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Neutrino Heating in 1D, 2D, and 3D core-collapse supernovae: characterizing the explosion of high-compactness stars

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read High-compactness supernova progenitors explode, not fail

desk verdict High-compactness stars probably do revive their shocks, but the paper's jump from revival to successful explosion is a real overreach. read the letter →

arxiv 2501.06784 v2 pith:7XRZRYDR submitted 2025-01-12 astro-ph.HE astro-ph.SR

Luca Boccioli , David Vartanyan , Evan P. O'Connor , Daniel Kasen This is my paper · ORCID
classification astro-ph.HEastro-ph.SR
keywords core-collapsesupernovaeneutrinoheatingcompactnessshockrevivalneutrino-drivenconvectionmixing-lengththeoryexplodabilityblackholeformation
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 the conventional cut between exploding and failed core-collapse supernovae is wrong at the high-density end: progenitors with high compactness $\xi_{2.0} \gtrsim 0.5$ do not quietly fail but revive their stalled shock through very strong neutrino heating. Compactness here is the ratio of $2\,M_\odot$ of enclosed baryonic mass to the radius enclosing it, a proxy for how dense the pre-collapse core is. The authors reach this conclusion by comparing about 150 two-dimensional and 20 three-dimensional simulations with spherically symmetric '1D+' models that approximate neutrino-driven convection by mixing-length theory. They find a common curve of maximum neutrino heating versus compactness that rises steeply for $\xi_{2.0} \gtrsim 0.5$, and identify the mechanism: convection keeps the shock stalled at large radius, so the gain region stays massive long enough for rising neutrino energies from the accreting proto-neutron star to power the explosion. If correct, this flips a standard assumption used in population synthesis and galactic chemical evolution, where high-compactness stars are assigned to black-hole formation without explosion, and it makes cheap large-scale explodability surveys of high-compactness stars feasible.

What carries the argument

The load-bearing object is the gain region--the volume behind the stalled shock where net neutrino heating is positive (defined here with density below $3\times10^{10}\,\mathrm{g\,cm^{-3}}$ and entropy per baryon above $6$)--together with the STIR closure, a mixing-length model that adds turbulent kinetic-energy generation, dissipation, and energy flux to spherically symmetric hydrodynamics. Convection does two things: it keeps the shock stalled at roughly constant radius for hundreds of milliseconds, so the gain-region mass $M_g$ does not collapse as it does in pure 1D, and it transports hot bubbles plus dissipates turbulence into heat near the shock. Because the proto-neutron star keeps accreting during that time, neutrino root-mean-square energies $\langle\epsilon_\nu^2\rangle$ rise, and since $\dot{Q}_\nu \propto M_g\langle\epsilon_\nu^2\rangle L_\nu/\bar{R}_g^2$, the net heating grows with time rather than peaking and decaying at about 100 ms. The paper packages this into three fitted curves for $\dot{Q}_\nu^{\max}(\xi_{2.0})$--one for 1D, one for multi-D and 1D+ below $\xi_{2.0}=0.72$, one above--that the simulation suites all follow.

What would settle it

A decisive check would be a long-term 3D simulation of a progenitor with $\xi_{2.0}\gtrsim0.5$ (for example the 25 $M_\odot$ model used here) that follows the shock for several seconds after bounce: if the shock is revived but then falls back and the proto-neutron star collapses to a black hole before the shock passes the envelope's sonic point, the paper's identification of revival with explosion would fail for that case. A simpler empirical falsifier is the black-hole mass distribution: a population of 20--30 $M_\odot$ remnants with no accompanying supernova ejecta would contradict the claim that these explosions typically accompany black-hole formation.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes a compactness--heating--outcome relation. Across about 150 2D and 20 3D simulations, every high-compactness progenitor with $\xi_{2.0} \gtrsim 0.5$ (except four 1D+ cases and one 2D case tied to very stiff equations of state) undergoes successful shock revival, and the maximum net neutrino heating $\dot{Q}_\nu^{\max}$ grows steeply with $\xi_{2.0}$, with a break near $\xi_{2.0} \simeq 0.72$ that the paper traces to neutrino luminosities rising during the accretion phase. The same trend is reproduced by the 1D+ models (GR1D+ and 1D+ FLASH) that include neutrino-driven convection through the STIR closure. The quantitative core is a semi-analytic heating identity, $\dot{Q}_\nu = 5.18\times10^{51}\,\mathrm{erg\,s^{-1}} (M_g/0.01\,M_\odot)(\bar{R}_g/100\,\mathrm{km})^{-2}\sum_{\nu_e,\bar\nu_e}\langle\epsilon_\nu^2\rangle/(18\,\mathrm{MeV})^2\, L_\nu(\bar{R}_g)/(3\times10^{52}\,\mathrm{erg\,s^{-1}})$, which reproduces the simulations and shows that the gain-region mass $M_g$, sustained by convection, is what lets heating climb during the stalled-shock phase. The paper concludes that high-compactness progenitors explode even though they also form black holes quickly, and that 1D+ models are adequate for future large explodability surveys.

Load-bearing premise

The load-bearing premise is that a successfully revived shock--one that expands to thousands of kilometres within the simulated few seconds--will go on to become a real supernova; if late-time black-hole formation cuts off the neutrino heating and the shock before breakout, the high-compactness 'explosions' would leave no visible supernova despite early revival.

Editorial extensions

If this is right

  • If the central claim holds, explodability studies should stop treating $\xi_{2.0}\gtrsim0.5$ as a failed-explosion zone: those stars can yield successful shock revival and, per the cited long-term simulations, eventual shock breakout.
  • Population synthesis and galactic chemical evolution calculations that currently assign high-compactness stars to direct black-hole formation should be re-run with a compactness-dependent explodability prescription, because a 20--30 $M_\odot$ black hole can be accompanied by a supernova.
  • The 1D+ STIR approach can serve as a cheap survey tool for the high-compactness regime, since it reproduces the multi-dimensional $\dot{Q}_\nu^{\max}$ trend and explosion outcomes to within the scatter among codes.
  • The accretion of the Si/O interface sets the explosion clock for $\xi_{2.0}\lesssim0.5$ but not for $\xi_{2.0}\gtrsim0.5$, and explosion time is not a reliable proxy for heating strength because high-compactness shocks move faster once revived.
  • Stiffer equations of state shift the whole heating-versus-compactness curve downward, so the precise critical compactness for revival depends on the nuclear equation of state.

Reading between the lines

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

  • A testable extension of the paper's fits would convert the $\dot{Q}_\nu^{\max}(\xi_{2.0})$ curve into a probabilistic explodability prescription by measuring the scatter of multi-D outcomes around the curve, including the equation-of-state dependence.
  • If high-compactness stars explode while forming black holes quickly, the gravitational-wave black-hole mass function could carry a fingerprint: a population of 20--30 $M_\odot$ remnants with associated supernova ejecta, which future detectors could separate from silent collapse.
  • The paper stops at shock revival; an observational inference is that the optical transients of such explosions should be fast and dim (with possibly strong fallback), which wide-field surveys targeting low-metallicity host galaxies could catch.
  • Because the paper notes that 1D+ models underestimate early neutrino heating at low compactness, a prompt-convection correction to the STIR closure might be needed before the method is trusted outside the high-compactness regime.
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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 / 5 minor

Summary. The paper uses a large set of one-dimensional, 1D+, 2D, and 3D core-collapse supernova simulations (~1500 runs, of which 173 are multi-D) to argue that the maximum neutrino heating in the gain region, Qdot_nu^max, rises steeply with pre-SN compactness xi_2.0, and that this rise is sufficient to revive the stalled shock for high-compactness progenitors (xi_2.0 ≳ 0.5). The authors further show that 1D+ models with the STIR mixing-length treatment reproduce the multi-D heating and explodability trend, derive piecewise semi-analytic fits for Qdot_nu^max(xi_2.0) based on the Janka (2012) heating formula, and compare their 1D+ results against other 1D explosion models (O'Connor & Ott 2011, PUSH, Ertl et al. 2016, Mueller et al. 2016, Pejcha & Thompson 2015). The central observational claim is that common assumptions that high-compactness stars fail are incorrect: instead, these stars undergo successful shock revival and, the authors argue, produce successful explosions.

Significance. If the central claim holds, this is an important result for CCSN theory and for population synthesis: it reverses a widely used rule that high-compactness progenitors form black holes without explosions, and it quantifies how neutrino heating grows with compactness. The strengths of the paper are its unusually large multi-dimensional sample (98 2D Fornax, 55 2D FLASH, 20 3D Fornax), the direct comparison of 1D+/multi-D heating rates, and the explicit, reproducible fit formulas in Eqs. (12)-(14) and Appendix B. The identification of t_max ≈ t_Si/O for xi_2.0 < 0.5 and the regime change at xi_2.0 ≈ 0.72 are useful diagnostics for the explosion mechanism. However, the inference from shock revival to successful explosion is not established by the simulations presented, and the semi-analytic curves carry less independent weight than the text suggests, because their coefficients are fitted to the same simulations. A careful revision that separates empirical trends from interpretive claims would make the paper much more solid.

major comments (4)
  1. [Section 3.1] The central inference equates shock revival with explosion. The text states 'we can assume that simulations, where the shock has been successfully revived, yield an explosion' and 'all of the 2D and 3D simulations with compactness xi_2.0 ≳ 0.5 explode.' The simulations are run only to 1-5 s post-bounce, which is not enough to guarantee shock breakout for high-compactness stars; the paper itself cites Kuroda et al. (2018), Summa et al. (2018), and Walk et al. (2020) for cases with no revival or with revival followed by early black-hole formation. The sonic-point criterion of Sykes & Müller (2025) is invoked but never evaluated on the shock trajectories analyzed here. I therefore do not think the abstract's language 'successful shock revival' can be equated with 'successful explosion' for the full high-compactness population without an additional breakout analysis.
  2. [Appendix B] The derivation of the Qdot_nu^max versus xi_2.0 curves is not an independent prediction. The slope and intercept of the neutrino-energy evolution in Eqs. (B2)-(B3), the luminosity-mass-radius combinations in Eqs. (B4) and (B5), and the t_Si/O relation in Eq. (B7) are all fits to the same 1D/1D+ simulations used for Figure 3, and an additional factor 0.8 is applied by hand in Section B2. Eq. (16) introduces the tuned radius Rbar_g, and Appendix A fixes a 0.6 net-to-total heating fraction. Consequently Eqs. (12)-(14) should be described as empirical fits with a physics-motivated functional form, not as a derivation that independently explains the observed trend. The current wording in Sections 3.1 and 4 ('we can show', 'the only difference is') overstates the explanatory power.
  3. [Equations (13)-(14)] The piecewise fit is discontinuous at the nominal transition xi_2.0 = 0.72. Evaluating the brackets at xi_2.0 = 0.72 gives approximately 1.9 for Eq. (13) and approximately 4.1 for Eq. (14), i.e. a factor ~2.2 jump in Qdot_nu^max. Since the observed Qdot_nu^max values in Figure 3 are a continuous function of compactness, the two expressions cannot both represent the data near the boundary. The fit discontinuity needs to be addressed numerically, or the piecewise representation should be explicitly qualified as a non-continuous approximation.
  4. [Section 3, first two paragraphs] The multi-D sample is heterogeneous in neutrino transport (co-moving-frame M1 in Fornax vs lab-frame M1 in FLASH), opacities (Kompaneets vs elastic neutrino-nucleon scattering), equations of state (SFHo and several Schneider et al. 2019 models), and grid geometry. The paper acknowledges that these differences 'prevent a detailed and thorough comparison,' yet the central claim treats all 2D and 3D simulations above xi_2.0 ~ 0.5 as one homogeneous population. The offset between 2D Fornax and 2D FLASH at low compactness and the shift of the heating curve with stiffer EOS show that these systematic differences are not negligible. A quantitative estimate of the resulting uncertainty in the threshold xi_2.0 ~ 0.5 is needed before this can be presented as a universal explodability condition.
minor comments (5)
  1. [Acknowledgements] The Acknowledgements contain the typo 'anonymus referee'; it should be 'anonymous referee'.
  2. [Section 6] The last paragraph of Section 6 states explosion energies of '0.01-3.5 10^51 erg/s'; explosion energies are measured in erg, not erg/s, and the typesetting '3.51051' is missing the multiplication sign.
  3. [Section 2.1] The acronym STIR is used throughout but never expanded; a brief expansion at first use (e.g., 'the subgrid turbulence model of Couch et al. 2020, known as STIR') would help readers unfamiliar with the literature.
  4. [Figure 3] The bottom panel plots failed explosions on top of successful ones, and the caption notes that overlapping points make the number of failures look larger than it is; a partially transparent marker or a separate panel would make the raw counts of successes/failures above xi_2.0 = 0.5 visible.
  5. [Appendix A] The net-to-total heating fraction of 0.6 is introduced in Appendix A with only a one-sentence justification; this value should be stated at Eq. (15) where it is first used, since it is a free parameter of the semi-analytic formula.

Circularity Check

2 steps flagged · score 6.0 of 10

Semi-analytic neutrino-heating curves are fitted to the same simulations they are said to confirm; the explosion-outcome claim itself is empirical, so circularity is partial.

  1. fitted input called prediction [Section 4, Eq. (16) and surrounding text; used in Eq. (15) and Fig. 4]
    "Instead, we do not use the neutrino luminosity at the gain radius 𝑅g, but rather at a slightly larger radius: ¯𝑅g=𝑅 g+0.15×(1+𝜉 2.0)(𝑅 s−𝑅 g) ... This was done to better reproduce the simulation results, especially in the 1D+ case."

    Eq. (15) is presented as a semi-analytical expression for neutrino heating, but its evaluation radius ¯𝑅g is explicitly tuned to match the very simulations later used for validation. Figure 4 then presents the agreement between Eq. (15) and the same simulations as 'excellent agreement', and Appendix B builds on Eq. (15) to derive the ¤𝑄max𝜈 vs compactness curves. The agreement is therefore by construction rather than an independent check, and the derived trend inherits the tuning.

  2. fitted input called prediction [Appendix B, Eqs. (B2)-(B5), the 0.8 correction after Eq. (B1), and resulting curves Eqs. (B6)-(B9) in Fig. 3]
    "𝑞1D+=127−83𝜉 1/3 2.0 𝑚1D+=1300𝜉 1/3 2.0 ... the superscripts 1D and 1D+ indicate the values resulting from fits to 1D and 1D+ simulations, respectively. ... To compensate for that, when we evaluate Eq. (B1) at 𝑡=𝑡max we multiply it by an extra factor of 0.8."

    The ¤𝑄max𝜈 vs compactness curves shown in Figure 3 are constructed from coefficients fitted to the same 1D/1D+ simulation data they are compared against, plus a hand-applied 0.8 correction. The statement that these curves 'reproduce the trend very well' and serve as 'further confirmation' is therefore a refitting exercise, not an independent prediction. The apparent derivation of ¤𝑄max𝜈(𝜉2.0) reduces to the input simulations by construction.

full rationale

The paper's headline claim — that high-compactness progenitors (𝜉2.0 ≳ 0.5) undergo successful shock revival/explosion — is taken directly from ~150 2D and 20 3D simulations; that empirical observation is not circular and has independent content. The circularity is in the supporting semi-analytic machinery. Eq. (16) defines ¯𝑅g by tuning to simulation results, Eq. (15) then 'agrees' with those same simulations, and Appendix B fits energy-slope coefficients (B2-B3), luminosity-mass-radius combinations (B4-B5), and applies a 0.8 correction before presenting Eqs. (B6)-(B9) as the trend in Fig. 3. These curves are fits to the same data they are said to confirm; presenting them as a quantitative explanation and 'further confirmation' is partly circular (pattern 2). The separate step in Sec. 3.1 equating shock revival with explosion is a physical assumption — the paper itself notes that breakout and explosion energy are 'not obvious' from simulations ending at 1-5 s and cites Sykes & Müller for the sonic-point criterion — but it is an extrapolation/limitation rather than a self-referential derivation. Section 6 also concedes that other groups see no shock revival or early black-hole quenching; that is a robustness caveat, not a circularity. No uniqueness theorem or load-bearing self-citation chain is invoked to force the result, and the multi-D simulation outcomes provide independent content. Score 6 reflects partial circularity in the derived heating curves, not in the core explosion-outcome dataset.

Assumptions & free parameters 13 free parameters · 7 assumptions · 0 invented entities

The central claim rests on empirical trends from simulations and on a semi-analytic model whose coefficients are fitted to the same simulations. The largest burden is the shock-revival-to-explosion equivalence and the representativeness of the mixed multi-D sample. No new particles or mediators are introduced.

free parameters (13)
  • alpha_MLT (GR1D+ STIR) = ~1.48-1.52
    Mixing-length parameter controlling convection strength in 1D+ models; calibrated to reproduce multi-D behavior in prior work.
  • alpha_MLT (FLASH 1D+) = ~1.23-1.27
    Equivalent mixing-length parameter in FLASH implementation; different because of Newtonian gravity and Brunt-Vaisala treatment.
  • Diffusion coefficients alpha_DK = 1/6
    Diffusion coefficients for turbulent energy, internal energy, electron fraction, and neutrino energy; fixed following Muller et al. 2016b and Couch et al. 2020.
  • Rbar_g offset coefficient = 0.15
    Eq. (16): places the effective heating radius between 15% and 30% of the gain region; chosen to better reproduce simulation results, especially 1D+.
  • Net-to-total heating fraction = 0.6
    Appendix A: net neutrino heating is approximated as 0.6 of total heating; value assumed, not derived from data.
  • Neutrino energy evolution intercept q = q1D+ = 127 - 83 xi^{1/3}; q1D = 127 - 83 xi^{1/3}
    Eqs. (B2)-(B3): intercept of linear fit to <eps^2> versus time post bounce for 1D+ and 1D simulations.
  • Neutrino energy evolution slope m = m1D+ = 1300 xi^{1/3}; m1D = 1400 xi^{1/3}
    Eqs. (B2)-(B3): slope of linear fit to <eps^2> versus time post bounce; fitted separately for 1D+ and 1D.
  • Low-compactness luminosity-mass fit coefficients = 1.75 and 3.84
    Eq. (B4): fit to L_nu M_g / Rbar_g^2 as a function of xi^{5/3} during accretion.
  • High-compactness luminosity-mass fit coefficients = 3.5, -255, 317
    Eq. (B5): fit for xi_2.0 > 0.72, where luminosity rises during accretion.
  • Energy overestimate correction factor = 0.8
    Appendix B2: applied when evaluating Eq. (B1) at t_max to compensate for nonlinear energy rise; chosen by hand.
  • t_Si/O versus compactness coefficients = 0.12, -0.13, 0.36, 0.07
    Eq. (B7): empirical relation between Si/O interface accretion time and compactness for the progenitors studied.
  • Critical compactness for regime switch = xi_2.0 ~ 0.72
    Boundary separating two scaling regimes in the Qdot_nu^max curves; determined from the simulation trend, not predicted a priori.
  • Explosion threshold compactness = xi_2.0 ~ 0.5
    Empirical threshold above which all multi-D and 1D+ simulations explode in this sample; used in the central claim.
assumptions (7)
  • standard math The mean value theorem justifies replacing the neutrino heating integral with a single representative radius R*.
    Appendix A, Eq. (A3). Standard mathematical step, though the choice of R* is empirical.
  • domain assumption Gain region is defined by net positive heating, density below 3e10 g/cm3, and entropy per baryon above 6.
    Section 2; these cuts exclude the PNS and unshocked material, but the entropy cut changes integrated heating by up to 10% in 2D Fornax runs.
  • domain assumption In the gain region Y_n ~ Y_p ~ 0.5.
    Appendix A; used to evaluate the absorption cross section; standard approximation in this regime.
  • ad hoc to paper Neutrino heating in 1D+ STIR is a reliable proxy for multi-D convective heating.
    Section 3; the paper validates this against selected multi-D runs but also notes STIR underestimates heating for low compactness and has a known inconsistency in the convective flux F_e.
  • domain assumption Shock revival implies a successful explosion.
    Section 3.1: 'we can assume that simulations, where the shock has been successfully revived, yield an explosion.' The paper acknowledges late black hole formation may quench the explosion, so this is an assumption.
  • domain assumption The SFHo equation of state is representative for the explosion outcome.
    Section 3; most simulations use SFHo; stiffer EOSs shift the Qdot_nu curve down and can suppress explosions, as the paper notes.
  • domain assumption The multi-D simulation sample is representative enough to define the explodability trend.
    Section 3 and Figure 3; simulations come from heterogeneous suites with different neutrino transport and opacities; the paper states this prevents a detailed comparison.

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Pith. "Pith review of Neutrino Heating in 1D, 2D, and 3D core-collapse supernovae: characterizing the explosion of high-compactness stars." pith.science (2026). https://pith.science/paper/7XRZRYDR

@misc{pith2026250106784,
  author       = {Pith},
  title        = {Pith review of: Neutrino Heating in 1D, 2D, and 3D core-collapse supernovae: characterizing the explosion of high-compactness stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7XRZRYDR}},
  note         = {Machine review of arXiv:2501.06784}
}
abstract

Massive stars can end their lives with a successful supernova explosion (leaving behind a neutron star or, more rarely, a black hole), or a failed explosion that leaves behind a black hole. The density structure of the pre-collapse progenitor star already encodes much of the information regarding the outcome and properties of the explosion. However, the complexity of the collapse and subsequent shock expansion phases prevents drawing a straightforward connection between the pre-collapse and post-explosion properties. In order to derive such a connection several explodability studies have been performed in recent years. However, different studies can predict different explosion outcomes. In this article, we show how compactness, which is related to the average density of the star's core, has an important role in determining the efficiency of neutrino heating, and therefore the outcome of the explosion. Commonly, high-compactness progenitors are assumed to yield failed explosions, due to their large mass accretion rates, preventing the shock from expanding. We show by analyzing $\sim$ 150 2D FLASH and Fornax simulations and 20 3D Fornax simulations that this is not the case. Instead, due to the rapid increase of neutrino heating with compactness, high-compactness progenitors lead to successful shock revival. We also show that 1D+ simulations that include $\nu$-driven convection using a mixing-length theory approach correctly reproduce this trend. Finally, we compare 1D+ models, which we show can reproduce some aspects of multi-D simulations with reasonable accuracy, with other widely used 1D models in the literature.

Figures

Figures reproduced from arXiv: 2501.06784 by the authors.

Figure 1
Figure 1. The first four rows of this Figure show the 9 1D+ simulations for the progenitors listed in [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Comparison of neutrino heating in the gain region in 1D, 1D+, 2D and 3D simulations. For the multi-dimensional simulations, we show both the raw data as a faded dashed line and a smoothing over a window of 20 ms as a solid line. The left panel shows the comparison for a 12 𝑀⊙ progenitor from Sukhbold et al. (2016). However, notice that the 2D Fornax simulation was done for a 12.15 𝑀⊙ 𝑀⊙ progenitor from Sukhbold et a… view at source ↗
Figure 3
Figure 3. Maximum of the neutrino heating as a function of compactness. The bottom panel shows only 1D+, 2D, and 3D simulations, color-coded based on explosion outcome. Notice that the failed explosions have been plotted on top of the successful ones, and since several points overlap, it looks like the number of failed explosions is much higher than it is in reality. All simulations (except for four 1D+ and one 2D simulation … view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Integrated turbulent energy generation rate in the gain region (left panel) and neutrino heating in the gain region (middle panel) for 1D+ and 1D simulations of the progenitors listed in [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Total mass in the gain region for 1D (dashed lines) and 1D+ (solid lines) simulations of the progenitors listed in [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: The left and middle panels show the evolution of the shock and gain radius, respectively, for 1D (dashed lines) and 1D+ simulations (solid lines) of the progenitors listed in [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Neutrino root mean squared energies (upper panel) and neutrino lu￾minosities calculated at 𝑅 = ⟨𝑅⟩𝑔 (lower panel) for electron-type neutrinos. These are 1D (dashed lines) and 1D+ (solid lines) simulations for the pro￾genitors listed in [PITH_FULL_IMAGE:figures/full_fi…
Figure 8
Figure 8. Figure 8: The vertical axis shows the time at which 𝑄¤ max 𝜈 is reached. For the left panel, the horizontal axis shows the explosion time, which is defined as the time when the shock crosses 500 km. The right panels have on the horizontal axis the time when the Si/O interface is…
Figure 9
Figure 9. Figure 9: Only successful explosions of the 341 1D+ simulations from Boc￾cioli & Fragione (2024) are shown in this Figure. The dashed line indicates where 𝑡Si/O = 𝑡expl. Therefore, points to the right of that refer to simulations for which the Si/O interface is accreted after th…

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.