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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

This study employs the upgraded 3D NLTE radiative transfer code $\texttt{ExTraSS}$ to model the nebular phase of a $9.0\,M_\odot$ neutrino-driven explosion, demonstrating that while 3D effects introduce viewing-angle-dependent variations in line profiles and luminosities, the models successfully reproduce observed spectra of SN 1997D and SN 2016bkv and confirm that asymmetric nickel plumes and explosion dynamics remain traceable in low-mass core-collapse supernovae.

Original authors: Bart F. A. van Baal, Anders Jerkstrand, Daniel Kresse, Hans-Thomas Janka

Published 2026-06-24

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CC BY 4.0

Original authors: Bart F. A. van Baal, Anders Jerkstrand, Daniel Kresse, Hans-Thomas Janka

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A Cosmic "X-Ray" Vision

Imagine a star as a giant, layered cake. When a massive star runs out of fuel, it collapses and explodes in a supernova. Usually, these explosions are so bright and chaotic that we can only see the outer frosting (the surface) for a long time.

However, months or years later, the debris cloud (the "ejecta") becomes thin enough that we can see deep inside, like looking through a foggy window that has finally cleared. This is called the nebular phase. At this stage, the gas glows with specific colors (emission lines) that act like a fingerprint, telling us exactly what elements are inside and how they are moving.

This paper is about building a 3D "X-ray" vision to understand these fingerprints for the smallest stars that can still explode.

The Problem: The "Flat Map" vs. The "Globe"

For a long time, scientists studied these explosions using 1D models. Think of this like looking at a flat map of the Earth. It's useful, but it misses the curves, the mountains, and the valleys. In a 1D model, the star is treated as perfect, concentric onion layers.

But real explosions are messy. They are 3D. Imagine a balloon being blown up unevenly; some parts shoot out faster, and some heavy chunks get flung in specific directions. The authors of this paper wanted to see what happens when they stop using the flat map and start using a 3D globe to simulate the explosion.

The Tools: A New "Cosmic Camera"

The team used a supercomputer code called ExTraSS. Think of this as a high-tech camera that doesn't just take a picture, but simulates how light travels through the messy, expanding cloud of gas.

The Upgrade: Previous versions of this camera were good for some types of stars, but they missed how light bounces around and gets absorbed in the thick, dense clouds of Type II supernovae (stars that still have their hydrogen "skin"). The new version of ExTraSS can track these light rays in 3D, accounting for how atoms get ionized (stripped of electrons) by the radiation itself.
The Target: They simulated a 9-solar-mass star. This is the "underdog" of supernovae. It's the smallest star heavy enough to explode, making it a perfect test case for understanding the lower limits of stellar death.

The Simulation: A "Ni-Plume" Surprise

When they ran the simulation, they found something interesting about the Nickel-56 (a radioactive isotope created in the explosion).

The Old Way (1D): In flat models, the radioactive nickel sits neatly in the very center, like a cherry in a cake.
The New Way (3D): In their 3D model, the explosion wasn't symmetrical. The nickel was shot out in a fast, narrow jet (a "plume"), shooting out like a cannonball in one specific direction.

This is crucial because the radioactive nickel acts as the "flashlight" that illuminates the rest of the debris cloud. Where the nickel goes, the light follows.

The Results: Looking from Different Angles

Because the explosion is lopsided (asymmetrical), what you see depends entirely on where you are standing relative to the explosion.

The "Viewing Angle" Effect: If you look at the explosion from the side of the nickel jet, the light looks different than if you look at it from the opposite side. The paper shows that the shape and brightness of the glowing lines change drastically depending on your viewpoint.
The "Fingerprint" Match: They compared their 3D simulation to real observations of two actual supernovae: SN 1997D and SN 2016bkv.
- Success: The 3D model did a great job matching the shapes of the lines for elements like Magnesium, Oxygen, and Calcium. It proved that the messy, 3D nature of the explosion is real and necessary to explain what we see.
- The Glitch: The model predicted that Hydrogen and Iron lines should be much brighter than what we actually see in the real stars. This suggests that while the 3D model is a huge step forward, there are still some details about how the gas cools or mixes that need fine-tuning.

Why This Matters

The paper argues that we can no longer rely on simple, flat models to understand these cosmic events. Just as a flat map can't tell you about the terrain of a mountain range, a 1D model can't tell you about the true structure of a supernova.

By using this new 3D "camera," scientists can now:

Decode the Asymmetry: By comparing the shape of the light lines to the model, we can figure out exactly how the explosion was tilted and where the heavy elements were flung.
Identify the "Smallest" Exploders: They confirmed that the specific chemical signatures used to tell apart different types of low-mass explosions (like Electron-Capture Supernovae vs. Iron-Core Collapse) still hold true even in this messy 3D reality.
Track the Fastest Particles: They showed that even the fastest-moving nickel particles leave a trace in the light, allowing us to "see" the speed of the explosion's most energetic parts long after the event.

Summary Analogy

Imagine a fireworks display where the explosion is supposed to be a perfect sphere.

The 1D Model assumes it is a perfect sphere and predicts the light will be uniform.
The 3D Model realizes the explosion was actually a weird, lopsided blob with a fast jet shooting out one side.
The Paper says: "If you stand on the left, you see a bright red streak. If you stand on the right, you see a dim blue glow. Our new computer code simulates this 3D mess perfectly, and when we compare it to real fireworks (supernovae), it matches the shapes of the light trails much better than the old flat models did, even if the brightness of the red streak is still a little too high."

This work proves that to understand the death of stars, we must stop looking at them as flat circles and start seeing them as complex, 3D sculptures of light and matter.

Technical Summary: 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

Problem and Motivation
The nebular phase of core-collapse supernovae (CCSNe), occurring months to years post-explosion, encodes the explosion's asymmetries into emission line profiles. While Non-Local Thermodynamic Equilibrium (NLTE) radiative transfer is essential for accurate predictions, previous studies of low-mass progenitors ( $M_{\text{ZAMS}} \approx 8-12 M_\odot$ ) have largely relied on 1D models. These 1D models suffer from artificial shell structures and cannot capture the complex 3D mixing and asymmetries inherent in neutrino-driven explosions. Specifically, it remains uncertain whether diagnostic features distinguishing iron-core CCSNe from electron-capture supernovae (ECSNe) persist in 3D geometries, and how viewing angle variations affect line luminosities and profiles in low-energy explosions. This work addresses these gaps by applying an upgraded 3D NLTE radiative transfer code to a hydrodynamic simulation of a 9.0 $M_\odot$ progenitor.

Methodology
The authors utilize the ExTraSS (EXplosive TRAnsient Spectral Simulator) code, recently upgraded from a 1D/2D framework to a full 3D NLTE radiative transfer solver. Key technical upgrades include:

Radiative Transfer: Implementation of full photoionization and photoexcitation rates derived from the radiation field, replacing previous "on-the-spot" approximations. The code employs a ray-tracing technique with domain decomposition (inspired by Brunner & Brantley 2009) to manage memory loads, using $\phi$ -based decomposition to parallelize calculations across azimuthal slices.
Microphysics: The code calculates energy deposition for non-thermal excitations, uses specific recombination rates for H I, O I, Mg I, Fe I, and Fe II, and incorporates updated photoionization cross-sections (Verner et al. 1996).
Explosion Model: The study uses the s9.0 model from Stockinger et al. (2020), a 3D neutrino-driven explosion of a 9.0 $M_\odot$ solar-metallicity progenitor. The simulation was evolved to 19.74 days post-bounce, at which point the ejecta were mapped to a homologous expansion grid ( $38 \times 15 \times 30$ cells) for spectral synthesis at nebular epochs (250 and 400 days).
Comparison: Synthetic spectra were generated for 400 viewing angles ( $20 \times 20$ grid) and compared against observations of SN 1997D and SN 2016bkv. Results were also benchmarked against a 1D model of the same progenitor from Jerkstrand et al. (2018, J18).

Key Results

Physical Conditions: The 3D model exhibits a more uniform temperature structure compared to the 1D J18 model. The lack of artificial shell stratification in 3D leads to a more distributed $\gamma$ -ray energy deposition throughout the ejecta, resulting in lower overall trapping efficiency (82% of the 1D deposition at 400 days) and lower electron fractions ( $x_e$ ) due to higher core densities and more efficient recombination.
Spectral Evolution and Element Distribution: The 3D ejecta show strong mixing, with the primary $^{56}$ Ni plume extending to velocities up to 1400 km s $^{-1}$ . This mixing significantly enhances Fe I emission in the 3D model compared to the 1D counterpart, particularly in the 6200–6700 Å and 7900–8400 Å ranges.
Comparison to Observations (SN 1997D and SN 2016bkv):
- The model reproduces the line profiles of He, C, O, and Mg lines reasonably well for SN 1997D.
- However, the model overpredicts the strength of H $\alpha$ and Fe I lines compared to SN 1997D.
- For SN 2016bkv, the model fails to reproduce the absence of strong Fe I lines in the 7900–8400 Å range, suggesting the model's Fe I emission is too strong for this object as well.
Viewing Angle Effects: Line profiles and luminosities vary significantly with viewing angle.
- H $\alpha$ : The most luminous profiles are blueshifted, while the least luminous are redshifted and broader. The luminosity variation between the brightest and dimmest views is approximately 16%.
- Mg I]: Shows even larger luminosity variations (factor of >2) due to higher opacity at shorter wavelengths.
- Centroid Shifts: Unlike high-kick models where hydrodynamical kicks dictate shifts, the low kick velocity in this model (dominated by neutrino-induced asymmetry) results in complex centroid shift patterns that do not strictly align with the neutron star kick vector.
Diagnostic Features: Key diagnostic lines used to distinguish Fe CCSNe from ECSNe (e.g., He I $\lambda$ 7065, [C I] $\lambda$ 8727, [C I] $\lambda\lambda$ 9824, 9850) remain present in the 3D model, supporting the validity of 1D-based diagnostics even in the presence of 3D mixing.

Significance and Claims
The paper demonstrates that 3D NLTE radiative transfer is necessary to accurately model the nebular phase of low-mass CCSNe, as 1D models fail to capture the mixing of radioactive nickel and the resulting impact on line profiles. The authors show that:

3D Diagnostics Hold: The primary spectral signatures distinguishing low-mass Fe CCSNe from ECSNe are robust against 3D mixing effects.
Asymmetry Detection: The strong dependence of line profiles on viewing angle allows for detailed comparisons with observed spectra to infer explosion asymmetries.
Tracing $^{56}$ Ni: Even the fastest $^{56}$ Ni ejecta (up to 1400 km s $^{-1}$ ) leave a traceable signature in nebular phase line profiles.
Model Limitations: The current s9.0 model tends to produce Fe I and H $\alpha$ lines that are too strong compared to observations of SN 1997D and SN 2016bkv, indicating that while the 3D framework is a significant improvement, specific explosion parameters or microphysics may still require refinement to match specific low-luminosity events.

The work establishes a pathway from 1D to 3D modeling for low-mass progenitors, providing a more realistic framework for interpreting future nebular phase observations of low-luminosity Type IIP supernovae.