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arxiv: 2605.01405 · v1 · submitted 2026-05-02 · 🌌 astro-ph.HE · gr-qc

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Black Hole Supernovae Outcomes Across a Wide Progenitor Range

Oliver Eggenberger Andersen , Evan O'Connor , Liubov Kovalenko , Haakon Andresen , Sean M. Couch
Authors on Pith no claims yet

Pith reviewed 2026-05-09 18:36 UTC · model grok-4.3

classification 🌌 astro-ph.HE gr-qc
keywords black hole supernovaecore-collapse supernovaestellar progenitorsblack hole formationsupernova explosion energyremnant masscompactness parameteraxisymmetric simulations
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The pith

Black hole formation after shock revival occurs across most progenitors from 19.5 to 60 solar masses.

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

The paper tests whether black hole supernovae, events in which a black hole forms after the explosion shock has revived but before the blast finishes, are rare and limited to the heaviest stars or arise more generally. The authors run 23 long axisymmetric simulations of stars from 19.51 to 60 solar masses and find 18 cases that produce a black hole between 0.7 and 4.4 seconds after core bounce, for progenitors whose structural compactness falls between 0.40 and 0.63. These events yield explosion energies from roughly 2 times 10 to the 49 to 3 times 10 to the 51 ergs and black hole masses from 3 to 26 solar masses. The work shows a trend between final black hole mass and the carbon-oxygen core mass of the star, yet that core mass alone does not fully predict the black hole mass at the low and high ends of the range. This broadens expectations for how black holes and supernova remnants form from massive stars.

Core claim

We find 18 black hole supernova outcomes across nearly the full zero-age main sequence mass range considered, corresponding to progenitors with 0.40 ≲ ξ2.5 ≲ 0.63. Black hole formation occurs between ∼0.7 s and ∼4.4 s after bounce. After black hole formation, we continue the evolution with an excision treatment to at least 5000 s. The final explosion energies span ∼2×10^49-3×10^51 erg, while the final black hole gravitational masses span ∼3-26 M⊙. We find a clear remnant-mass trend with CO-core mass, but show that the CO core alone is not an adequate proxy for the final black hole mass, especially for progenitors at the low- and high-mass ends of the CO-core distribution. Except for the high

What carries the argument

Long-term axisymmetric core-collapse simulations with neutrino transport, extended past shock revival to black hole formation and then continued with excision to track the final explosion energy and remnant mass.

If this is right

  • Black hole formation after shock revival is a systematic outcome for progenitors with compactness between 0.40 and 0.63.
  • Final black hole masses range from 3 to 26 solar masses and follow a trend with carbon-oxygen core mass.
  • The carbon-oxygen core mass is not an adequate standalone predictor of black hole mass at the low and high ends of the distribution.
  • No single spherical mass coordinate cleanly separates ejecta from remnant material except for the highest carbon-oxygen core models.
  • Two-dimensional axisymmetric results differ from three-dimensional geometry in the details of the evolution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A larger fraction of stellar-mass black holes may form through this post-revival channel than models limited to pre-revival collapse would predict.
  • The wide range of predicted explosion energies and black hole masses can be tested against observed supernova remnants and gravitational-wave events from core collapse.
  • Full three-dimensional calculations for the same progenitors would likely shift the exact compactness boundaries where black hole supernovae occur.
  • Longer post-excision runs beyond 5000 seconds could reveal additional fallback or accretion effects on the final remnant.

Load-bearing premise

The two-dimensional axisymmetric geometry and the chosen neutrino transport and progenitor models sufficiently capture the three-dimensional dynamics and microphysics that determine whether and when a black hole forms after shock revival.

What would settle it

A three-dimensional simulation of a progenitor with compactness near 0.5 that produces no black hole after shock revival, or forms the black hole only before revival, would falsify the reported prevalence and timing of these outcomes.

Figures

Figures reproduced from arXiv: 2605.01405 by Evan O'Connor, Haakon Andresen, Liubov Kovalenko, Oliver Eggenberger Andersen, Sean M. Couch.

Figure 1
Figure 1. Figure 1: Compactness ξ2.5 as a function of ZAMS mass for the progenitor suite of Sukhbold et al. (2018). Crosses indicate models evolved with the nominal mass-loss rate, while dots indicate models evolved with one-tenth of this rate. Black markers highlight the 23 progenitors selected for this study, spanning 19.51–60 M⊙ and a compactness range of 0.31 ≲ ξ2.5 ≲ 0.63. The sample covers the first compact￾ness peak ne… view at source ↗
Figure 2
Figure 2. Figure 2: Mass–radius relations for the progenitor suite, showing enclosed mass out to 3.25 M⊙ as a function of radius, color￾coded by the progenitor ZAMS mass. The models are nearly equally compact below 1.75 M⊙, but diverge beyond this point. While shock revival impacts the accretion rate, the underlying mass–radius relation remains closely linked to the subsequent accretion rate, PNS mass growth, BH formation tim… view at source ↗
Figure 3
Figure 3. Figure 3: Mean shock radius evolution. All models undergo shock revival, which we attribute to the high neutrino-heating rate in high-compactness models, the SFHo EOS used, and possibly the 2D axisymmetric constraint. Shock expansion triggered by the accretion of density jumps is evident in some models, and occurs especially early in the 37 M⊙ and 39 M⊙ models, both of which later produce remarkably energetic BHSNe.… view at source ↗
Figure 4
Figure 4. Figure 4: Central density evolution of the PNSs. Collapse to a BH is marked by a sudden rapid rise in central density. 18 out of 23 models form BHs between ∼ 0.7–4.1 s after bounce. The central density at BH formation lies within the range of 1.3 × 1015 g cm−3 to 1.8 × 1015 g cm, with the upper end reached by models that form BHs late. The lower-density models are discontinued before 2 s, as they appear less likely … view at source ↗
Figure 5
Figure 5. Figure 5: The baryonic mass evolution of the PNSs, explicitly labeled by each progenitor ZAMS mass (left) and by compactness (right). Black dots indicate the moment of BH formation, which generally correlates with the compactness. However, predicting the detailed path to BH formation and the growth rate of the PNS, requires taking into account the entire inner mass–radius relation of the progenitor (see view at source ↗
Figure 6
Figure 6. Figure 6: Gravitational mass of the PNS as a function of its entropy (see text for definition, colored lines), with black dots indicating BH formation. The gray U-shaped line repre￾sents the maximum baryonic mass, M max(s), of a spherically symmetric, constant entropy NS, assuming the SFHo EOS. Despite PNS entropy profiles that are not constant in the simulations, BH formation occurs close to the general rela￾tivist… view at source ↗
Figure 7
Figure 7. Figure 7: Diagnostic explosion energy, Ediag, explicitly labeled (left), and color-coded by compactness (right). Large variations are seen in how the explosions develop, reflecting the wide range of progenitor structures, supplemented by the stochastic dynamical nature. Immediately after shock revival, the explosion energy tends to build faster with higher compactness. On the other hand, lower-compactness models can… view at source ↗
Figure 8
Figure 8. Figure 8: Diagnostic explosion energy curves (Equation 3) for the models that form BHs, plotted on a logarithmic scale up to 0.3 × 1051 erg and on a linear scale above this value. The energy peaks around BH formation when the neutrino engine ceases, then decreases as the energy in the neutrino-heated bubbles is drained while they propagate through the overburden. It rises again after the shock has exited the helium-… view at source ↗
Figure 9
Figure 9. Figure 9: Gravitational mass of the compact object for the BH-forming models. More massive progenitors leave more massive BHs behind because they possess more massive and more compact CO cores. Consequently, the overburden ahead of the shock at BH formation increases with CO-core mass (see view at source ↗
Figure 10
Figure 10. Figure 10: The overburden, i.e., the energy required to bring the total energy of the overlying material to zero, as a function of radius. The dots are Ediag at BH formation, placed at the radius of the shock at BH formation. Generally, the more massive the progenitor and its CO-core mass, the larger the disparity between Ediag and the overburden at BH formation. Four models have an Ediag higher than their overburde… view at source ↗
Figure 11
Figure 11. Figure 11: The fraction of each spherical mass shell at BH formation that ultimately escapes the BH and contributes to the ejecta. The long arrows denote the position of the shock in mass coordinate at BH formation, while the short arrows indicate the outer boundary of the helium-depleted CO core. For models of 51 M⊙ and above, only loosely bound hydrogen envelope is ejected, marked by the sharp transition from ∼ 0 … view at source ↗
Figure 12
Figure 12. Figure 12: The final BH mass (black dots), the ejecta mass (orange circles), the helium-depleted CO-core mass (blue dots), and the hydrogen-depleted He-core mass (red dots). The remnant mass increases approximately linearly with ZAMS progenitor mass, owing to the approximately linear relation between the CO-core mass and ZAMS mass in this progenitor suite; higher mass models have more mass that is simultaneously mor… view at source ↗
Figure 13
Figure 13. Figure 13: BH mass distribution (bottom panel, black line) obtained by convolving the progenitor mass–remnant mass relation with the function ϕ(M) PBH(M), where ϕ(M) ∝ M−2.3 is the initial mass function (top panel, gray line), and where PBH(M) is representing regions in ZAMS mass where we do not explicitly obtain BHs in the simulations (top panel, red line). The dashed lines in the bottom panel is the distributions … view at source ↗
read the original abstract

Black hole supernovae (BHSNe), the term we use for core-collapse events in which black hole (BH) formation occurs after shock revival but before the explosion is complete, have emerged as a natural outcome of multidimensional simulations as these calculations have been extended to seconds after bounce. Yet they remain one of the least studied outcomes of core collapse. Here, we assess whether they are confined to the most compact and massive progenitors, whose birth rates are low, or whether they arise systematically across a wider range of progenitor structures. We perform 23 long-term axisymmetric core-collapse simulations of progenitors spanning 19.51-60$\,M_\odot$ and compactnesses $0.31 \lesssim \xi_{2.5} \lesssim 0.63$. We find 18 BHSN outcomes across nearly the full ZAMS mass range considered, corresponding to progenitors with $0.40 \lesssim \xi_{2.5} \lesssim 0.63$. BH formation occurs between $\sim0.7$ s and $\sim4.4$ s after bounce. After BH formation, we continue the evolution with an excision treatment to at least 5000 s. The final explosion energies span $\sim2\times10^{49}$-$3\times10^{51}$ erg, while the final BH gravitational masses span $\sim3$-$26\,M_\odot$. We find a clear remnant-mass trend with CO-core mass, but show that the CO core alone is not an adequate proxy for the final BH mass, especially for progenitors at the low- and high-mass ends of the CO-core distribution. Except for the highest CO-core mass models, no single spherical mass coordinate cleanly separates ejecta from remnant material. Finally, a 2D axisymmetric and a 3D model are compared as we discuss differences between the two geometries.

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

0 major / 2 minor

Summary. The paper presents results from 23 long-term axisymmetric core-collapse simulations of progenitors spanning 19.51-60 M_⊙ with compactnesses 0.31 ≲ ξ_{2.5} ≲ 0.63. It reports 18 black hole supernova (BHSN) outcomes for progenitors with 0.40 ≲ ξ_{2.5} ≲ 0.63, where black hole formation occurs between ~0.7 s and ~4.4 s after bounce. Post-BH formation evolution uses excision up to at least 5000 s, yielding explosion energies from ~2×10^{49} to 3×10^{51} erg and BH gravitational masses from ~3 to 26 M_⊙. Trends with CO-core mass are discussed, noting that CO core is not a sufficient proxy for final BH mass at the extremes, and a comparison between 2D and 3D geometries is included.

Significance. If these results hold, the work demonstrates that black hole supernovae are not restricted to the most massive and compact progenitors but occur systematically across a wide range of progenitor structures. This has important implications for the rates of black hole formation and the diversity of core-collapse supernova outcomes. The assessment is strengthened by the explicit set of 23 simulations, the clear reporting of trends in remnant mass and explosion energy, and the inclusion of a 2D-to-3D comparison, which provides a computational foundation for the claims.

minor comments (2)
  1. [Discussion section on 2D vs 3D] The comparison of one 2D axisymmetric and one 3D model is a positive step, but the manuscript does not quantify the potential impact of three-dimensional effects on the post-revival accretion rates and neutrino heating that determine BH formation timing across the ξ2.5 range. This could be addressed by discussing how the reported BH formation window of 0.7-4.4 s might shift in 3D, particularly for the lower compactness cases near 0.40.
  2. [Results on remnant mass trends] The statement that 'no single spherical mass coordinate cleanly separates ejecta from remnant material' except for highest CO-core models is significant; ensure that this is supported by explicit figures or tables showing the mass coordinate evolution for representative models at low, mid, and high CO-core masses.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending minor revision. The summary accurately captures the scope of our 23 axisymmetric simulations and the key findings on black hole supernova outcomes across the progenitor range. No major comments were raised in the report.

Circularity Check

0 steps flagged

Direct numerical simulations with no analytical derivation chain

full rationale

The paper reports outcomes from 23 long-term axisymmetric core-collapse simulations across progenitors with 19.51-60 M⊙ and 0.31 ≲ ξ2.5 ≲ 0.63. Central claims (18 BHSN events for 0.40 ≲ ξ2.5 ≲ 0.63, BH formation at 0.7-4.4 s post-bounce, explosion energies ~2e49-3e51 erg, BH masses ~3-26 M⊙, and remnant-mass trends) are direct results of these computations, continued with excision to 5000 s. No equations, derivations, or predictions are presented that reduce by construction to fitted inputs, self-definitions, or self-citation chains. The single 2D-3D comparison is noted but does not bear the load of the main results. The work is a self-contained computational experiment against external benchmarks (progenitor models, neutrino transport), with no renaming of known results or imported uniqueness theorems.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The results rest on established numerical methods for core-collapse hydrodynamics and neutrino transport drawn from the prior literature; no new free parameters, axioms beyond standard domain assumptions, or invented entities are introduced.

axioms (1)
  • domain assumption Standard assumptions of general relativistic hydrodynamics, neutrino transport, and equation of state in core-collapse supernova modeling
    Invoked for all 23 simulations and the excision treatment.

pith-pipeline@v0.9.0 · 5662 in / 1349 out tokens · 41131 ms · 2026-05-09T18:36:07.577466+00:00 · methodology

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