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Luminosity predictions for the first three ionisation stages of W, Pt and Au to probe potential sources of emission in kilonova

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Doubly ionised tungsten (W III) is identified as the source of the 4.5-micron emission in two kilonovae, and its measured luminosity is used to infer how much tungsten the explosions ejected.

desk verdict A solid, honest atomic-data paper whose headline W III mass estimates rest on two clearly stated assumptions, so the masses are conditionally useful upper limits rather than closed measurements. read the letter →

arxiv 2411.16476 v2 pith:HHXHLKTD submitted 2024-11-25 physics.atom-ph astro-ph.HEnucl-th

M. McCann , L. P. Mulholland , Z. Xiong , C. A. Ramsbottom , C. P. Ballance , O. Just , A. Bauswein , G. Martínez-Pinedo
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F. McNeill S. A. Sim
This is my paper · ORCID
classification physics.atom-phastro-ph.HEnucl-th
keywords kilonovar-processnucleosynthesistungstencollisional-radiativemodellingR-matrixatomicdataAT2017gfoAT2023vfimid-infraredspectroscopy
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 argues that the unexplained 4.5-micron emission seen in two kilonovae, AT2017gfo and AT2023vfi, is produced by doubly ionised tungsten (W III), and uses this identification to measure how much tungsten the explosions ejected. It builds collisional-radiative models from new R-matrix electron-impact excitation data for the first three ionisation stages of tungsten, platinum and gold, then computes optically thin line luminosities at kilonova nebular conditions. For tungsten, enforcing the observed 4.5-micron luminosity yields W III masses of about $1.65 \times 10^{-4}\,M_\odot$ for AT2017gfo and $9.4 \times 10^{-4}\,M_\odot$ for AT2023vfi. These estimates are broadly consistent with tungsten yields from neutron-star merger nucleosynthesis models, especially for AT2017gfo, and the paper shows that a measured tungsten mass can be converted, via model correlations, into abundance constraints for lanthanides, actinides and third r-process peak elements. The result matters because it would make tungsten a practical observational tracer of very neutron-rich ejecta in kilonovae.

What carries the argument

The engine is a steady-state collisional-radiative model solved with the colradpy package, driven by R-matrix effective collision strengths and Einstein A-coefficients for W I-III, Pt I-III and Au I-III. Line emission is expressed through photon emissivity coefficients (PEC, the upper-level population times the A-coefficient divided by electron density), and the luminosity formula $L = (hc/\lambda)\, n_e\, \mathrm{PEC}\, (M_{\mathrm{ion}}/m_{\mathrm{ion}}) / \sum_i N_i$ lets the authors invert an observed line luminosity into an ion mass once temperature and density are fixed. The two W III lines at 4432.23 and 4535.16 nm are the strongest computed features at kilonova nebular conditions, which is what carries the identification of the 4.5 $\mu$m feature.

What would settle it

Look for the predicted 6.05 $\mu$m W I/W II blend in the same late-time spectra: the model predicts it should be comparable in luminosity to the 4.5 $\mu$m feature when W I or W II masses are similar to W III, so its absence would contradict the W III identification; alternatively, a high-resolution mid-infrared spectrum that fails to show the two W III components at their predicted ~6:1 intensity ratio would falsify the claim.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that the 4.5 $\mu$m excess in AT2017gfo and AT2023vfi can be attributed to the two strongest fine-structure transitions of W III, at 4432.23 nm and 4535.16 nm within the $5d^4\,^5D$ ground term, and that inverting the observed luminosity with a full collisional-radiative model gives W III masses of about $1.65 \times 10^{-4}\,M_\odot$ for AT2017gfo (adopting $5 \times 10^{37}\,\mathrm{erg\,s^{-1}}$ from the Spitzer band) and $9.4 \times 10^{-4}\,M_\odot$ for AT2023vfi (adopting $1.0 \times 10^{38}\,\mathrm{erg\,s^{-1}}$). With assumed total ejecta masses this corresponds to roughly 0.33% and 1.6% of the ejecta as W III, and up to about 1.0% and 4.7% as tungsten if neighbouring ion stages contribute similarly. Compared with hydrodynamical merger models and nuclear network yields, the AT2017gfo estimate sits near the top of the predicted range $4 \times 10^{-5}$ to $2 \times 10^{-4}\,M_\odot$, while the AT2023vfi estimate exceeds the models by up to an order of magnitude; the paper interprets this as either an observational overestimate from blending or evidence that AT2023vfi ejected more neutron-rich material, possibly from a neutron star-black hole merger.

Load-bearing premise

The 4.5 $\mu$m feature is assumed to be dominated by W III emission rather than Se III or other species, and W III is taken as the dominant tungsten ionisation stage; the adopted electron temperature and density enter the mass estimate directly and change it by up to three orders of magnitude across the explored grid.

Editorial extensions

If this is right

  • The 4.5 $\mu$m feature in AT2017gfo and AT2023vfi can be modelled as blended W III 4432.23 nm and 4535.16 nm emission, with combined luminosity $5 \times 10^{37}\,\mathrm{erg\,s^{-1}}$ (AT2017gfo) or $1.0 \times 10^{38}\,\mathrm{erg\,s^{-1}}$ (AT2023vfi).
  • The implied W III masses are $1.65 \times 10^{-4}\,M_\odot$ (AT2017gfo) and $9.4 \times 10^{-4}\,M_\odot$ (AT2023vfi), corresponding to roughly 0.33% and 1.6% of each ejecta, and possible total W fractions up to about 1.0% and 4.7%.
  • These masses are broadly consistent with theoretical W yields from neutron-star merger models for AT2017gfo; for AT2023vfi the estimate exceeds the models by up to an order of magnitude, which may indicate more neutron-rich ejecta or an observational overestimate.
  • A measured W mass fraction can be converted into constraints on lanthanide plus actinide and third-peak r-process element mass fractions (1.8% to 5.5% and 1.6% to 9.9% for AT2017gfo using the adopted correlations), connecting the line to r-process yield and opacity.
  • The predicted W III line profile shape, computed from merger-model velocity distributions, could distinguish short-lived versus long-lived neutron-star remnants because low-velocity W is depleted in long-lived remnant models.

Reading between the lines

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

  • If the W III identification survives, the 4.5 $\mu$m band becomes a direct probe of the mass of ejecta with electron fraction below about 0.2, effectively a calorimeter for the most neutron-rich component of a kilonova; this extends the paper's correlation argument.
  • A clean test is to look for the predicted 6.05 $\mu$m W I/W II blend at comparable luminosity to the 4.5 $\mu$m feature in the same objects: detection would strengthen the identification, while non-detection would challenge the assumed ionisation balance.
  • The paper's mass estimates scale almost inversely with the fraction of the observed band assigned to W III; future JWST/MIRI observations at higher spectral resolution could separate the two W III components from any Se III contribution and break that degeneracy.
  • Because R-matrix datasets now exist for W, Pt, and Au, the same forward-modelling pipeline could be applied to other r-process elements with available collision data, turning kilonova spectra into a systematic abundance inventory.
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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

4 major / 6 minor

Summary. The paper constructs steady-state collisional-radiative (CR) models for the first three ionization stages of W, Pt and Au using published Dirac R-matrix effective collision strengths (Smyth et al. 2018; Dunleavy et al. 2022; McCann et al. 2024; Bromley et al. 2023; McCann et al. 2022) and applies them to late-time kilonova conditions (Te = 0.15–0.35 eV, ne = 10^5–10^7 cm^-3). It presents photon emissivity coefficients, line luminosities for the ten strongest lines of each ion (Tables 1–3), and synthetic spectra (Figures 2–5). The W III fine-structure lines at 4432.23 and 4535.16 nm are identified as the strongest 4.5 μm features. Imposing the observed 4.5 μm luminosities, the authors invert equation (3) to obtain W III masses of 1.65e-4 M_sun for AT2017gfo and 9.4e-4 M_sun for AT2023vfi. These are compared with total W masses from neutron-star merger nucleosynthesis models (4e-5 to 2e-4 M_sun, Table 4); the body reports broad consistency mainly for AT2017gfo, with the AT2023vfi estimate exceeding models by up to an order of magnitude. The paper also converts the inferred W fraction into lanthanide/actinide and third-peak mass fractions using model correlations, and uses merger models to predict W line-profile shapes that may distinguish short- from long-lived remnants.

Significance. The atomic-physics core is solid: the mass estimates follow from equation (3) with no parameter fitted to the target observations, and the full effective-collision-strength tables in Appendix A are a valuable community resource. The paper is also honest about its input assumptions—the limiting role of the Spitzer band fraction is stated in Section 3.2, the Te–ne–mass degeneracy is mapped openly in Figure 6, and Section 4 notes that the comparison with models could be an overestimate or an upper limit. If the W III identification holds, this is a genuinely new third-peak r-process diagnostic for kilonovae and a potentially powerful proxy for neutron-rich ejecta, with falsifiable line-profile predictions (Section 5). The significance is currently capped by the two load-bearing assumptions the review process flagged: the fraction of the 4.5 μm band assigned to W III is taken as an upper bound without a quantitative Se III model, and the W III-to-total-W ionization correction is assumed rather than derived. Both are acknowledged in the text but not bounded, so the headline 'broad agreement' claim runs ahead of what is demonstrated.

major comments (4)
  1. [Sections 2, 3.2, and 4] The inferred masses are W III ion masses, but the comparison in Table 4 and the mass-fraction statements (0.33%, 1.6%, and the lanthanide/third-peak conversions of Figure 10) are phrased in terms of total elemental W. The CR model deliberately omits ionization and recombination (Section 2), so it cannot determine whether W III is the dominant tungsten stage; the paper instead states the assumption directly ('We assume Wiii to be the dominant ionization state', Section 4; 'Assuming reasonably similar fractions for the near neutral stages of W', Section 3.2). Because the total-W comparison and the X(W) ≈ 0.3% central value are linearly sensitive to this ionization-correction factor, the agreement claim is conditional on an unquantified quantity. I recommend either adding a quantitative ionization-balance estimate (e.g., Saha at the adopted Te/ne with published ionization potentials) or explicitly reframing the Table 4 comparison as a bounded W III-to-total-W statement rather than a point comparison.
  2. [Section 3.2] For AT2017gfo the input luminosity is 5e37 erg/s, quoted from Hotokezaka et al. (2022) as the maximum W III contribution to a 2e38 erg/s Spitzer 4.5 μm band, and the mass estimate scales linearly with this number. The paper candidly notes that the band-fraction assignment is 'the limiting factor,' but in Section 4 and the abstract the resulting 1.65e-4 M_sun is treated as a point mass whose proximity to the upper end of the model range (4e-5 to 2e-4 M_sun, Table 4) is described as 'particularly good' agreement. Without a quantitative model for the Se III or continuum fraction of the band, the AT2017gfo comparison should be framed as an upper-envelope consistency test rather than a two-sided match, or else a quantitative bound on the Se III contribution should be supplied.
  3. [Section 3.2 and Figure 6] The quoted masses assume single (Te, ne) points (3500 K, 1e6 cm^-3 for AT2017gfo; 3000 K, 3e5 cm^-3 for AT2023vfi), while Figure 6 shows the required mass varying by close to three orders of magnitude across the explored grid—for example ~2.1e-1 M_sun at 500 K versus ~5.6e-4 M_sun at 0.86 eV for L = 1e38 erg/s at fixed density. The paper deserves credit for displaying this degeneracy, but the abstract and conclusions do not carry it: the 'broad agreement' statement is made without attaching any systematic range to the headline masses. The central claims should propagate the Figure 6 range explicitly, and the agreement with nucleosynthesis should be reported against the allowed grid rather than at single points.
  4. [Abstract and Section 4] The abstract's 'broad agreement with the inferred ion masses of W' is stronger than what the body itself supports: Section 4 states that for AT2023vfi the inferred 9.4e-4 M_sun exceeds the simulation predictions by 'up to one order of magnitude,' and for AT2017gfo most models give W masses a factor of 2–3 below the estimate, with the spread of models merely encompassing it. The conclusions (Section 6) repeat 'broad consistency' while also reporting the factor-2–3 offset. The abstract should carry the same qualification as the body: good agreement for AT2017gfo at the upper end of the model range, with a genuine tension for AT2023vfi that the paper itself discusses.
minor comments (6)
  1. [Equation (3)] As printed, equation (3) multiplies by Σ_i N_i, but with N_j defined relative to the ground level (Section 2) the renormalization to total ion population requires division by Σ_i N_i (or equivalently sum-normalized populations with Σ_i N_i = 1). The numerical entries of Table 1 are consistent with the division form, so the printed equation should be corrected or clarified.
  2. [Section 3.1] The text assigns the W I lines at 6041.42 nm and 6646.86 nm to 5D1–5D3 and 5D3–5D4, while Table 1 lists them as 5D1–5D2 and 5D2–5D3; the text should match the table.
  3. [Section 3.2] The 'ground configuration' of W III is written as (5d4 6s2), but the W III ground configuration is 5d4; the 6s2 belongs to the W I ground configuration. The transitions discussed are the 5d4 fine-structure lines, so the configuration label is a typo.
  4. [Section 4] The statement 'neutron-rich material should roughly amount to about 40 times (14 times) the inferred W mass for HFB21 (DZ31), i.e. to 6.6e-3 M_sun (2.3e-3 M_sun) for AT2017gfo and to 2.8e-2 M_sun (9.8e-3 M_sun) for AT2023vfi' is internally inconsistent for AT2023vfi: 40 × 9.4e-4 = 3.76e-2 and 14 × 9.4e-4 = 1.32e-2, neither matching the printed values; please reconcile the numbers.
  5. [Sections 4 and 6] The converted elemental ranges differ between the two sections: Section 4 gives 1.8% ≲ X_La+X_Ac ≲ 5.5% and 1.6% ≲ X(3rd peak) ≲ 9.9%, while Section 6 gives 0.85%–11% and 0.73%–19%. The factor-of-two uncertainty propagation needs to be defined once and applied consistently.
  6. [Throughout] Minor presentation items: 'colradpypackage' (Section 2) and 'spectropscopic' (Section 5) need fixing; the references for Kasliwal et al. (2019) and Kasliwal et al. (2022) carry identical volume/page data (510, L7) and should be checked; and the introduction's outline omits Section 5.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the W III mass estimates are direct inversions of externally supplied observed luminosities using independent atomic data, and the merger-model comparison is falsifiable.

full rationale

The derivation chain is self-contained and non-circular. Equation (3) is a forward conversion from line luminosity to ion mass; the mass estimates in Section 3.2 are obtained by inverting this relation for fixed adopted observed luminosities (5e37 erg/s for AT2017gfo from Hotokezaka et al. 2022; 1e38 erg/s for AT2023vfi from Gillanders & Smartt 2024). No parameter of the atomic model is fitted to these luminosities: the R-matrix effective collision strengths and Einstein A-values (Smyth et al. 2018; Dunleavy et al. 2022; McCann et al. 2024; Bromley et al. 2023; McCann et al. 2022) are parameter-free scattering calculations whose assumptions do not include the inferred W mass, and the cited atomic data papers are independent, externally checkable calculations rather than results defined by the kilonova observations. The paper's own caveats are correctly framed as assumptions, not hidden circular inputs: Section 3.2 explicitly says the limiting factor is 'what fraction of the Spitzer band to assign to this emission line', and Section 4 states 'Without a quantitative treatment of ionization fraction, an elemental mass is difficult to quantify' and 'We assume Wiii to be the dominant ionization state'. These are data-assignment and ionization-balance uncertainties, not circular reductions. The comparison with nucleosynthesis models in Table 4 uses hydrodynamical simulations (Just et al. 2023; Sneppen et al. 2024) that are not adjusted to match the inferred W mass; indeed the paper reports that AT2023vfi is up to an order of magnitude above the models, which shows the comparison is falsifiable rather than forced. The only self-citations are to the atomic-data papers and to merger simulations with overlapping authors, but neither is load-bearing as an unverified premise: the atomic data are external scattering calculations and the merger models have independent dynamical and nuclear input. No step reduces, by the paper's own equations or by self-citation, to its own inputs.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The paper's inferences rest on six stated modeling choices: steady-state populations, excitation/de-excitation and emission only (ionization and recombination omitted for lack of data), optically thin emission, the W III identification of the 4.5 μm feature, accuracy of the prior R-matrix data, and W III dominance in the ionization balance for the model comparison. The free parameters are all inputs or assumed scalings: the W III band fraction, Te and ne point values, the ionization-budget factor, and a continuum temperature used only for a display spectrum. No new physical entities are introduced.

free parameters (5)
  • Assumed W III fraction of the Spitzer 4.5 μm band in AT2017gfo = 5e37 of 2e38 erg/s, i.e. 25%
    Adopted from Hotokezaka et al. (2022); the inferred W III mass in Section 3.2 scales linearly with this fraction.
  • Electron temperature Te = 3500 K (AT2017gfo), 3000 K (AT2023vfi)
    Literature values; Figure 6 shows the required W III mass varies by up to three orders of magnitude across the explored Te grid.
  • Electron density ne = 1e6 cm^-3 (AT2017gfo), 3e5 cm^-3 (AT2023vfi)
    Literature values; in the coronal regime the required mass is inversely proportional to ne, as shown by the contours in Figure 6.
  • Ionization-budget factor from W III mass to elemental W mass = Factor of about 3 (0.33% to about 1.0%)
    Section 3.2 assumes the other near-neutral ion stages are produced in similar amounts; this factor converts the W III mass fraction into the total W fraction used in the model comparison.
  • Continuum blackbody temperature for the AT2023vfi synthetic spectrum = 620 K
    Chosen in Section 3.2 so that the model spectrum plus continuum matches the JWST data in Figure 5; cosmetic to the central mass estimate.
assumptions (6)
  • domain assumption Level populations are in steady state at late times (dN_i/dt = 0 in equation (1)).
    Section 2 argues atomic timescales are fast compared with ejecta expansion; this is the standard nebular approximation.
  • domain assumption Only electron-impact excitation/de-excitation and spontaneous emission are included; ionization and recombination are neglected.
    Section 2: 'there is very limited data for the accurate modelling of ionisation... or recombination for the high-Z elements. Therefore, the analysis is restricted to electron-impact excitation/de-excitation and emission.'
  • domain assumption The emission is optically thin.
    Stated throughout ('optically thin intensities', 'optically-thin emission line profile shapes'); equation (3) assumes the escaping photon rate equals the emission rate.
  • domain assumption The 4.5 μm feature in AT2017gfo and AT2023vfi is attributed to W III fine-structure lines.
    Adopted from Hotokezaka et al. (2022) and used for the mass inversion in Section 3.2; the Se III alternative is acknowledged in the introduction but not folded into the uncertainty.
  • domain assumption The R-matrix effective collision strengths and A-values from the authors' prior papers are accurate.
    The scattering data (Smyth et al. 2018; Dunleavy et al. 2022; McCann et al. 2024; McCann et al. 2022; Bromley et al. 2023) are taken as given, without validation against experiment in this paper.
  • domain assumption W III is the dominant tungsten ionization stage when comparing with model W yields.
    Section 4 states 'We assume Wiii to be the dominant ionization state' and uses X(W) = 0.3% for the model comparison in Figure 10.

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Cite this review

Pith. "Pith review of Luminosity predictions for the first three ionisation stages of W, Pt and Au to probe potential sources of emission in kilonova." pith.science (2026). https://pith.science/paper/HHXHLKTD

@misc{pith2026241116476,
  author       = {Pith},
  title        = {Pith review of: Luminosity predictions for the first three ionisation stages of W, Pt and Au to probe potential sources of emission in kilonova},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HHXHLKTD}},
  note         = {Machine review of arXiv:2411.16476}
}
read the original abstract

A large number of R-matrix calculations of electron impact excitation for heavy elements (Z > 70) have been performed in recent years for applications in fusion and astrophysics research. With the expanding interest in heavy ions due to kilonova (KN) events such as AT2017gfo and AT2023vfi, this new data can be utilised for the diagnosis and study of observed KN spectra. In this work recently computed electron-impact excitation effective collision strengths are used, for the first three ionisation stages of tungsten (W, Z = 74), platinum (Pt, Z = 78) and gold (Au, Z = 79), to construct basic collisional radiative models tailored for the late stage nebular phases of KN. Line luminosities are calculated at a range of electron temperatures and densities and the strengths of these lines for a representative ion mass are compared. For the case of W III, these optically thin intensities are additionally used to constrain the mass of this ion in both AT2017gfo and AT2023vfi. Comparing with theoretical predictions of nucleosynthesis yields from neutron-star merger simulations, broad agreement with the inferred ion masses of W is found. Furthermore, we highlight the value of W measurements by showing that the abundance of other groups of elements and outflow properties are constrained by exploiting theoretically motivated correlations between the abundance of W and that of lanthanides or third r-process peak elements. Based on simple estimates, we also show that constraints on the distribution of tungsten in the ejecta may be accessible through the line shape, which may also yield information on the neutron-star merger remnant evolution.

Figures

Figures reproduced from arXiv: 2411.16476 by the authors.

Figure 1
Figure 1. PECs for W i-iii for a range of temperatures and densities (𝑇𝑒 = 0.15, 0.25 and 0.35 eV, 𝑛𝑒 = 105 , 106 and 107 cm−3 ) 1000 2000 3000 4000 5000 6000 7000 8000 9000 Wavelength (nm) 0 1 2 3 4 5 Luminosity density (1035 erg s −1 nm −1) 0.25eV W I 0.25eV W II 0.25eV W III 0.15eV W I 0.15eV W II 0.15eV W III [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Luminosity density plot as a function of wavelength (nm) for W i - iii generated at 𝑇𝑒 = 0.15/0.25 eV, 𝑛𝑒 = 1 × 106 cm−3 and a mass of 1 × 10−3𝑀⊙. MNRAS 000, 1–14 (2024) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Luminosity density plot as a function of wavelength (nm) for Au i - iii generated at 𝑇𝑒 = 0.15/0.25 eV, 𝑛𝑒 = 1 × 106 cm−3 and a mass of 1 × 10−3𝑀⊙. MNRAS 000, 1–14 (2024) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Luminosity density plot as a function of wavelength (nm) for Pt i - iii generated at 𝑇𝑒 = 0.15/0.25 eV, 𝑛𝑒 = 1 × 106 cm−3 and a mass of 1 × 10−3𝑀⊙. MNRAS 000, 1–14 (2024) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: The calculated W iii spectrum at 𝑇𝑒 = 0.26 eV and 𝑛𝑒 = 3 × 105 cm−3 , with full-width-half-maximum set to 0.110𝑐 = 486 nm (Gillanders & Smartt 2024). A blackbody and powerlaw continuum is employed. This is overlaid on the JWST spectrum (Levan et al. 2024). The dashed b…
Figure 7
Figure 7. Figure 7: Luminosity density plot as a function of wavelength (nm) for W i - iii generated at 𝑇𝑒 = 0.86 eV, 𝑛𝑒 = 1 × 106 cm−3 and a mass of 1 × 10−3𝑀⊙. Merger simulation sym-n1-a6 sym-n10-a3 asy-n1-a6 asy-n10-a3 sym-n1-a6-short asy-n1-a6-short sym-n1-a6 asy-n1-a6-short Nuclear m…
Figure 9
Figure 9. Figure 9: Histogram of W mass fraction measured at 1 month with respect to the electron fraction 𝑌𝑒 for models sym-n1-a6 and asy-n1-a6-short with HFB21 and DZ31 nuclear mass inputs. This figure adopts the electron fraction of the individual tracer particles when they reach a tem…
Figure 10
Figure 10. Figure 10: Correlation plots of W mass fraction with the total mass fraction of lanthanides and actinides, 𝑋La + 𝑋Ac, (upper panel) and with the mass fraction of third-peak 𝑟-process elements, 𝑋(3rd peak), (lower panel) for all models listed in [PITH_FULL_IMAGE:figures/full_fig…
Figure 11
Figure 11. Figure 11: Histograms of 𝑊 mass (solid lines) as a function of radial velocity for models sym-n1-a6 and asy-n1-a6-short with HFB21 and DZ31 nuclear mass inputs (plotted for composition at 1 mth post merger). Dashed histograms show the total mass distributions, which are identica…

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    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.