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Kilonova ejecta opacity inferred from new large-scale HFR atomic calculations in all elements between Ca (Z = 20) and Lr (Z = 103)

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Lanthanides do not dominate kilonova opacity, new atomic data show.

desk verdict A solid, citable full-periodic-table opacity resource whose main claims hold up; the lanthanide conclusion depends on one abundance model, and the composition-mixing procedure deserves a proper multi-element Saha test. read the letter →

arxiv 2412.16688 v1 pith:5X3CIEKI submitted 2024-12-21 astro-ph.HE

Jérôme Deprince , Gururaj Wagle , Sirine Ben Nasr , Helena Carvajal Gallego , Michel Godefroid , Stéphane Goriely , Oliver Just , Patrick Palmeri
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Pascal Quinet Sophie Van Eck
This is my paper · ORCID
classification astro-ph.HE
keywords kilonovaneutronstarmergeropacityatomicdatalanthanidesactinidesr-processexpansion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper builds a complete set of atomic data and opacities for every element from calcium ($Z=20$) to lawrencium ($Z=103$), in the first four ionization stages, using the pseudo-relativistic Hartree-Fock (HFR) method, for the temperature and density conditions of a kilonova photosphere one day to one week after a neutron-star merger. It then folds these per-element opacities into the r-process abundance pattern of a realistic merger simulation. The central claim is that, at least on average, lanthanides are not the dominant opacity sources: their single-element opacities are orders of magnitude larger than those of other elements, but their abundances in this model are so low that abundant 3d- and 4d-shell elements around $Z\simeq 24$ and $Z\simeq 40$ contribute just as much. The paper further argues that single-element expansion opacities cannot be averaged with abundances afterward, because that shortcut gives $0.11\ \mathrm{cm^2\,g^{-1}}$ instead of the correct $1.13\ \mathrm{cm^2\,g^{-1}}$. These opacities shift the predicted bolometric light-curve peak from about 1-2 days to 7-8 days after merger.

What carries the argument

The machinery is the composition-weighted expansion opacity, built on the standard Sobolev expansion formula $\kappa_{\mathrm{exp}}(\lambda) = (1/ct\rho)\sum_l (\lambda_l/\Delta\lambda)(1-e^{-\tau_l})$ and its Planck mean. The defining move is to scale each element's lower-level number density inside the optical depth by its molar abundance, $n_{l,Z} = y_Z n_l$, so the mixture opacity is computed before summing over elements rather than by averaging completed single-element opacities. The atomic input comes from large multiconfiguration pseudo-relativistic Hartree-Fock calculations for ions I-IV of all elements from calcium to lawrencium; the paper argues that the level errors and inverted ground states these models leave (18-30% for most ions, 49% for Nd III) have little effect on expansion opacities, based on tests for Nd, U, and Er. The line-binned opacity $\kappa^{\mathrm{bin}}_\nu\propto \sum_l N_l f_l$ scales linearly with abundance and therefore does not suffer from the a posteriori averaging problem.

What would settle it

Recompute the full-ejecta Planck opacity at $t=3.5$ d, $T=6000$ K, $\rho=10^{-13}\ \mathrm{g\,cm^{-3}}$ with the paper's HFR tables but with r-process abundances from a different nuclear mass model or fission prescription; if the lanthanide and actinide contribution then exceeds the d-shell contribution, the average non-dominance claim fails. A second check is to compare the predicted $\sim$7-8 day bolometric peak with the observed AT2017gfo light curve; if the HFR-opacity model is conclusively excluded by the timing, the opacity shift is not the right description.

Watch

Extended reading notes

Core claim

The discovery is a change in who controls kilonova opacity when the ejecta composition is taken seriously. For the sym-n1-a6 merger model at 3.5 days ($T=6000\ \mathrm{K}$, $\rho=10^{-13}\ \mathrm{g\,cm^{-3}}$), the composition-weighted HFR Planck opacity is $1.13\ \mathrm{cm^2\,g^{-1}}$, about 25% below the $1.43\ \mathrm{cm^2\,g^{-1}}$ obtained from a parametric formula that links opacity to the lanthanide-plus-actinide molar fraction. The opacity budget is shared among lanthanides and actinides and the much more abundant elements near $Z\simeq 24$ and $Z\simeq 40$. The paper's second result is methodological: because the expansion opacity is a nonlinear Sobolev sum over lower-level populations, replacing those populations by abundance-scaled ones inside the formula is not the same as averaging single-element opacities; the a posteriori average gives $0.11\ \mathrm{cm^2\,g^{-1}}$, an order of magnitude too low. When the HFR opacities replace the parametric formula in light-curve simulations, the bolometric peak moves from roughly 1-2 days to about 7-8 days, with a slightly lower peak luminosity for the full ejecta.

Load-bearing premise

The load-bearing premise is that the single abundance pattern from the sym-n1-a6 merger simulation with the BSkG3 mass model is representative enough that the cancellation between low lanthanide abundance and high lanthanide opacity holds in real kilonova ejecta, because other r-process models vary that abundance by orders of magnitude.

Editorial extensions

If this is right

  • Kilonova light curves computed with these opacities peak at roughly 7-8 days rather than 1-2 days, a shift that is directly testable against the observed evolution of AT2017gfo.
  • Lanthanide and actinide molar fraction alone is not a reliable opacity proxy; the parametric formula built on it is 25% high for the full ejecta and a factor of two low for the dynamical ejecta.
  • Single-element expansion opacity tables should not be combined with arbitrary abundance patterns a posteriori; the correct composition-weighted calculation changes the answer by an order of magnitude here.
  • The published grid of HFR atomic data and expansion/line-binned opacity tables for $Z=20$-103, ions I-IV, over $t=1$-7 days, $\rho=10^{-17}$-$10^{-13}\ \mathrm{g\,cm^{-3}}$, and $T=1000$-10000 K provides a common baseline for kilonova modeling.
  • When only the fast dynamical ejecta is considered, the HFR opacities give a brighter peak than the parametric opacity, so atomic data matter even in the lanthanide-dominated component.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's lanthanide-non-dominance conclusion should be read as abundance-pattern dependent: replacing the BSkG3-based abundances with another r-process mass model or fission prescription, which can change lanthanide fractions by orders of magnitude, could restore lanthanide dominance, and this test is not performed in the paper.
  • The same composition-weighting failure likely affects any kilonova or transient model that stores Planck mean opacities per element and later mixes them with abundances; line-binned opacities, being linear in abundance, are the safer stored quantity for such post-processing.
  • Recomputing the light curve with per-trajectory compositions instead of the uniform composition assumed here could sharpen or soften the 7-8 day peak shift; the paper identifies this as future work.
  • If the non-dominance holds broadly, the atomic-data bottleneck shifts from all lanthanides to a short list of species (Cr, Fe, Zr, Mo, Sm, Nd, Dy, Er, U, Np, Pu), and improving those atoms experimentally and theoretically would be the highest-value next step.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This paper presents new pseudo-relativistic Hartree-Fock (HFR) atomic structure calculations for all elements from Ca (Z = 20) to Lr (Z = 103) in ionization stages I-IV, together with expansion and line-binned opacities for a kilonova-relevant grid (T = 1000-10000 K, rho = 1e-17 to 1e-13 g/cm^3, t = 1-7 days). The data are made publicly available on Zenodo. The authors compare their Planck mean opacities with Tanaka et al. (2020) and Fontes et al. (2020, 2023), and apply the opacities to the neutron star merger model sym-n1-a6 from Just et al. (2023). Their central result is that, for this model, the composition-weighted HFR expansion opacity is 1.13 cm^2/g, about 25% lower than the parametric prescription of Just et al. (2022), and that lanthanides are not the dominant contributors 'at least on average'; instead, 3d-shell (Z ~ 24) and 4d-shell (Z ~ 40) elements contribute substantially. They also find that abundance-weighted single-element Planck opacities (0.11 cm^2/g) underestimate the mixture opacity by an order of magnitude, and that HFR opacities shift the modeled bolometric peak from roughly 1-2 days to roughly 7-8 days.

Significance. The database is a major community resource: consistent HFR oscillator strengths and energy levels for 84 elements in four charge states are not currently available elsewhere with this coverage. The comparison with existing data sets and the public release are valuable. If the central claim survives scrutiny, it challenges the common practice of treating lanthanide opacity as the sole determinant of kilonova red/infrared emission and the practice of building mixture opacities by abundance-weighting single-element tables. The result is, however, conditional on the adopted nucleosynthesis composition and on the composition-mixing approximation discussed below. The manuscript is generally careful in hedging ('for a given model', 'at least on average'), but the headline result deserves stronger validation.

major comments (3)
  1. [§6, Eq. (9)] The composition-weighted opacity is constructed by scaling pure-element lower-level densities n_l by the elemental molar fraction y_Z, i.e., n_{l,Z} = y_Z n_l. This does not solve the Saha equation (Eq. 5) with a common electron density n_e and charge conservation for the mixture; it implicitly assumes that each element's ionization balance in the mixture is identical to that in a pure plasma of that element at the same bulk density. Because n_e in a mixture is dominated by the abundant lighter elements, while the trace lanthanides (molar fraction 8.4e-5 in the full ejecta) have their own pure-plasma n_e, the ion fractions of the important species are not established. The claimed totals (1.13 cm^2/g for the full ejecta, 5.42 cm^2/g for the dynamical component) and the factor-10 discrepancy with the abundance-weighted single-element value (0.11 cm^2/g) therefore rest on an untested approximation. Please either implement a self-consistent multi-element LTE calculation for the sym-n1-a6 composition, or provide a quantitative demonstration that the pure-element Saha fractions are insensitive to n_e over the relevant range.
  2. [§2] The paper states that HFR energy-level discrepancies of 18-30% (49% for Nd III) and inverted ground states in 23 of the 120 lanthanide/actinide ions leave expansion opacities essentially unaffected, but this claim is demonstrated only for Nd II/III, U II/III, and Er III. The extrapolation to all 429 ions is a load-bearing step because the main astrophysical conclusion depends on the relative opacities of d-shell, lanthanide, and actinide species. A sensitivity test covering representative ions from each group (e.g., Cr, Mo, Sm, U) with and without level-energy calibration, or a propagated uncertainty estimate on the total mixture opacity, would substantially strengthen the robustness of the result.
  3. [§6] The 'lanthanides are not dominant' conclusion is drawn from a single r-process abundance pattern, model sym-n1-a6 with the BSkG3 mass model. The lanthanide-plus-actinide molar fraction in this model is 8.4e-5 in the full ejecta and 8.7e-4 in the dynamical component. Because single-element lanthanide/actinide opacities exceed those of the abundant d-shell elements by several orders of magnitude (Section 3), the ranking is a cancellation between per-element opacity and abundance. Published r-process calculations with other mass models or fission treatments show lanthanide fractions varying by orders of magnitude. The paper should either test the sensitivity of the ranking and of the 1.13 cm^2/g total to variations in the lanthanide/actinide fraction within the range of current models, or explicitly narrow the claim to this specific nucleosynthesis model in the abstract.
minor comments (4)
  1. [Figure captions 2-5] The density unit in the figure captions is given as '10^-13 cm^-1'; it should be '10^-13 g cm^-3' as in the text.
  2. [Section 7] Typos: 'The purpose of this work is to is to build' and 'impoortance' should be corrected; 'Eriii' should be 'Er III'; in the reference list, 'Astronomy & Astroohysics' should be 'Astronomy & Astrophysics'.
  3. [Acknowledgements] The reference to 'KILONOV A' should be 'KILONOVA'.
  4. [Eq. (7)] The Planck mean opacity definition uses B_lambda(T) in both numerator and denominator; it may be worth noting explicitly that the integration is over the full wavelength range, as stated in the text, to avoid confusion with the line-binned version.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the opacities are forward-computed from HFR atomic structure calculations and are benchmarked against independent methods and experimental levels.

full rationale

The paper's central outputs—per-element expansion opacities, Planck-mean opacities, and the composition-weighted ejecta opacity—are obtained from ab initio atomic structure calculations (HFR) combined with an external r-process abundance pattern, with no parameter fitted to opacity or light-curve targets. The comparison between the Eq. (9) mixture treatment and abundance-averaged single-element opacities is a computed consequence of the nonlinear expansion-opacity formula, not an input assumed into the result. The self-citations to Flörs et al. (2023) and Deprince et al. (2023, 2024) serve as convergence and accuracy studies that include independent benchmarks (FAC and experimental energy levels), so they do not reduce the argument to an unverified self-citation. The lanthanide non-dominance conclusion depends on one nucleosynthesis model, which is a robustness limitation rather than a circularity. No load-bearing step in the derivation is equivalent by construction to its own output.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central results rest on standard atomic-physics and LTE assumptions plus two domain-specific premises. The two free numeric choices (Slater scaling 0.85 and log gf >= -5) are argued to leave opacities nearly unchanged, and the per-ion configuration lists are the main modeling degrees of freedom. The two load-bearing domain assumptions are the BSkG3-generated abundance pattern of the single merger model (the lanthanide fraction 8.4e-5 drives the headline result) and the claimed insensitivity of expansion opacities to the documented level errors and ground-state inversions. No new entities (particles, forces, dimensions) are introduced.

free parameters (3)
  • Slater integral scaling factor = 0.85
    Cowan (1981) recommended scaling applied to all Slater integrals; Section 2 notes scaling 0.8-0.95 leaves opacities nearly unchanged (Carvajal Gallego et al. 2023a), so the opacity impact is claimed to be small.
  • log gf cut-off = -5
    Transitions with log gf below -5 are discarded; Section 2 states this does not modify expansion opacity, citing Carvajal Gallego et al. (2022a).
  • Configuration list restrictions = per-ion lists in Table 1 (Appendix)
    For ions with very large Hamiltonian matrices, 'a few isolated restrictions' are applied to double excitations (Section 2); justified by convergence studies for Nd II-III, U II-III (Flörs et al. 2023) and Er III (Deprince et al. 2024), then extrapolated by homology to all other ions.
assumptions (6)
  • domain assumption LTE holds in the KN photosphere from 1 day to about 1 week post-merger
    Section 3 chooses the 1-7 day grid and Saha-Boltzmann populations (Eqs. 5-6) on the basis of Pognan et al. (2022); beyond one week NLTE effects become important, limiting the tables' validity window.
  • domain assumption Only ionization stages I-IV are relevant at T <= 10000 K
    Section 3 states that for 1000-10000 K only neutral through triply-ionized species are present, citing Tanaka et al. (2020) and Flörs et al. (2023); the entire database covers only these four stages.
  • standard math Sobolev expansion opacity formalism is valid for NS merger ejecta
    Equations 3-4 follow Eastman and Pinto (1993), Kasen et al. (2013), Tanaka and Hotokezaka (2013); Section 3 justifies the Sobolev approximation by the high expansion velocities (about 0.1c).
  • domain assumption The sym-n1-a6 abundance pattern (BSkG3 mass model) is representative for the opacity-dominance question
    Section 6 draws the headline lanthanide conclusion from this single model, whose lanthanide plus actinide molar fraction is 8.4e-5 in the full ejecta; other r-process prescriptions can differ by orders of magnitude in this fraction.
  • domain assumption Expansion opacities are insensitive to the documented HFR level errors and ground-state inversions
    Section 2 asserts robustness for high-spectral-density ions based on the authors' earlier calibration studies (Deprince et al. 2023, 2024) and extrapolates it to all 429 ions by homology.
  • domain assumption CI models built by homologous sequence from studied ions are converged for every element
    Section 2 constructs configuration lists for unstudied ions (fourth row, fifth row, Cs-Ba-Fr-Ra) by analogy with fourth-row elements, without per-ion convergence tests.

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Pith. "Pith review of Kilonova ejecta opacity inferred from new large-scale HFR atomic calculations in all elements between Ca (Z = 20) and Lr (Z = 103)." pith.science (2026). https://pith.science/paper/5X3CIEKI

@misc{pith2026241216688,
  author       = {Pith},
  title        = {Pith review of: Kilonova ejecta opacity inferred from new large-scale HFR atomic calculations in all elements between Ca (Z = 20) and Lr (Z = 103)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5X3CIEKI}},
  note         = {Machine review of arXiv:2412.16688}
}
read the original abstract

In the context of kilonova (KN) modeling, the present work focusses on large-scale atomic data and opacity computations for all heavy elements from Ca to Lr, with a special effort on lanthanides and actinides, for a grid of typical KN ejecta conditions between one day and one week after the merger (corresponding to the LTE photosphere phase of the KN ejecta). In order to do so, we used the pseudo-relativistic Hartree-Fock (HFR) method, in which the choice of the interaction configuration model is of crucial importance. In this paper, HFR atomic data and opacities for all elements between Ca (Z = 20) and Lr (Z = 103) are presented, with a special focus on lanthanides and actinides. Besides, we also discuss the contribution of every single element to the total KN ejecta opacity for a given neutron star merger model, depending on their Planck mean opacities and elemental abundances. An important result is that lanthanides are found to not be the dominant sources of opacity, at least on average. The impact on KN light curves of considering such atomic-physics based opacity data instead of typical crude approximation formulae is also evaluated. In addition, the importance of taking the ejecta composition into account directly in the expansion opacity determination (instead of estimating single-element opacities) is highlighted. A database containing all the relevant atomic data and opacity tables has also been created and published online along with this work.

Figures

Figures reproduced from arXiv: 2412.16688 by the authors.

Figure 1
Figure 1. Time evolution of the density and temperature at the pho [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Expansion opacities of the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 5
Figure 5. Lanthanide and actinides expansion opacities for [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figures from the paper (8 more)
Figure 3
Figure 3. Figure 3: Expansion opacities of the np group elements for t = 1 day, T = 5000K and ρ = 10−13 cm−1 (left panels) and their corresponding Planck mean opacities (right panels) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png]
Figure 4
Figure 4. Figure 4: Expansion opacities of the ns group elements for t = 1 day, T = 5000K and ρ = 10−13 cm−1 (left panels) and their corresponding Planck mean opacities (right panels). Tanaka et al. (2020) were not computed using all the energy lev￾els from the calculation but were approx…
Figure 7
Figure 7. Figure 7: Lanthanide Planck line-binned opacities for [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Actinide Planck line-binned opacities for [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 9
Figure 9. Figure 9: Single-element Planck mean opacities for each species [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 11
Figure 11. Figure 11: Temperature and density dependence of the Planck mean [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 12
Figure 12. Figure 12: Comparison of light curves obtained with the kilonova scheme developed in Just et al. (2022) for the NS merger model [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 13
Figure 13. Figure 13: Time evolution of the photospheric properties and the [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Calibrated Lanthanide Atomic Data for Kilonova Radiative Transfer. I. Atomic Structure and Opacities

    astro-ph.HE 2025-07 conditional novelty 6.0 of 10

    A new calibrated atomic dataset for all singly and doubly ionized lanthanides provides 66,591 experimentally anchored transition wavelengths for kilonova modeling.

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