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Thorium in Kilonova Spectra: Exploring the Heaviest Detectable Element

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Thorium is the likely heaviest element whose signature can appear in kilonova spectra, showing up as a broad absorption trough near 18,000 Å under actinide-boosted conditions.

desk verdict Careful forward-modeling paper that turns a hint into a testable Th III prediction worth refereeing, but the factor-of-3 uncertainty in the input gf-values makes the quantitative threshold softer than the abstract claims. read the letter →

arxiv 2411.16998 v1 pith:IZZE5HTL submitted 2024-11-26 astro-ph.HE astro-ph.SRphysics.atom-ph

Nanae Domoto , Shinya Wanajo , Masaomi Tanaka , Daiji Kato , Kenta Hotokezaka This is my paper · ORCID
classification astro-ph.HEastro-ph.SRphysics.atom-ph
keywords thoriumkilonovaspectrar-processnucleosynthesisactinidesneutronstarmergerradiativetransferThIIInear-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

This paper argues that thorium is the heaviest element whose signature can realistically appear in the photospheric spectra of a kilonova, and that its fingerprint is a broad absorption trough in the near-infrared near 18,000 Å. The authors build an updated line list for the actinide ions Ra II, Ac III, and Th III, then run radiative transfer simulations of neutron star merger ejecta. They find that Th III stands out as the only candidate with strong near-infrared lines, and that those lines form a visible absorption feature when the actinide-to-lanthanide mass ratio exceeds the solar r-process value and the lanthanide mass fraction is $X_{\rm lan}\lesssim 6\times10^{-4}$. If real, a space-based or high-altitude spectrum taken one to two and a half days after a merger would give direct, unambiguous evidence that neutron star mergers synthesize elements heavier than the third r-process peak.

What carries the argument

The central machinery is a hybrid atomic line list for ions beyond the third r-process peak, anchored by experimentally calibrated data for Ra II and Ac III and by a set of near-infrared Th III transition probabilities estimated from measured relative intensities. The Th III estimates assume a single Boltzmann excitation temperature of $T=6000$ K, fixed by least-squares comparison between measured and calculated intensities of known optical lines. Under LTE, Saha–Boltzmann population statistics feed Sobolev optical depths for each bound-bound transition, and a Monte Carlo radiative transfer code converts those opacities into synthetic spectra. The decisive property is the temperature window: doubly ionized thorium exists over a narrower temperature range than doubly ionized cerium, so the near-infrared trough appears only while the photosphere stays near 5000–7000 K, which sets both the early observing epoch and the strict upper limit on the lanthanide fraction.

What would settle it

Measure the oscillator strengths of the Th III lines near 18,000 Å in the laboratory. If the true values are more than a factor of three smaller than the estimates used here, the required thorium fraction would exceed the actinide-boost range and the predicted trough would not appear, while a high signal-to-noise, space-based spectrum of a suitable kilonova at 1–2.5 days that shows no trough at 18,000 Å despite an inferred actinide-boost composition would also rule the prediction out.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that Th III is the most promising actinide for kilonova spectroscopy because its dense low-lying $5f$-shell energy levels place many allowed transitions at 10,000–25,000 Å with relatively large estimated oscillator strengths. In the authors' radiative transfer models these lines blend into a broad absorption feature near 18,000 Å. The feature appears when the line-forming region has a lanthanide mass fraction $X_{\rm lan}\lesssim 6\times10^{-4}$ and an actinide-to-lanthanide ratio at least as large as the solar r-process ratio, and it fades as the ejecta cools below the temperature window where Th III survives. The authors therefore conclude that detecting this feature would be unambiguous evidence of actinide nucleosynthesis in neutron star mergers, and that the most likely hosts are mergers of unequal-mass neutron stars or black hole-neutron star binaries.

Load-bearing premise

The detection threshold rests on near-infrared transition strengths for Th III that have never been directly measured; they are recovered from laboratory relative intensities by assuming a single excitation temperature, and the calibration scatter is about a factor of three.

Editorial extensions

If this is right

  • A space-based or high-altitude spectrum of a neutron star merger at 1–2.5 days, showing a broad absorption trough near 18,000 Å, would be direct spectroscopic evidence that actinides are synthesized in the event.
  • The feature is short-lived in the models: it is present from about one day after the merger and fades by about 3.5 days, so early near-infrared follow-up is essential.
  • The detectability criterion doubles as a composition diagnostic: the line-forming region must be dominated by relatively light r-process elements, with only a small admixture of very neutron-rich material that raises the actinide-to-lanthanide ratio.
  • Unequal-mass neutron star mergers and black hole–neutron star binaries, which numerical nucleosynthesis models associate with high actinide-to-lanthanide ratios, are the most promising observational targets.
  • A non-detection does not mean actinides are absent: if the lanthanide fraction is too high or the ratio is only solar-like, the thorium feature stays hidden even when thorium itself is abundant.

Reading between the lines

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

  • Because the required thorium mass fraction scales linearly with the estimated transition strengths, laboratory measurements of the Th III near-infrared lines would shrink the main uncertainty and sharpen the detectability criterion.
  • Non-LTE effects, which the paper notes can keep some heavy elements in doubly ionized states for weeks, may extend the visible phase of the thorium feature well past the 3.5-day limit found under LTE, making late-time spectra worth examining as well.
  • The same line-list calibration recipe could be applied to protactinium and heavier actinides once experimental data exist, potentially revealing additional near-infrared actinide features beyond the thorium trough.
  • Archival space-based near-infrared spectra of GW170817/AT2017gfo, if they cover the 1.8 micron region with sufficient quality, could provide an immediate test of the prediction, although the paper itself does not attempt that identification.
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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. The paper investigates whether elements beyond the third r-process peak can be identified in kilonova photospheric spectra. The authors construct and update line lists for Ra II, Ac III, and Th III, combine them with their existing hybrid line list, compute Sobolev optical depths under LTE, and run Monte Carlo radiative transfer for two abundance models (Light and Solar). They conclude that Th III is the most promising candidate, producing broad absorption near 18000 Å when the lanthanide mass fraction X(lan) is ≲ 6×10^-4 and the actinide-to-lanthanide ratio is at least the solar r-process value. They argue such conditions are plausible in mergers of unequal-mass neutron stars or black hole-neutron star binaries, and recommend space- or high-altitude observations in the telluric-affected NIR region.

Significance. If the central claim holds, the paper provides a concrete, falsifiable spectroscopic prediction for actinide production in neutron star mergers, with a specific wavelength, epoch window (roughly 1 to 2.5 days), and abundance condition. The forward modeling is transparent and systematic: the authors compute Sobolev optical depths for candidate heavy species, identify why Th III is special (dense low-lying levels, favorable ionization balance), and present with/without-Th III spectral comparisons that isolate the predicted feature. They also make the estimated Th III line list available in Appendix A. The main weakness is the atomic-data basis: the NIR Th III gf-values are not measured but recovered from relative intensities via a single Boltzmann temperature, and the Ce III gf-values near 20000 Å are theoretical. These uncertainties propagate linearly into the abundance condition that is the paper's principal quantitative result, so the criterion should be presented with an explicit uncertainty range.

major comments (3)
  1. [Section 2.1, Eq. (1), and Figure 1] The central detection criterion is not yet robust as stated because the Th III NIR gf-values are calibrated from a single least-squares Boltzmann temperature T=6000 K applied to optical lines, while Figure 1 shows a factor-of-three scatter between measured and calculated intensities and the NIR lines reach upper-level energies up to roughly 28000 cm^-1, outside the calibration range. The authors acknowledge in Section 4 that the required Th mass fraction scales linearly with the gf-values, but they do not propagate the factor-of-three uncertainty into the X(lan) threshold or the actinide-to-lanthanide ratio. A factor-of-three overestimate of the true NIR gf-values would raise the required Th abundance by the same factor and push the criterion to the boundary of the factor-of-three actinide-boost range invoked in Section 3.2. I request a sensitivity calculation with the Th III NIR gf-values scaled by 1/3 and 3, and a restatement of the detection threshold as an allowed range rather than a single value.
  2. [Sections 3.2 and 4] The visibility of the Th feature is set against the Ce III opacity near 20000 Å, and the gf-values of these Ce III lines are theoretical and uncalibrated except for the strongest lines near 16000 Å, as the authors state in Section 4. Because the threshold X(lan) is effectively the value at which the Ce III background drops below the Th III opacity, an uncertainty in the Ce III gf-values translates directly into an uncertainty in the threshold. The paper should include a sensitivity study with the Ce III gf-values varied by a factor of 2–3 and should state whether the conclusion survives those variations.
  3. [Section 4] The observational claim that JWST/NIRSpec or high-altitude telescopes 'will give sufficient signal to noise ratio' to detect the Th feature is asserted without a quantitative estimate. Given that the feature sits in a region of strong telluric absorption and the synthetic fluxes in Figures 10 and 11 are only shown for an AT2017gfo-like event, a simple S/N estimate for a GW170817-like event at ~200 Mpc with a proposed instrument configuration would make the detectability statement much stronger. This is not the central modeling result, but it is part of the paper's stated practical conclusion.
minor comments (4)
  1. [Abstract and Section 3.2] The phrase 'solar r-process ratio' should be defined more carefully: the L model's Th-to-lanthanide ratio is about a factor of two higher than the present solar r-residual ratio because of 232Th decay over ~13 Gyr, so the criterion is not directly comparing to the present solar photospheric ratio.
  2. [Section 2.1] The cross-reference 'Table 2.1' should be 'Table 2', and the footnote referring to 'gl-values' appears to mean 'gf-values' or should be rewritten for clarity.
  3. [Throughout] There are several typographical errors: 'kilonvoae' in the Introduction, 'Soboelv' in Section 2.3, 'λ /greaterorsimilar20000' in Section 3.2, and 'faction' in Section 4. These should be corrected.
  4. [Figure 1] The axes 'Calculated intensity' and 'Relative intensity (NIST)' would be clearer with explicit labels and a note that intensities are in arbitrary units; the red/blue circle legend should also be explained more fully in the caption.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Th III feature is a forward prediction from laboratory-calibrated atomic data, not fitted to any kilonova spectrum.

full rationale

The paper's central claim is a forward radiative-transfer prediction. The Th III NIR gf-values are estimated from laboratory relative intensities (Engleman 2003; NIST ASD) via Eq. (1) with T=6000 K obtained by least-squares against optical lines with known gf-values (Biémont et al. 2002); no kilonova absorption is used to set these values. The detection criterion (X(lan) lesssim 6e-4 and actinide/lanthanide ratio at least the solar r-process value) is derived by varying the L-model abundances and reading off when a feature appears at about 18000 angstroms. The authors explicitly do not claim detection: "we do not attempt to identify Th III in the spectra of AT2017gfo." The main caveat, that the required Th mass fraction scales linearly with the uncertain gf-values, is a data-uncertainty limitation, not an input-output equivalence. Self-citations to Domoto et al. (2022) supply the hybrid line list and the L abundance model, but the conclusion does not reduce to those citations; any error in the atomic data would weaken the prediction, not make it tautologically true.

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

The central prediction rests on laboratory intensity calibrations with a fitted 6000 K temperature, the fiducial L abundance model from the authors' prior work, LTE and Sobolev approximations, and the assumption that missing actinide opacity does not mask the Th III feature. No new physical entities are introduced. The gf-values in Table 2 are the most quantitatively important inputs and carry a factor-of-3 uncertainty.

free parameters (5)
  • Th III NIR gf-values = log gf from -3.099 to +1.153 (Table 2)
    Derived from measured relative intensities using Eq. (1) with an assumed Boltzmann excitation temperature; the scatter with calculated intensities is roughly a factor of 3, and the required Th mass fraction scales linearly with gf.
  • Excitation temperature T_exc for Th III intensity calibration = 6000 K
    Found by least squares matching measured and calculated optical line intensities in Section 2.1; this single temperature sets all the estimated NIR gf-values.
  • Heavy-element scaling factor in L abundance model = 3% of r-process residuals for A=100-205
    The fiducial L model from Domoto et al. (2022) matches r-process residuals at A=66-69 and 3% of those at A=100-205; this scaling sets X(Th)=1.0e-5 and X(lan)=5.8e-4 at 1.5 days, which are the values around which the detectability condition is defined.
  • Lanthanide mass fraction X(lan) = 5.8e-4 fiducial, varied by 1/3x to 3x
    Not fitted to a Th detection but varied by hand. The paper's central condition X(lan) <= 6e-4 is essentially the fiducial L-model value, so the threshold is not independently derived.
  • Actinide-to-lanthanide ratio = 1x to 10x fiducial, with 3x motivated by actinide-boost stars
    Scaling factor applied to X(Z>=82) to explore detectability; the abstract condition 'larger than solar ratio' is one boundary of this explored range.
assumptions (6)
  • domain assumption LTE holds for ionization and excitation in the line-forming region
    Saha and Boltzmann populations are used for Sobolev optical depths and radiative transfer (Sections 2.2 and 3.1). Non-LTE could change ionization fractions and the timescale over which Th III persists, as acknowledged in Section 4.
  • standard math Sobolev approximation is valid for homologously expanding ejecta
    Used to compute line optical depth in Section 2.2, Eq. (2); standard for high-velocity-gradient, homologously expanding ejecta.
  • domain assumption Experimental Th III level populations follow a Boltzmann distribution at a single excitation temperature
    Eq. (1) and Section 2.1: required to convert measured relative intensities into gf-values. The factor-of-3 scatter in Figure 1 shows this is approximate.
  • domain assumption Elements with Z=82-88 and Z>90 (except Ac III and Th III) contribute negligibly to NIR opacity
    Section 3.2 states that the line list lacks Z=89-100 except Ac/Th and that these are expected not to seriously affect the Th III feature; Fontes et al. (2023) is cited as suggesting Pa may affect NIR opacity, so this assumption is not fully verified.
  • domain assumption The L model abundance pattern represents the line-forming region rather than the whole ejecta
    Section 2.2 states the L model is not intended to represent the whole ejecta but the line-forming region; the detectability condition depends on this pattern being realized above the photosphere.
  • domain assumption Homogeneous abundance distribution within ejecta layers
    Section 4 notes the assumption of a simplistic homogeneous distribution of elements; density and Ye stratification from self-consistent merger simulations could alter the temperature and opacity coupling.

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Pith. "Pith review of Thorium in Kilonova Spectra: Exploring the Heaviest Detectable Element." pith.science (2026). https://pith.science/paper/IZZE5HTL

@misc{pith2026241116998,
  author       = {Pith},
  title        = {Pith review of: Thorium in Kilonova Spectra: Exploring the Heaviest Detectable Element},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IZZE5HTL}},
  note         = {Machine review of arXiv:2411.16998}
}
abstract

Kilonova spectra provide us with the direct information of r-process nucleosynthesis in neutron star mergers. In this paper, we study the signatures of elements beyond the third r-process peak expected to be produced in neutron-rich ejecta in the photospheric spectra of kilonova. Ra II, Ac III, and Th III are our candidates because they have a small number of valence electrons and low-lying energy levels, which tend to result in strong absorption features. We systematically calculate the strength of bound-bound transitions of these candidates by constructing the line list based on the available atomic database. We find that Th III is the most promising species showing strong transitions at the NIR wavelengths. By performing radiative transfer simulations, we find that Th III produces broad absorption features at ~18000 A in the spectra when the mass ratio of actinides to lanthanides is larger than the solar r-process ratio and the mass fraction of lanthanides is $\lesssim 6\times10^{-4}$. Our models demonstrate that the Th feature may be detectable if the bulk of the ejecta in the line-forming region is dominated by relatively light r-process elements with the mixture of a small fraction of very neutron-rich material. Such conditions may be realized in the mergers of unequal-mass neutron stars or black hole-neutron star binaries. To detect the Th absorption features, the observations from the space (such as JWST) or high-altitude sites are important as the wavelength region of the Th features is overlapped with that affected by the strong telluric absorption.

Figures

Figures reproduced from arXiv: 2411.16998 by the authors.

Figure 1
Figure 1. Comparison of intensities (green circles) for Th III lines between those calculated with gf-values from Bi´emont et al. (2002) and those measured by experiments (Engleman 2003; Kramida et al. 2023). Gray dashed and dotted lines correspond to the perfect agreement and the deviations by a factor of 3 and 10, respectively. Red circles indicate the lines whose gf-values are estimated from the measured intensities. we wi… view at source ↗
Figure 2
Figure 2. Left: final abundances (at 1 yr; all trans-Pb nuclei except for Th and U are assumed to have decayed) of the L (blue) and S (green) models as a function of mass number. Black circles show the r-process residual pattern (Prantzos et al. 2020), which are scaled to match those for the S model at A = 138. Right: abundances at t = 1.5 days for each model as a function of atomic number. Abundances of an r-process-deficien… view at source ↗
Figure 3
Figure 3. Sobolev optical depth of bound-bound tran￾sitions for the L model. The ions with large contributions and of interest are shown with colors. The top to bottom panels show the results with the temperature of T = 7000, 5000, and 4000 K, respectively, and the density of ρ = 10−14 g cm−3 at t = 1.5 days. To investigate the important species for absorption features in kilonova spectra among the heaviest el￾ements, we syst… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Energy distributions of the six low-lying con￾figurations for Ce III (left) and Th III (right). The bottom and top edges in each box correspond to the lowest and high￾est energies in each configuration, respectively. The first two configurations for Ce III are involved…
Figure 5
Figure 5. Figure 5: Energy diagrams for Ca II, Sr II, Ba II, and Ra II. Each arrow shows the triplet transition with the value of the transition wavelength (in vacuum). The energy terms for these triplet lines are 2D3/2– 2P o 3/2 , 2D5/2– 2P o 3/2 , and 2D3/2– 2P o 1/2 from the shorter to…
Figure 7
Figure 7. Figure 7: Ionization fractions of Ce (orange) and Th (light￾blue) under LTE, assuming the density of 10−14 g cm−3 . The dashed, solid, and dotted lines show the fractions of II, III, and IV, respectively. 0 2000 4000 6000 8000 10000 12000 0.05 0.10 0.15 0.20 0.25 0.30 Temperatur…
Figure 8
Figure 8. Figure 8: Temperature structure of the ejecta at t = 1.5, 2.5, and 3.5 days after the merger for the L (thick lines) and S (thin lines) models. For Ac III, the available data reside in the forest of lines at the UV and optical wavelengths (yellow lines in [PITH_FULL_IMAGE:figur…
Figure 9
Figure 9. Figure 9: Left: synthetic spectrum (blue and black curves as original and smoothed results, respectively) and Sobolev optical depth of each transition (vertical lines) at t = 1.5 days for the L model. The flux is presented by assuming the source at 40 Mpc as that for GW170817/AT…
Figure 10
Figure 10. Figure 10: Left: synthetic spectra (smoothed) with the fiducial X(lan) and various X(Z ≥ 82) at t = 1.5 (top) and 2.5 (bottom) days. The dark-orange, blue, and green curves show the spectra for the ratio of actinides to lanthanides being 3, 1, and 1/3 of the fiducial ratio, resp…
Figure 11
Figure 11. Figure 11: Same as the top panels of [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 12
Figure 12. Figure 12: Histogram of electron fraction Ye for the L model. Denser colors show the histograms with an original interval (∆Ye = 0.01), while lighter colors show those with a grouped interval (∆Ye = 0.05). elements. This demonstrates that we may be able to detect the Th III feat…

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Forward citations

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