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arxiv: 2511.07540 · v2 · submitted 2025-11-10 · 🌌 astro-ph.HE

Emission line models for the lowest mass core-collapse supernovae -- II. 3D NLTE radiative transfer modelling of a 9.0\,M_odot neutrino-driven explosion

Bart F.A. van Baal , Anders Jerkstrand , Daniel Kresse , Hans-Thomas Janka This is my paper

Pith reviewed 2026-05-17 23:11 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords core-collapse supernovaenebular phase3D radiative transfernickel distributionemission lineslow-mass progenitorsasymmetriesSN 1997D
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The pith

Three-dimensional NLTE models of a 9 solar mass supernova match observed emission lines and trace nickel plumes.

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

The paper applies full three-dimensional non-local thermodynamic equilibrium radiative transfer to a neutrino-driven explosion model of a nine solar mass star. Synthetic spectra are generated for multiple viewing angles and compared directly to observations of SN 1997D and SN 2016bkv. Line shapes correlate tightly with the location of the main nickel plume in the ejecta. The calculations preserve the diagnostic lines that separate different types of low-mass core-collapse supernovae when moving from one to three dimensions. If correct, the approach shows that nebular spectra can be used to map explosion asymmetries and detect the fastest-moving nickel.

Core claim

The authors perform 3D NLTE radiative transfer calculations with the ExTraSS code on a 3D explosion model of a 9.0 solar mass H-rich progenitor evolved to the homologous phase. The resulting spectra produce good line profile matches to both SN 1997D and SN 2016bkv, with reasonable luminosity matches for He, C, O and Mg lines in SN 1997D, although H alpha and Fe I lines are too strong. Key diagnostic lines that differentiate iron-core from electron-capture events remain valid in three dimensions. Both line profiles and luminosities vary across viewing angles because of ejecta asymmetries, and even the fastest 56Ni is traceable in the nebular phase line profiles.

What carries the argument

The primary nickel plume embedded in the three-dimensional element distribution of the homologous-phase ejecta from the 9 solar mass neutrino-driven explosion, processed through the ExTraSS code that includes full photoionization and line-by-line transfer.

Load-bearing premise

The input 3D explosion simulation accurately places nickel and other elements in their final spatial distribution once the ejecta reach homologous expansion.

What would settle it

A low-mass supernova whose nebular spectra at several epochs or angles show line profiles or luminosities for the diagnostic lines that cannot be matched by any viewing direction in the model.

Figures

Figures reproduced from arXiv: 2511.07540 by Anders Jerkstrand, Bart F.A. van Baal, Daniel Kresse, Hans-Thomas Janka.

Figure 1
Figure 1. Figure 1: Mass fractions of the angle-averaged ejecta for s9.0. The 13 𝛼−nuclei from 1H to 52Fe are shown (the 54Fe is added to 52Fe), together with 56Ni (which contains the 56Ni, 56Co and 56Fe and all ’element X’). The neutron star mass (1.355 𝑀⊙, Janka & Kresse 2024) is excluded in this plot. The top axis indicates the velocity of the ejecta. The total ejecta masses for each element are also listed in [PITH_FULL_… view at source ↗
Figure 2
Figure 2. Figure 2: The cumulative 𝛾-ray energy deposition (coloured lines) and cu￾mulative mass (black). Solid lines show the cumulative fraction, while dashed lines show the fraction per unit velocity. The 400 day deposition curve in the 1D model of J18 is shown in dotted brown: the dense “wall” present in 1D gives a sharp rise at ∼ 400 km s−1 which does not happen in 3D. Instead, there is a distributed deposition in the 10… view at source ↗
Figure 3
Figure 3. Figure 3: Electron fraction (𝑥𝑒, top) and temperature (bottom) in the s9.0 model at 400 days. Angle-averaged values are plotted as dark blue lines, and 1𝜎 angle variation as light blue shaded region. Also shown are cumulative distributions of H, O, NiCoFeX, and total ejecta. only at 80 % of what was deposited in the 1D model (2.37 × 1039 erg versus 1.90 × 1039 erg), predominantly due to a lower trapping rate in 3D –… view at source ↗
Figure 4
Figure 4. Figure 4: The spectrum of s9.0 at 400 days, colour coded by emission origin, in the wavelength range 4000 − 10000 Å, for the observer that is most directly approached by the neutron star. The spectrum has a resolution of R=2665. 4000 5000 6000 7000 8000 9000 Wavelength (Å) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 L (erg s 1 Å 1 ) 1e37 400 Days H He C O Ne Mg Si S Ar Ca Ti Cr Fe Co [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The same as [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of model spectra (same viewing angle as in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The model spectra for the same viewing angle as in [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The line properties for the six spectral features Mg I] 𝜆 4571 (top left), [O I] 𝜆, 6300 (top right), H𝛼 (mid left), [Fe II] 𝜆 7155 (mid right), [Ca II] 𝜆𝜆 7291, 7323 (bottom left) and [C I] 𝜆 8727 (bottom right) for all viewing angles, colour coded for the angle Ψ which is the angle between the direction vector to the viewer and the neutron star motion vector, i.e. the black points (small Ψ) correspond to… view at source ↗
Figure 9
Figure 9. Figure 9: A comparison between SN 1997D at 459 days (blue) to the model spectra at 400 days (orange). For rows 1-5, the viewing angle is the one giving the best 𝜒 2 fit for the line with white background. In column order; Mg I] 𝜆 4571, [O I] 𝜆𝜆 6300, 6364, H𝛼, [Fe II] 𝜆 7155, [Ca II] 𝜆𝜆 7291, 7323. For row six, the viewing angle is the one giving best overall fit for all lines together. The centres of the [O I] prof… view at source ↗
Figure 10
Figure 10. Figure 10: The same as [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The full set of H𝛼-profiles at 400 days for all viewing angles, separated by the polar angle 𝜃. In each panel, the set of 20 equatorial observers is shown, with the most luminous line in purple, the least luminous line in green and the others in orange. All line profiles are normalized relative to the most luminous observer. The integrated luminosities for the most and least luminous profiles are noted in… view at source ↗
Figure 12
Figure 12. Figure 12: The same as [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The [O I] line profiles in s9.0 at 400 days, similar as in [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The fraction of neutral Fe throughout the ejecta, for the normal ExTraSS setup (in blue), the photoionization boosted setup (in orange) and for the 1D results of J18. The ionized fraction is 1 minus neutral, as doubly ionized is negligible. both setups and alongside the 1D model from J18. In 1D, the sharp spike in neutral Fe corresponds to the composition-shell transitions from the Ni-rich core into the O… view at source ↗
read the original abstract

The nebular phase of a supernova (SN) occurs several months to years after the explosion, with asymmetries created by the explosion encoded into the line profiles of the emission lines. To make accurate predictions for these line profiles, Non-Local Thermodynamic Equilibrium (NLTE) radiative transfer calculations need to be carried out. In this work, we use $\texttt{ExTraSS}$ (EXplosive TRAnsient Spectral Simulator) -- which was recently upgraded into a full 3D NLTE radiative transfer code (including photoionization and line-by-line transfer effects) -- to perform such calculations. $\texttt{ExTraSS}$ is applied to a 3D explosion model of a $9.0\,M_\odot$ H-rich progenitor, evolved into the homologous phase. Synthetic spectra are computed and lines from different elements are studied for varying viewing angles. Line profile properties strongly correlate with a primary Ni plume in the ejecta. The model spectra are compared against observations of SN 1997D and SN 2016bkv. The model can create good line profile matches for both SNe, and reasonable luminosity matches for He, C, O, and Mg lines for SN 1997D -- however H$\alpha$ and Fe I lines are too strong. Key diagnostic lines of low-mass core-collapse SNe (CCSNe), e.g. differentiating Fe CCSNe from electron capture SNe, are upheld from 1D to 3D. However, both line profiles and line luminosities differ in 3D across viewing angles, enabling the possibility of detailed comparisons to observed spectra to infer asymmetries imprinted by the explosion. We show that even the fastest $^{56}$Ni is traceable in nebular phase line profiles.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper applies the upgraded 3D NLTE radiative transfer code ExTraSS to a neutrino-driven 3D explosion model of a 9.0 M_⊙ H-rich progenitor evolved to the homologous phase. Synthetic nebular spectra are computed for multiple viewing angles, with line profiles and luminosities from elements including He, C, O, Mg, H, and Fe compared to observations of SN 1997D and SN 2016bkv. The model produces good line profile matches for both SNe and reasonable luminosity matches for several lines in SN 1997D, but overpredicts Hα and Fe I strengths. Key diagnostic lines distinguishing low-mass CCSNe (e.g., Fe CCSNe vs. ECSNe) are reported as preserved from 1D to 3D, and high-velocity 56Ni is claimed to remain traceable in the profiles despite 3D viewing-angle variations.

Significance. If robust, this work advances understanding of 3D explosion asymmetries encoded in nebular spectra of low-mass core-collapse supernovae. It demonstrates viewing-angle dependence in line properties, extends prior 1D modeling, and offers a potential observational probe for the fastest 56Ni material. The preservation of diagnostic lines across dimensions strengthens the case for using nebular spectra to classify explosion mechanisms.

major comments (3)
  1. [Abstract] Abstract and results sections: The claim that key diagnostic lines are upheld from 1D to 3D is central but rests on the specific 9 M_⊙ model; the over-strong Hα and Fe I lines (noted in the abstract) require explicit discussion of whether they indicate systematic offsets that could affect these diagnostics or the luminosity matches for He/C/O/Mg.
  2. [Results (Ni plume and line profiles)] Results on 56Ni traceability: The assertion that even the fastest 56Ni remains traceable in nebular line profiles depends on the accuracy of the input 3D explosion model's 56Ni spatial and velocity distribution. The manuscript does not report resolution or mixing-convergence tests on the hydrodynamical simulation, which directly impacts the predicted line wings and the robustness of this claim.
  3. [Comparison to SN 1997D and SN 2016bkv] Comparison to observations: While good profile matches are reported for SN 1997D and SN 2016bkv, the lack of quantitative error analysis or sensitivity tests to code assumptions (e.g., photoionization rates or NLTE approximations in ExTraSS) leaves unclear how robust the matches are to variations in the input abundance field.
minor comments (2)
  1. [Figures] Figures showing spectra for different viewing angles should include clear labels for the primary Ni plume orientation and quantitative measures of profile asymmetry (e.g., velocity shifts or equivalent widths).
  2. [Methods] Notation for elemental lines (e.g., Fe I) and model parameters should be consistently defined in the methods section to aid reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed report, which has helped us identify areas for clarification and improvement. We address each major comment below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results sections: The claim that key diagnostic lines are upheld from 1D to 3D is central but rests on the specific 9 M_⊙ model; the over-strong Hα and Fe I lines (noted in the abstract) require explicit discussion of whether they indicate systematic offsets that could affect these diagnostics or the luminosity matches for He/C/O/Mg.

    Authors: We agree that the over-strong Hα and Fe I lines merit additional discussion to assess potential systematic effects. In the revised manuscript we will expand the abstract slightly and add a dedicated paragraph in the results section that examines possible origins of these discrepancies (e.g., uncertainties in the progenitor’s hydrogen envelope or NLTE rate approximations) and explicitly evaluates whether they compromise the key diagnostic lines used to distinguish Fe CCSNe from ECSNe. Those diagnostics rely primarily on well-matched lines such as [O I] λλ6300,6364 and [Ca II] λλ7291,7324, whose luminosities and profiles remain robust across the 1D-to-3D comparison for this model. revision: yes

  2. Referee: [Results (Ni plume and line profiles)] Results on 56Ni traceability: The assertion that even the fastest 56Ni remains traceable in nebular line profiles depends on the accuracy of the input 3D explosion model's 56Ni spatial and velocity distribution. The manuscript does not report resolution or mixing-convergence tests on the hydrodynamical simulation, which directly impacts the predicted line wings and the robustness of this claim.

    Authors: The 3D explosion model and its 56Ni distribution are taken from a previously published neutrino-driven simulation (Janka et al., in prep.; see also the model description in Section 2). While we did not perform additional resolution or mixing-convergence tests within the present study, the high-velocity Ni plume is a prominent, well-resolved feature of the simulation at the adopted grid resolution. We will add a short caveats subsection noting that the traceability of the fastest 56Ni in the line wings is subject to the numerical resolution of the input hydro model and that future higher-resolution runs could refine the wing strengths. Within the current model, however, the viewing-angle variations still allow the high-velocity Ni to be distinguished from the bulk ejecta. revision: partial

  3. Referee: [Comparison to SN 1997D and SN 2016bkv] Comparison to observations: While good profile matches are reported for SN 1997D and SN 2016bkv, the lack of quantitative error analysis or sensitivity tests to code assumptions (e.g., photoionization rates or NLTE approximations in ExTraSS) leaves unclear how robust the matches are to variations in the input abundance field.

    Authors: We acknowledge that a full quantitative error budget or exhaustive sensitivity study would further strengthen the comparison. Performing such tests for every NLTE parameter is computationally demanding, but we will revise the discussion section to include a concise assessment of the principal assumptions in ExTraSS (photoionization cross-sections, collisional rates, and the treatment of the input abundance field) and their expected influence on the reported line-profile matches. This will clarify the robustness of the good matches obtained for He, C, O, and Mg lines while noting the remaining tension in Hα and Fe I. revision: yes

Circularity Check

0 steps flagged

No significant circularity: forward NLTE modeling from independent 3D explosion input

full rationale

The paper takes a pre-existing 3D neutrino-driven explosion model of the 9 M⊙ progenitor (evolved to homologous phase) as input and computes synthetic spectra and line profiles via the ExTraSS NLTE radiative transfer code. These are direct computational outputs, not parameters fitted to the SN 1997D or SN 2016bkv data. Comparisons to observations occur after computation, with explicit discrepancies noted (over-strong Hα and Fe I). No equations reduce predictions to fitted quantities by construction, no self-definitional loops appear, and any self-citations (e.g., for the ExTraSS upgrade) are not load-bearing for the central claims. The derivation chain remains self-contained as predictive forward modeling.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the fidelity of the supplied 3D explosion model and the numerical implementation of NLTE radiative transfer; no new physical entities are postulated and the main free parameters are inherited from the input simulation rather than fitted here.

axioms (2)
  • domain assumption The 3D explosion model has reached the homologous expansion phase with fixed velocity field and composition.
    Invoked when applying the radiative transfer code to the evolved ejecta structure.
  • standard math Standard atomic data and NLTE rate equations govern the level populations and line formation.
    Underlying the ExTraSS photoionization and line-by-line transfer calculations.

pith-pipeline@v0.9.0 · 5655 in / 1657 out tokens · 44893 ms · 2026-05-17T23:11:40.975021+00:00 · methodology

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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.

  1. Low-Luminosity Type IIP Supernovae from the Zwicky Transient Facility Census of the Local Universe. III: Hunting for electron-capture supernovae using nebular spectroscopy

    astro-ph.HE 2026-05 unverdicted novelty 6.0

    Nebular spectroscopy of low-luminosity Type IIP SNe from ZTF identifies two plausible ECSN candidates but derives an upper limit on the ECSN rate of ≲(5–8)×10² Gpc⁻³ yr⁻¹ implying a sAGB mass window narrower than 0.06 M⊙.

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Works this paper leans on

1 extracted references · 1 canonical work pages · cited by 1 Pith paper

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    Springer International Publishing, Cham, pp 795--842, @doi 10.1007/978-3-319-21846-5_29 , https://doi.org/10.1007/978-3-319-21846-5_29

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    work page doi:10.1007/978-3-319-21846-5_29 1996