the potential of mean force, which includes realistic ionic structure, to results using an average atom potential, which includes only a crude treatment of ionic structure. Comparisons with less approximate but more expensive DFT-MD simulations for aluminum plasma reveal that the mean force generally improves agreement for DC conductivity. We also see improvement when applying the mean force to free-free transitions, whereas for bound-bound and bound-free transitions the mean force leads to poorer agreement on transition energies. Further, we assess the impact of accounting for correlations within the plasma at the temperature and density conditions relevant to iron opacity measurements at Sandia’s Z machine facility [Bailey et al., Nature 517:56-59, 2015] and find that these correlations do not account for the discrepancy between the measurements and leading opacity calculations.

Plasma opacity calculations using the Starrett and Saumon average-atom model with ion correlations

We present the opacities of iron, aluminum, and bromine plasmas calculated using the Starrett and Saumon average-atom model allowing for ion correlations. We show that the use of earlier average-atom ion-correlation model of Rozsnyai, as has recently been done in the solar opacity calculations, overestimates the effect of ion correlations on plasma opacities. The reason for this overestimation is discussed.

Subsonic structure and optically thick winds from Wolf–Rayet stars

Mass loss by stellar wind is a key agent in the evolution and spectroscopic appearance of massive main sequence and post-main sequence stars. In Wolf–Rayet stars the winds can be so dense and so optically thick that the photosphere appears in the highly supersonic part of the outflow, veiling the underlying subsonic part of the star, and leaving the initial acceleration of the wind inaccessible to observations. Here we investigate the conditions and the structure of the subsonic part of the outflow of Galactic Wolf–Rayet stars, in particular of the WNE subclass; our focus is on the conditions at the sonic point of their winds. We compute 1D hydrodynamic stellar structure models for massive helium stars adopting outer boundaries at the sonic point. We find that the outflows of our models are accelerated to supersonic velocities by the radiative force from opacity bumps either at temperatures of the order of 200 kK by the iron opacity bump or of the order of 50 kK by the helium-II opacity bump. For a given mass-loss rate, the diffusion approximation for radiative energy transport allows us to define the temperature gradient based purely on the local thermodynamic conditions. For a given mass-loss rate, this implies that the conditions in the subsonic part of the outflow are independent from the detailed physical conditions in the supersonic part. Stellar atmosphere calculations can therefore adopt our hydrodynamic models as ab initio input for the subsonic structure. The close proximity to the Eddington limit at the sonic point allows us to construct a sonic HR diagram, relating the sonic point temperature to the luminosity-to-mass ratio and the stellar mass-loss rate, thereby constraining the sonic point conditions, the subsonic structure, and the stellar wind mass-loss rates of WNE stars from observations. The minimum stellar wind mass-loss rate necessary to have the flow accelerated to supersonic velocities by the iron opacity bump is derived. A comparison of the observed parameters of Galactic WNE stars to this minimum mass-loss rate indicates that these stars have their winds launched to supersonic velocities by the radiation pressure arising from the iron opacity bump. Conversely, stellar models which do not show transonic flows from the iron opacity bump form low-density extended envelopes. We derive an analytic criterion for the appearance of envelope inflation and of a density inversion in the outer sub-photospheric layers.

Hohlraum modeling for opacity experiments on the National Ignition Facility

This paper discusses the modeling of experiments that measure iron opacity in local thermodynamic equilibrium (LTE) using laser-driven hohlraums at the National Ignition Facility (NIF). A previous set of experiments fielded at Sandia's Z facility [Bailey et al., Nature 517, 56 (2015)] have shown up to factors of two discrepancies between the theory and experiment, casting doubt on the validity of the opacity models. The purpose of the new experiments is to make corroborating measurements at the same densities and temperatures, with the initial measurements made at a temperature of 160 eV and an electron density of 0.7 × 1022 cm−3. The X-ray hot spots of a laser-driven hohlraum are not in LTE, and the iron must be shielded from a direct line-of-sight to obtain the data [Perry et al., Phys. Rev. B 54, 5617 (1996)]. This shielding is provided either with the internal structure (e.g., baffles) or external wall shapes that divide the hohlraum into a laser-heated portion and an LTE portion. In contrast, most inertial confinement fusion hohlraums are simple cylinders lacking complex gold walls, and the design codes are not typically applied to targets like those for the opacity experiments. We will discuss the initial basis for the modeling using LASNEX, and the subsequent modeling of five different hohlraum geometries that have been fielded on the NIF to date. This includes a comparison of calculated and measured radiation temperatures.

Computation of Atomic Astrophysical Opacities

The revision of the standard Los Alamos opacities in the 1980–1990s by a group from the Lawrence Livermore National Laboratory (OPAL) and the Opacity Project (OP) consortium was an early example of collaborative big-data science, leading to reliable data deliverables (atomic databases, monochromatic opacities, mean opacities, and radiative accelerations) widely used since then to solve a variety of important astrophysical problems. Nowadays the precision of the OPAL and OP opacities, and even of new tables (OPLIB) by Los Alamos, is a recurrent topic in a hot debate involving stringent comparisons between theory, laboratory experiments, and solar and stellar observations in sophisticated research fields: the standard solar model (SSM), helio and asteroseismology, non-LTE 3D hydrodynamic photospheric modeling, nuclear reaction rates, solar neutrino observations, computational atomic physics, and plasma experiments. In this context, an unexpected downward revision of the solar photospheric metal abundances in 2005 spoiled a very precise agreement between the helioseismic indicators (the radius of the convection zone boundary, the sound-speed profile, and helium surface abundance) and SSM benchmarks, which could be somehow reestablished with a substantial opacity increase. Recent laboratory measurements of the iron opacity in physical conditions similar to the boundary of the solar convection zone have indeed predicted significant increases (30–400%), although new systematic improvements and comparisons of the computed tables have not yet been able to reproduce them. We give an overview of this controversy, and within the OP approach, discuss some of the theoretical shortcomings that could be impairing a more complete and accurate opacity accounting.

Radiative opacities of iron using a difference algebraic converging method at temperatures near solar convection zone

An interpolation method named difference algebraic converging method for opacity (DACMo) is proposed to study the opacities and transmissions of metal plasmas. The studies on iron plasmas at temperatures near the solar convection zone show that (1) the DACMo values reproduce most spectral structures and magnitudes of experimental opacities and transmissions. (2) The DACMo can be used to predict unknown opacities at other temperature Te′ and density ρ′ using the opacity constants obtained at (Te, ρ). (3) The DACMo may predict reasonable opacities which may not be available experimentally but the least-squares (LS) method does not. (4) The computational speed of the DACMo is at least 10 times faster than that of the original difference converging method for opacity.

A note on the contribution of multi-photon processes to radiative opacity

Recently, Bailey et al. performed iron opacity measurements on the Z machine at Sandia National Laboratory in conditions close to the ones of the base of the convective zone of the Sun. Such experiments have raised questions about the physical models commonly used in opacity codes. To understand the discrepancy between experiment and theory, More et al. investigated the role of two-photon processes. In the present work we show, by simple estimate and using hydrogenic formulas, that due to the intensity of the backlight radiation seen by the sample, such processes are likely to play an important role only for highly excited states.

Diffusion-plus-drift models for the mass leakage from centrifugal magnetospheres of magnetic hot-stars

In the subset of luminous, early-type stars with strong, large-scale magnetic fields and moderate to rapid rotation, material from the star's radiatively driven stellar wind outflow becomes trapped by closed magnetic loops, forming a centrifugally supported, co-rotating magnetosphere. We present here a semi-analytic analysis of how this quasi-steady accumulation of wind mass can be balanced by losses associated with a combination of an outward, centrifugally driven drift in the region beyond the Kepler co-rotation radius, and an inward/outward diffusion near this radius. We thereby derive scaling relations for the equilibrium spatial distribution of mass, and the associated emission measure for observational diagnostics like Balmer line emission. We discuss the potential application of these relations for interpreting surveys of the emission line diagnostics for OB stars with centrifugally supported magnetospheres. For a specific model of turbulent field-line-wandering rooted in surface motions associated with the iron opacity bump, we estimate values for the associated diffusion and drift coefficients.

Tamper asymmetry and its effect on transmission for x-ray driven opacity simulations

This paper reports on synthetic transmission results from Lasnex [Zimmerman and Kruer, Comments Plasma Phys. 2, 51 (1975)] radiation-hydrodynamics simulations of opacity experiments carried out at Sandia National Laboratories' recently upgraded ZR facility. The focus is on experiments utilizing disk targets composed of a half-moon Fe/Mg mixture tamped on either end with 10-μm CH and an additional 35-μm beryllium tamper accessory on the end facing the spectrometer. Five x-ray sources with peak power ranging from 10 to 24 TW were used in the simulations to heat and backlight the opacity target. The dominant effect is that the beryllium behind the Fe/Mg mixture is denser and more opaque than the beryllium unshielded by metal during the times of greatest importance for the transmission measurement for all drives. This causes the simulated transmission to be lower than expected, and this is most pronounced for the case using the lowest drive power. While beryllium has a low opacity, its areal density is sufficiently high such that the expected reduction of the measured transmission is significant. This situation leads to an overestimate of iron opacity by 10%–215% for a photon energy range of 975–1775 eV for the 10-TW case. It is shown that if the tamper conditions are known, the transmission through each component of the target can be calculated and the resulting opacity can be corrected.

Local Stability and Global Instability in Iron-opaque Disks

Abstract The thermal stability of accretion disks and the possibility of seeing a limit-cycle behavior strongly depends on the ability of the disk plasma to cool down. Various processes connected with radiation–matter interaction appearing in hot accretion disk plasma contribute to opacity. For the case of geometrically thin and optically thick accretion disks, we can estimate the influence of several different components of function κ, given by the Roseland mean. In the case of high temperatures of ∼107 K, the electron Thomson scattering is dominant. At lower temperatures, atomic processes become important. The slope can have a locally stabilizing or destabilizing effect on the disk. Although the local MHD simulation postulates the stabilizing influence of the atomic processes, only the global time-dependent model can reveal the global disk stability range estimation. This is due to the global diffusive nature of those processes. In this paper, using the previously tested GLADIS code with a modified prescription of the viscous dissipation, we examine the stabilizing effect of the iron opacity bump.

Opacity from two-photon processes

The recent iron opacity measurements performed at Sandia National Laboratory by Bailey and collaborators have raised questions about the completeness of the physical models normally used to understand partially ionized hot dense plasmas. We describe calculations of two-photon absorption, which is a candidate for the observed extra opacity. Our calculations do not yet match the experiments but show that the two-photon absorption process is strong enough to require careful consideration.

The Effects of Magnetic Fields on the Dynamics of Radiation Pressure–dominated Massive Star Envelopes

Abstract We use three-dimensional radiation magnetohydrodynamic simulations to study the effects of magnetic fields on the energy transport and structure of radiation pressure–dominated main sequence massive star envelopes at the region of the iron opacity peak. We focus on the regime where the local thermal timescale is shorter than the dynamical timescale, corresponding to inefficient convective energy transport. We begin with initially weak magnetic fields relative to the thermal pressure, from 100 to 1000 G in differing geometries. The unstable density inversion amplifies the magnetic field, increasing the magnetic energy density to values close to equipartition with the turbulent kinetic energy density. By providing pressure support, the magnetic field’s presence significantly increases the density fluctuations in the turbulent envelope, thereby enhancing the radiative energy transport by allowing photons to diffuse out through low-density regions. Magnetic buoyancy brings small-scale magnetic fields to the photosphere and increases the vertical energy transport, with the energy advection velocity proportional to the Alfvén velocity, although in all cases we study, photon diffusion still dominates the energy transport. The increased radiative and advective energy transport causes the stellar envelope to shrink by several scale heights. We also find larger turbulent velocity fluctuations compared with the purely hydrodynamic case, reaching at the stellar photosphere. The photosphere also shows vertical oscillations with similar averaged velocities and periods of a few hours. The increased turbulent velocity and oscillations will have strong impacts on the line broadening and periodic signals in massive stars.

Numerical investigations of potential systematic uncertainties in iron opacity measurements at solar interior temperatures.

Iron opacity calculations presently disagree with measurements at an electron temperature of ∼180-195 eV and an electron density of (2-4)×10^{22}cm^{-3}, conditions similar to those at the base of the solar convection zone. The measurements use x rays to volumetrically heat a thin iron sample that is tamped with low-Z materials. The opacity is inferred from spectrally resolved x-ray transmission measurements. Plasma self-emission, tamper attenuation, and temporal and spatial gradients can all potentially cause systematic errors in the measured opacity spectra. In this article we quantitatively evaluate these potential errors with numerical investigations. The analysis exploits computer simulations that were previously found to reproduce the experimentally measured plasma conditions. The simulations, combined with a spectral synthesis model, enable evaluations of individual and combined potential errors in order to estimate their potential effects on the opacity measurement. The results show that the errors considered here do not account for the previously observed model-data discrepancies.

Capsule implosions for continuum x-ray backlighting of opacity samples at the National Ignition Facility.

Direct drive implosions of plastic capsules have been performed at the National Ignition Facility to provide a broad-spectrum (500-2000 eV) X-ray continuum source for X-ray transmission spectroscopy. The source was developed for the high-temperature plasma opacity experimental platform. Initial experiments using 2.0 mm diameter polyalpha-methyl styrene capsules with ∼20 μm thickness have been performed. X-ray yields of up to ∼1 kJ/sr have been measured using the Dante multichannel diode array. The backlighter source size was measured to be ∼100 μm FWHM, with ∼350 ps pulse duration during the peak emission stage. Results are used to simulate transmission spectra for a hypothetical iron opacity sample at 150 eV, enabling the derivation of photometrics requirements for future opacity experiments.

Detailed Opacity Calculations for Astrophysical Applications

Nowadays, several opacity codes are able to provide data for stellar structure models, but the computed opacities may show significant differences. In this work, we present state-of-the-art precise spectral opacity calculations, illustrated by stellar applications. The essential role of laboratory experiments to check the quality of the computed data is underlined. We review some X-ray and XUV laser and Z-pinch photo-absorption measurements as well as X-ray emission spectroscopy experiments involving hot dense plasmas produced by ultra-high-intensity laser irradiation. The measured spectra are systematically compared with the fine-structure opacity code SCO-RCG. The focus is on iron, due to its crucial role in understanding asteroseismic observations of β Cephei-type and Slowly Pulsating B stars, as well as of the Sun. For instance, in β Cephei-type stars, the iron-group opacity peak excites acoustic modes through the “kappa-mechanism”. Particular attention is paid to the higher-than-predicted iron opacity measured at the Sandia Z-machine at solar interior conditions. We discuss some theoretical aspects such as density effects, photo-ionization, autoionization or the “filling-the-gap” effect of highly excited states.

Replicating the Z iron opacity experiments on the NIF

X-ray opacity is a crucial factor of all radiation-hydrodynamics calculations, yet it is one of the least validated of the material properties in the simulation codes. Recent opacity experiments at the Sandia Z-machine have shown up to factors of two discrepancies between theory and experiment, casting doubt on the validity of the opacity models. Therefore, a new experimental opacity platform is being developed on the National Ignition Facility (NIF) not only to verify the Z-machine experimental results but also to extend the experiments to other temperatures and densities. The first experiments will be directed towards measuring the opacity of iron at a temperature of ∼160eV and an electron density of ∼7 ×1021 cm−3. Preliminary experiments on NIF have demonstrated the ability to create a sufficiently bright point backlighter using an imploding plastic capsule and also a hohlraum that can heat the opacity sample to the desired conditions. The first of these iron opacity experiments is expected to be performed in 2017.

Computational design of short pulse laser driven iron opacity experiments

The resolution of current disagreements between solar parameters calculated from models and observations would benefit from the experimental validation of theoretical opacity models. Iron's complex ionic structure and large contribution to the opacity in the radiative zone of the sun make iron a good candidate for validation. Short pulse lasers can be used to heat buried layer targets to plasma conditions comparable to the radiative zone of the sun, and the frequency dependent opacity can be inferred from the target's measured x-ray emission. Target and laser parameters must be optimized to reach specific plasma conditions and meet x-ray emission requirements. The HYDRA radiation hydrodynamics code is used to investigate the effects of modifying laser irradiance and target dimensions on the plasma conditions, x-ray emission, and inferred opacity of iron and iron-magnesium buried layer targets. It was determined that plasma conditions are dominantly controlled by the laser energy and the tamper thickness. The accuracy of the inferred opacity is sensitive to tamper emission and optical depth effects. Experiments at conditions relevant to the radiative zone of the sun would investigate the validity of opacity theories important to resolving disagreements between solar parameters calculated from models and observations.