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A New Generation of Los Alamos Opacity Tables
J. Colgan, D. P. Kilcrease, N. H. Magee, M. E. Sherrill, J. Abdallah, Jr., P. Hakel, C. J. Fontes, J. A. Guzik, K. A. Mussack
TL;DR
Opacity calculations are relevant to stellar modeling, and revised solar abundances have left a discrepancy between standard solar models and helioseismic observations. The authors generate new Los Alamos opacity tables with ATOMIC and report improved helioseismic agreement in solar modeling, though the solar-abundance problem is not fully resolved.
Problem
Revised solar abundances disrupted earlier agreement between standard solar models and helioseismic observations, and the solar-abundance problem remains unresolved.
Source: §1 · p. 2Method
Results
Use of the new tables in solar modeling improves agreement with helioseismology but does not fully resolve the solar-abundance problem.
Source: §4 · p. 19Takeaways & Limitations
The publicly available tables are intended to be useful to the astrophysical modeling community, with their effects on stellar objects left for further exploration.
Source: §4 · p. 19The configuration-selection prescription cannot guarantee that all opacity-significant configurations are included, and completeness is difficult to demonstrate at every temperature-density point.
Source: §2.1 · p. 4
Abstract
from arXiv · showhide
We present a new, publicly available, set of Los Alamos OPLIB opacity tables for the elements hydrogen through zinc. Our tables are computed using the Los Alamos ATOMIC opacity and plasma modeling code, and make use of atomic structure calculations that use fine-structure detail for all the elements considered. Our equation-of-state (EOS) model, known as ChemEOS, is based on the minimization of free energy in a chemical picture and appears to be a reasonable and robust approach to determining atomic state populations over a wide range of temperatures and densities. In this paper we discuss in detail the calculations that we have performed for the 30 elements considered, and present some comparisons of our monochromatic opacities with measurements and other opacity codes. We also use our new opacity tables in solar modeling calculations and compare and contrast such modeling with previous work.
1. Introduction
Opacity differences matter for stellar models, including unresolved solar-abundance and helioseismology discrepancies. The paper introduces replacement Los Alamos tables and compares them with measurements, other calculations, and solar-modeling results.
1. Introduction
- Radiative opacity affects radiation transport and is important to stellar evolution, pulsation, and the determination of large-scale stellar quantities.Opacity differences between OP and OPAL calculations have also been associated with discrepancies in β-Cepheid pulsation modeling.Source: §1 · pp. 1–2
- Revised solar abundances disrupted earlier agreement between standard solar models and helioseismic observations, while the solar-abundance problem remains unresolved.A 5–20% opacity increase for some major solar elements in the radiative zone was proposed as a way to restore agreement.Source: §1 · p. 2
- The new ATOMIC-generated OPLIB tables cover hydrogen through zinc and are intended to replace the earlier LEDCOP-based Los Alamos tables.The paper compares new opacities with measurements and earlier theoretical work.Source: §1 · p. 2
- The paper compares monochromatic opacities with measurements, including Sandia Z-pinch measurements, and with other opacity calculations.It also presents solar-mixture opacity calculations and discusses their implications for solar modeling.Source: §1 · pp. 2–3
2. Theoretical Methods
The theoretical methods use ATOMIC to calculate monochromatic and mean opacities across a broad range of elements and plasma conditions. The calculations combine detailed atomic data with separate opacity contributions.
2. Theoretical Methods
- The calculations use ATOMIC, a plasma-modeling code that can run in LTE or non-LTE and at different levels of atomic-data refinement.The atomic data used here were generated with the semi-relativistic capability of the Los Alamos atomic-physics codes.Source: §2 · p. 3
- The tables provide monochromatic, Rosseland mean, and Planck mean opacities for hydrogen through zinc over broad temperature and density ranges.Temperatures span 0.5 eV to 100 keV, and densities cover at least 12 orders of magnitude, starting around 10^-8 g/cm^3 or lower depending on conditions.Source: §2 · p. 3
- The frequency-dependent opacity combines bound-bound, bound-free, free-free, and scattering contributions, with stimulated-emission factors in the first three.Source: §2 · p. 3
2.1. Choice of configuration model for opacity calculations
The opacity model selects configurations to capture populated states and transitions, then uses different fine-structure strategies across elements. The configuration-selection prescription is inclusive but cannot guarantee completeness.
2.1. Choice of configuration model for opacity calculations
- Configurations were selected to cover likely populated states and bound-bound transitions, including configurations within about twice the ground-configuration ionization energy and dipole-allowed promotions.The selection also includes valence-sub-shell excitations up to nl = 10m.Source: §2.1 · pp. 3–4
- The prescription does not guarantee inclusion of every opacity-significant configuration, and completeness is difficult to demonstrate at every temperature-density point.The authors consider it sufficiently inclusive for large-scale tables and discuss a configuration increase for one Fe calculation.Source: §2.1 · p. 4
2.2. Bound-bound opacity contribution
- For Be-like through neutral stages of Be–Si, level-resolved calculations use full configuration interaction for Li-like and more highly ionized stages, but a single-configuration approximation for more-electron stages.A small configuration-interaction calculation replaces energies for L-shell 1s2[2]w configurations to improve Δn = 0 line positions.Source: §2.2 · p. 5
- For P–Zn, MUTA retains the strongest fine-structure lines while using configuration-average populations, reducing the cost of full level-resolved calculations.The approach appears accurate above about 10 eV; below this, statistical splitting of configuration populations may be less accurate because configuration-average transition energies may poorly approximate fine-structure energies.Source: §2.2 · pp. 5–6
2.3. Bound-free opacity contribution
Bound-free opacity is calculated from photoionization data, with edge blending to smooth the transition from bound states to continuum. Free-free opacity uses tabulated results and additional plasma corrections.
2.3. Bound-free opacity contribution
- Bound-free opacity uses configuration-average distorted-wave photoionization cross sections between neighboring ion stages, plus H− photodetachment data.Occupation probabilities blend Rydberg series into bound-free edges, smoothing monochromatic opacity while conserving oscillator strength.Source: §2.3 · p. 6
2.4. Free-free opacity contribution
- Free-free opacity uses Nakagawa et al. tables with plasma-screening and low-frequency multiple-collision corrections.The H−, He−, and C− contributions matter mainly below about 1.0 eV; the C− contribution was not included in the earlier LEDCOP calculations.Source: §2.4 · p. 6
2.5. Photon scattering opacity contribution
The calculations include modified Compton scattering and Rayleigh scattering in the photon-scattering opacity contribution, with effects that depend on photon energy, density, and temperature.
2.5. Photon scattering opacity contribution
- Compton scattering uses Sampson’s tables, modified for Pauli blocking, collective effects, strong coupling, and electron degeneracy.Bound electrons are treated as free for Compton scattering when photon energy reaches or exceeds their binding energy.Source: §2.5 · pp. 6–7
- At high photon energies, Compton scattering lowers opacity relative to Thomson scattering.Pauli blocking and collective effects decrease the Rosseland mean opacity at very high densities.Source: §2.5 · p. 7
- Rayleigh scattering is included for the low-energy side of the lowest ground-state transition of neutral atoms and can be important at low temperatures.Neutral-species contributions often dominate opacity in that temperature regime.Source: §2.5 · p. 7
2.6. Line broadening
The line-broadening treatment combines ion and neutral broadening prescriptions with a far-wing choice informed by scattering and absorption physics. For cold helium, that far-wing choice can strongly affect the Rosseland mean opacity.
2.6. Line broadening
- The broadening package includes Stark broadening for H-like and He-like lines, neutral resonance and van der Waals broadening, and Voigt profiles for lines outside the Stark package.Natural broadening is included with Stark broadening; electron collisional broadening follows Armstrong’s approach. Neutral broadening gives a small contribution in low-temperature regions, especially for He.Source: §2.6 · p. 7
- The far red wing of all absorption lines uses the ω^4 behavior chosen after considering scattering and absorption processes within a QED framework.The choice addresses differing conclusions in earlier studies about the appropriate far-wing line shape.Source: §2.6 · pp. 7–8
- Without the ω^4 line shape, the Rosseland mean opacity for He near 1 eV may increase by more than three orders of magnitude.At those conditions, the far wing of the nearest bound-bound transition is essentially the only opacity contributor; the effect is much smaller at higher temperatures and for other elements with smaller ionization potentials.Source: §2.6 · pp. 7–8
2.7. Equation-of-state used in opacity calculations
ATOMIC uses ChemEOS, which determines atomic-state populations by minimizing Helmholtz free energy in the chemical picture. Its free-energy terms and occupation probabilities account for particle contributions and plasma effects across the modeled states.
2.7. Equation-of-state used in opacity calculations
- ChemEOS writes total free energy as F = F1 + F2 + F3 + F4 + F5, combining ideal atom-and-ion gas, internal energy, ideal Fermi-electron gas, Coulomb, and excluded-volume terms.The Coulomb term includes ion-ion, ion-electron, and electron-electron contributions; the excluded-volume term uses an all-order hard-sphere packing term.Source: §2.7 · pp. 8–9
- The internal-energy term depends on a converged partition function, whose excited-state statistical weights are progressively reduced by occupation probabilities to account for plasma perturbations.The hard-sphere occupation-probability term is included for all atoms and ions and eliminates unphysical atomic-state populations at high densities.Source: §2.7 · p. 8
- The occupation-probability model uses screened microfield distributions for H and He, but unscreened distributions for other elements because screened calculations are prohibitively costly for systems with many states.The hard-sphere contribution is included for all atoms and ions.Source: §2.7 · p. 8
- The partition function extends its explicitly listed configurations through n = 10 to n = 100 using analytic quantum-defect terms.This extension was also used in the previous LEDCOP calculations.Source: §2.7 · pp. 8–9
2.8. The Los Alamos National Laboratory Opacity Website
The OPLIB website provides access to the new ATOMIC tables and the previous LEDCOP tables, with options for elements, mixtures, and several opacity forms. The new tables offer a finer temperature grid and generally extend to higher densities.
2.8. The Los Alamos National Laboratory Opacity Website
- Users can request monochromatic, multigroup, Rosseland mean, or Planck mean opacities for individual elements or arbitrary mixtures from hydrogen through zinc.Monochromatic opacities use a temperature-scaled grid of 14,900 photon energies; absorption and scattering contributions are also tabulated separately.Source: §2.8 · p. 9
- Rosseland means on the website assume a refractive index of 1 above the plasma frequency and 0 below it, facilitating mixture calculations.Mixtures are generated from pure-element tables assuming electron-temperature and electron-degeneracy equilibrium.Source: §2.8 · p. 9
- The ATOMIC tables provide 24 more isotherms than the LEDCOP tables and generally extend to higher mass densities.The finer temperature grid should help reduce interpolation errors; pre-calculated mixtures are also available.Source: §2.8 · pp. 9–10
3. Results
The single-element comparisons show agreement with some measurements and opacity calculations, alongside a substantial unresolved Fe discrepancy at newer Sandia conditions. In solar models, ATOMIC opacities improve sound-speed agreement with helioseismic inferences, but do not resolve the discrepancy.
3.1. Single-Element Opacity Comparisons
- At solar convection-zone-base conditions, Mg’s broad monochromatic-opacity features agree reasonably between ATOMIC and OP, while OP’s Heα line is broader.OPAS opacity is close to ATOMIC, and the three calculations show very close agreement in Mg ionization balance.Source: §3.1 · p. 10, Figure 1 · p. 11
- ATOMIC agrees very well with the 2007 Sandia Fe measurements in line positions, inter-line valleys, and underlying opacity, though some line heights differ.The authors suggest incomplete treatment of instrument resolution may account for some line-height differences.Source: §3.1 · pp. 10, 12, Figure 2 · p. 13
- At the newer Sandia Fe conditions, ATOMIC matches major line positions but has a persistent background-opacity discrepancy, especially where L-shell bound-free opacity dominates.If confirmed, the measurements and disagreement with theory have implications for solar opacities near the base of the radiative convection zone.Source: §3.1 · p. 12, Figure 2 · p. 13
- Expanding the Fe atomic model by about an order of magnitude through four-electron L-shell promotions produced only small monochromatic-opacity changes, with bound-free opacity almost unchanged.Full configuration interaction had minor effects, and calculations were insensitive to the tested screening microfield distribution at these conditions.Source: §3.1 · pp. 12, 14
- For Cr, ATOMIC opacity is shifted to higher photon energies than OP at both conditions; their Rosseland means are closer at the higher-density condition.At the lower-density condition, OP’s Rosseland mean is considerably higher; LEDCOP agrees very well with ATOMIC, and the shift may reflect OP’s use of scaled atomic data.Source: §3.1 · pp. 14, 16, Figure 3 · p. 15
3.2. Solar Model Results
- With AGSS09 abundances, the ATOMIC-opacity solar model’s sound-speed profile agrees better with helioseismic inference, but both ATOMIC and OPAL models retain a too-shallow convection zone and too-low convection-zone helium fraction.A similar sound-speed improvement was found in AGSS09 models evolved with MESA.Source: §3.2 · pp. 16, 19, Figure 4 · p. 17
- ATOMIC opacity temperature derivatives are steeper near the convection-zone base and around log T = 6.8, where the solar models’ sound-speed profiles change slope.Across the radiative interior, OPAL opacities are slightly higher; ATOMIC becomes higher in the convection zone, where opacity is not important to solar structure because convection transports nearly all emergent luminosity.Source: Figure 5 · p. 18, §3.2 · p. 19
4. Conclusions
The new OPLIB tables use ATOMIC and improve on the previous Los Alamos tables in physics approximations and calculation detail. Solar models using them agree better with helioseismology, though long-standing discrepancies remain.
4. Conclusions
- ATOMIC-generated OPLIB tables improve the underlying physics approximations and calculation detail over the previous Los Alamos generation.The tables also improve agreement with B-star pulsation observations.Source: §4 · p. 19
- Using the new tables in solar modeling improves agreement with helioseismology but does not fully resolve long-standing discrepancies.Source: §4 · p. 19
- The publicly available tables are intended for astrophysical modeling, with further study of their effects on stellar objects identified as future work.Source: §4 · p. 19
5. Appendix: Rayleigh scattering details
The appendix describes low-energy Rayleigh scattering treatments for neutral atoms, primarily using static dipole polarizability while using more detailed dynamic treatments for selected elements.
5. Appendix: Rayleigh scattering details
- For neutral atoms, low-energy Rayleigh scattering is approximated from static dipole polarizability, with dynamic-polarizability treatments used for H, He, Li, C, N, O, Ne, and Ar.Source: §5 · p. 20
- For elements without more complete expressions, the appendix uses the static polarizability α(ω = 0) approximation for scattering opacity.The dipole polarizability α(0) is in Bohr radii cubed.Source: §5 · p. 21
- The scattering-opacity contribution is specified using mass density and the neutral atom's ground-state population.Source: §5 · p. 22