Channels of Stellar-mass Black Hole Formation

Adam Burrows; David Vartanyan; Tianshu Wang

REVIEW 4 major objections 5 minor 11 cited by

Channels of Stellar-mass Black Hole Formation

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Stellar-mass black holes form through four distinct collapse channels, at least two of which produce visible supernovae.

desk verdict Useful four-channel taxonomy of stellar-mass black hole formation from late-time 3D simulations; Channel 4 is the weakest pillar but the authors already know and say so, and the explosive channels are the real news. read the letter →

arxiv 2412.07831 v2 pith:2XXV7ZBM submitted 2024-12-10 astro-ph.SR astro-ph.GAastro-ph.HEnucl-th

Adam Burrows , Tianshu Wang , David Vartanyan This is my paper · ORCID

classification astro-ph.SRastro-ph.GAastro-ph.HEnucl-th PACS 97.60.Bw97.60.Lf

keywords core-collapsesupernovaeblackholeformationchannelscompactnessparameterfallbackaccretionpulsationalpair-instabilityneutrino-drivenexplosions3Dsupernovasimulationsstellar-massholes

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 old picture — a massive star collapses, nothing shines, and a black hole is born silently — is incomplete. Using late-time three-dimensional simulations of core collapse, the authors identify four distinct routes to a stellar-mass black hole: a vigorous asymmetric explosion forms one, a modest explosion whose late fallback pulls enough matter back forms another, an abortive explosion (often after a pulsational-pair-instability eruption) leaves a tens-of-solar-mass black hole, and a genuinely quiet collapse forms one. The stakes are practical: if these channels exist, some supernovae that look ordinary are actually black-hole births, and the birth masses and kicks of black holes in X-ray binaries and gravitational-wave mergers depend on which channel dominates. The paper also suggests, without proving, that the silent channel may not be the most common.

What carries the argument

The organizing quantity is the compactness parameter $\xi_{1.75}$, the ratio of the 1.75-solar-mass interior mass to the radius enclosing it, which crudely measures how shallow the core density profile is at collapse; higher compactness means higher post-bounce accretion rates, higher neutrino heating, and heavier residues. The mechanism that decides the channel is a race between that accretion fattening the newborn neutron star toward black-hole collapse and the extra neutrino heating (amplified by neutrino-driven convection and a spiral standing accretion shock instability) trying to unbind the envelope. The methodological step that makes the taxonomy visible is following the three-dimensional explosions well past the usual one second — to hours and days — by mapping the late flow onto a longer-timescale hydrodynamics framework with a point-mass inner boundary; this is what turns an apparent neutron-star outcome (the 23-solar-mass model) into a black hole via late fallback, and what revises the earlier 40-solar-mass black hole mass upward to about 9 solar masses.

What would settle it

A systematic census of black-hole birth sites would settle the matter: if most stellar-mass black holes show no associated supernova remnant and high-cadence searches record silent disappearances at the rate needed to account for the population, the paper's suggestion that the silent channel is not dominant would be contradicted, while finding late-time $^{56}$Ni fallback or remnant shells around a sizable fraction of black holes would support the multi-channel picture.

Watch

Extended reading notes

Core claim

The central claim is that black hole formation in the core-collapse context is heterogeneous and is usually accompanied by at least some explosive display. The load-bearing examples are a 40-solar-mass and a 19.56-solar-mass solar-metallicity star that explode asymmetrically and energetically yet leave black holes (Channel 1); a 23-solar-mass star that explodes with ordinary energy but later falls back about 3 solar masses, leaving a ~4.9-solar-mass black hole that would be hard to distinguish from a normal neutron-star-forming supernova (Channel 2); a 100-solar-mass, one-tenth-solar-metallicity star that undergoes a pulsational-pair-instability, starts a highly asymmetric explosion, and then aborts it, leaving a ~37-solar-mass black hole (Channel 3); and 12.25- and 14-solar-mass stars whose shock never revives, producing the only truly quiescent 'silent' black holes (Channel 4). The paper reports for each channel the explosion energy, $^{56}$Ni yield, recoil kick, and residual black hole mass, and stresses that the outcome is set by the density and binding-energy profiles of the progenitor core at collapse, indexed by compactness.

Load-bearing premise

The taxonomy rests on whether the stellar-evolution cores used to build the collapsing progenitors (including the single 100-solar-mass pulsational-pair-instability model) faithfully represent real massive-star cores at collapse; the paper itself concedes that the mapping from initial stellar mass to core structure at collapse is still unsettled.

Editorial extensions

If this is right

Some ordinary-looking core-collapse supernovae are black-hole births, so classifying all supernovae as neutron-star births and all black holes as silent collapses misassigns a fraction of both populations.
Channel 1 black holes receive large recoil kicks, hundreds to more than a thousand kilometers per second, which can eject them from binaries and helps explain the black-hole lower mass gap as a true observational gap for this subset.
Channel 2 can leave roughly 3-to-10-solar-mass black holes in weak or moderate explosions with low kicks, making them hard to pick out and potentially responsible for eccentric, wide black-hole binaries.
In the Channel 3 scenario the core-collapse supernova adds little to the pulsational-pair-instability light curve, and a ~37-solar-mass black hole can be left in an event that looks mostly like a PPISN.
Channel 4 silent collapses should have low kicks near 6.5 to 7 km/s and neutrino and gravitational-wave signals that continue for minutes to hours, unlike the abrupt signals expected from immediate black-hole formation.

Reading between the lines

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

A consequence the paper leaves implicit is that if the fallback channel is common, supernova surveys have been counting black-hole births as ordinary neutron-star births, so the true black-hole birth fraction is higher than estimates based on silent collapses alone.
The taxonomy also suggests that single-parameter 'explodability' prescriptions cannot capture the outcome; population synthesis should instead draw from a multi-peaked mapping with fallback and aborted-explosion branches.
A testable extension would be to assemble the kick distribution of astrometric black holes in wide binaries: Channel 1 predicts a high-kick tail, Channels 2 and 4 predict small kicks, so the observed eccentricity and velocity distribution can weigh the channel fractions.
Because removing the hydrogen envelope removes the reverse shock that drives late fallback, binary-stripped versions of the same progenitors should shift toward lower black-hole masses and higher kicks; this is a concrete, testable consequence of the channel picture.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague, read this one if you care about where stellar-mass black holes come from. The punchline: Burrows et al. use their late-time 3D Fornax/FLASH runs to argue black hole formation is not mostly silent. They lay out four channels, two of which produce recognizable supernovae. The genuinely new stuff is the 19.56 Msun run, the 100 Msun PPISN run, and the late-time 23 Msun run; the 40 Msun model now ends up at ~9 Msun once fallback is followed for hours, not 3.5. Those are real data points.

What it does well: the simulations are state of the art and run longer than most published 3D CCSN work, and the paper is careful about what is speculative. There is no fitting to observed BH masses; these are simulation outputs. The four-channel frame is a useful way to organize results that were scattered across groups.

The soft spots are real but mostly acknowledged. Channel 4, the silent channel, rests on the 12.25 and 14 Msun models that are not run to BH formation; the inference is standard but the non-explodable island is explicitly contingent on the Sukhbold/KEPLER progenitors and resolution. The paper says so. If another progenitor code explodes those cores, Channel 4 dissolves into the NS channel and the taxonomy loses a member. The 100 Msun PPISN progenitor is private, so that channel is not independently checkable until Woosley's paper appears. Data only on request is annoying but not disqualifying. The 23 Msun boundary condition uses a power-law wind extrapolation; that is a minor parametric choice, not a load-bearing flaw.

There is an argument that the central claim survives anyway: even if Channel 4 goes away, channels 1-3 establish that explosive BH formation is real and possibly common. The paper does not overclaim; the abstract says 'suggest, but have not proven' about the silent channel's dominance.

Who this is for: anyone working on core-collapse theory, LIGO/Virgo mass functions, the lower mass gap, or BH natal kicks. It deserves a serious referee; the main revisions I would want are making the 100 Msun model public or describing it better, and an honest discussion of what would falsify Channel 4. Yes, send it to review.

Referee Report

4 major / 5 minor

Summary. This paper synthesizes a large suite of three-dimensional Fornax and FLASH core-collapse supernova simulations and argues that stellar-mass black hole formation is heterogeneous, with four distinct channels: (1) energetic, asymmetric explosions that leave a black hole (exemplified by the 40 and 19.56 solar-mass models), (2) weak explosions followed by late-time fallback that forms a black hole (the 23 solar-mass model), (3) aborted explosions, often with a pulsational-pair-instability supernova precursor, leaving a more massive black hole (the 100 solar-mass model), and (4) a quiescent or 'silent' channel in which no shock revival occurs and a black hole forms over long timescales (the 12.25 and 14 solar-mass models). For each channel the paper reports black hole birth masses, explosion energies, nickel yields, recoil kicks, and some gravitational-wave and neutrino signatures, and it discusses the dependence of the outcomes on compactness, binding energy, metallicity, and the nuclear equation of state.

Significance. If the four-channel picture survives scrutiny, it is an important contribution: it directly challenges the common assumption that most black hole formation is silent, it connects black hole birth to observable supernova diversity, and it provides concrete predictions for kicks, nickel yields, and gravitational-wave and neutrino diagnostics. The paper's strengths are that the simulations are carried much later than most published 3D core-collapse runs, the results are genuine simulation outputs rather than fits to observed black hole masses, and the authors are candid about the dependence of their conclusions on stellar evolution models. However, the central taxonomic claim rests on one channel that is inferred rather than simulated to completion and on another channel whose progenitor model is not yet public, so the current manuscript needs additional support before the four-channel claim can be accepted as stated.

major comments (4)

[Section 4.4, Table 1] Channel 4 is inferred rather than simulated. The 12.25 and 14 solar-mass Fornax runs terminate at 2.090 s and 2.824 s after bounce, and the paper states that black hole formation would occur on minute-to-hour timescales without presenting a continued post-shock calculation or a quantitative argument that the accretion rate cannot be reversed on those timescales. Since the abstract claims 'we identify four channels,' this overstates the evidence for the silent channel. Please either extend the simulations with an appropriate boundary treatment or explicitly relabel Channel 4 as a candidate/inferred channel in the abstract, Section 4.4, and Section 5.
[Section 2, Section 4.3] The 100 solar-mass progenitor is a private model provided by S. Woosley and is described as 'in preparation,' so Channel 3 is not reproducible or independently checkable. The outcome of this channel, including the aborted explosion and the final black hole mass near 37 solar masses, depends on the structure of a star that has already undergone three PPISN pulses. Please make the progenitor model publicly available, or provide a complete quantitative description in an appendix, including mass coordinates, density/entropy/electron-fraction profiles, binding energy, compactness, and the history and energetics of the three pulsations.
[Section 2, Section 4.2] The Channel 2 final state depends sensitively on the post-Fornax boundary treatment: for the 23 solar-mass model a wind inner boundary condition at 500 km is constructed from the witnessed flow and extrapolated with a power-law fit, and at 50 s the flow is mapped into FLASH with a diode boundary condition. The final black hole mass of about 4.9 solar masses and the fallback mass of about 3.2 solar masses are exactly the quantities that such ad hoc boundary choices can affect. No sensitivity study is reported; please quantify the uncertainty by varying the boundary radius and the power-law index, or provide a physical argument that the fallback mass is insensitive to these choices.
[Section 4.4, footnote 11] The existence and location of the silent channel are explicitly conceded to be contingent on the Sukhbold/KEPLER progenitor suite and possibly on resolution, and observational searches do not find a 12-15 solar-mass progenitor gap. This makes Channel 4 the least secure of the four channels. Please either add a cross-check with an independent stellar evolution suite, such as the Limongi et al. or Laplace et al. progenitor structures cited in the paper, or restrict the claim about the silent channel to 'within the Sukhbold/KEPLER progenitor suite' throughout the abstract and conclusions.

minor comments (5)

[Section 4.1, Table 1] The text states that the 40 solar-mass model was carried to about 6000 seconds after bounce, but Table 1 lists a FLASH simulation time of 38,000 seconds for this model; please reconcile these numbers.
[Figure 7, Table 1] The Figure 7 caption says the 19.56 solar-mass model leaves a black hole of about 3.07 solar masses, while Table 1 and the main text give 3.12 solar masses; please make these values consistent.
[Section 4.1, Table 1 footnote] The kick velocities for black hole formers are defined as the momentum at the Fornax-to-FLASH mapping divided by the final central object mass; for Channels 2 and 3 this definition neglects later fallback momentum exchange and may not represent the asymptotic recoil. Please clarify whether the quoted kicks include fallback and, if not, state the resulting uncertainty.
[Section 2] The list of Fornax publications after the first sentence of Section 2 is long and includes many papers not directly used for this work; a shorter citation of the method papers would improve readability.
[Data Availability] The data availability statement says data can be made available upon reasonable request; for a paper making quantitative claims about specific black hole masses and kicks, depositing the relevant simulation outputs or a reduced dataset in a public archive would be preferable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the four-channel taxonomy is a classification of simulation outcomes, not a fitted or self-referential prediction.

full rationale

The paper's central claim is the identification of four black-hole-formation channels from a suite of 3D Fornax simulations. The channel assignments, black-hole masses, explosion energies, kicks, and nickel yields are simulation outputs; they are not tuned to reproduce observed black-hole masses or to force the channel taxonomy. The KEPLER/Sukhbold progenitors and SFHo equation of state are stated inputs, and the paper repeatedly flags the non-convergence of stellar-evolution models and the provisional nature of Channel 4, but those are robustness caveats, not circular reductions. Where prior work by the same group is cited (e.g., Burrows et al. 2023 for the early behavior of the 40-solar-mass model, and Burrows et al. 2024a for compactness trends), those citations supply independently published simulation results or code validation, while the paper also presents new 19.56-solar-mass, 100-solar-mass, and late-time 23-solar-mass runs. The Section 4.4 'island of non-explodability' is supported by the presented 12.25- and 14-solar-mass simulations and is cross-referenced to independent analyses by Couch et al. (2020), Pan et al. (2021), and Sykes & Muller (2024b), so its use does not reduce to a self-citation chain. No equation is defined in terms of the conclusion, and no fitted parameter is relabeled as a prediction. Therefore no circular step is exhibited; the relevant weaknesses are scientific uncertainty and progenitor-model dependence, which the authors explicitly concede.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The paper introduces no fitted parameters in the sense of tuning to observations; all masses, energies, and kicks are simulation outputs. The free parameters listed are numerical or simulation choices: the power-law wind extrapolation for the 23-M_sun model and the inner boundary radii for the FLASH phase. The axioms are the standard physical framework (neutrino-driven explosions, KEPLER progenitor structures, SFHo EOS) plus the post-black-hole boundary-condition modeling. The Channel 4 extrapolation is an ad hoc assumption flagged by the authors. No new entities are postulated.

free parameters (2)

Wind power-law extrapolation for the 23-M_sun post-Fornax boundary condition = not specified (power-law index and amplitude)
The wind boundary condition at 500 km is constructed from the flow witnessed in the Fornax run and extrapolated using a power-law fit (Section 2). This drives the long-term fallback that converts the 23-M_sun model into a ~4.9-M_sun black hole.
Inner boundary radii for the FLASH post-black-hole mapping = 500 km for 23 and 19.56 M_sun, 100 km for 100 M_sun
Numerical choices for the diode inner boundary when continuing with FLASH after black hole formation (Section 2). These radii affect the accretion and fallback solutions and hence the final black hole masses.

assumptions (5)

domain assumption Neutrino-driven convection and turbulence revive the stalled shock in 3D; 1D models generally do not explode.
Section 3 presents this as the standard narrative, relying on prior work (Bethe & Wilson, Janka, Burrows et al.).
domain assumption KEPLER/Sukhbold progenitor models provide representative core structures at collapse, and the Woosley 100-M_sun PPISN model is accurate.
All simulations start from these progenitors (Section 2). The paper concedes stellar evolution models are not converged (Sections 1 and 4.4).
domain assumption SFHo is the correct nuclear equation of state for the collapse and black hole formation physics.
Used for all Fornax runs (Section 2). Final masses and explosion energies depend on the EOS, as the authors note in Section 5.
domain assumption The point-mass plus diode/wind inner boundary conditions in FLASH faithfully capture post-black-hole fallback accretion.
Used to continue simulations after Fornax crashes at black hole formation (Sections 2, 4.1-4.3).
ad hoc to paper The 12.25- and 14-M_sun models, which show no shock revival within 2-3 seconds, would continue to accrete and form black holes over minutes to hours.
Channel 4 relies on extrapolation beyond the simulated time. The authors flag that this may be a matter of resolution (Section 4.4 footnote).

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Cite this review

Pith. "Pith review of Channels of Stellar-mass Black Hole Formation." pith.science (2026). https://pith.science/paper/2XXV7ZBM

@misc{pith2026241207831,
  author       = {Pith},
  title        = {Pith review of: Channels of Stellar-mass Black Hole Formation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2XXV7ZBM}},
  note         = {Machine review of arXiv:2412.07831}
}

abstract

On the basis of a large collection of detailed 3D core-collapse supernova simulations carried to late times, we identify four channels of stellar mass black hole formation. Our examples for Channel 1 involve the formation of lower-gap and above black holes in energetic asymmetric supernova explosions. Our Channel 2 example involves a modest supernova explosion that may leave behind a lower-gap to $\sim$10 $M_{\odot}$ black hole. The latter may not be easily distinguishable from ``standard" supernovae that birth neutron stars. Our Channel 3 example experiences an aborted core-collapse explosion, more often in the context of a low-metallicity progenitor, whose residue is a black hole with a mass perhaps up to $\sim$40 $M_{\odot}$. The latter may be accompanied by a pulsational-pair instability supernova (PPISN). Channel 4 is the only quiescent or ``silent" scenario for which perhaps $\sim$5 to 15 $M_{\odot}$ black holes are left. Where appropriate, we estimate $^{56}$Ni yields, explosion energies, approximate recoil speeds, and residual black hole masses. The progenitor mass density and binding energy profiles at collapse influence the outcome in a systematic way. We speculate that the statistics and prevalence of these various channels depend not only on still evolving supernova theory, but on remaining issues with the theory of massive star evolution, binary interaction, wind mass loss, metallicity, and the nuclear equation of state. Importantly, we suggest, but have not proven, that the silent channel for black hole formation may not be the dominant formation modality.

Figures

Figures reproduced from arXiv: 2412.07831 by the authors.

**Figure 1.** Left: The progenitor mass density profile at collapse for many of our recent 3D CCSN simulations, colored by compactness (ξ1.75) from low (violet) to high (red). The progenitor models were taken from Sukhbold et al. (2016) and Sukhbold et al. (2018). The dotted lines are for those models that formed, or will form, black holes. The others leave neutron stars. Right: The evolution of the gravitational mass of the prot… view at source ↗

**Figure 2.** Left: The mean shock radius versus time after core bounce for a collection of our detailed 3D CCSN models, colored by compactness (ξ1.75). As the compactness increases the time to explosion first increases and then decreases for the highest compactnesses and associated mass accretion rates (M˙ ). The dotted curves indicate those models that eventually form black holes via one of the channels discussed in this paper.… view at source ↗

**Figure 3.** This figure depicts the three dipole components of the spherical harmonic decomposition of the shock radius as a function of time for the 20 M⊙ model. The ∼100 Hz spiral-SASI mode becomes significant at around 0.4 seconds post bounce and lasts for about 0.3 seconds until the model explodes at about 0.7 seconds post bounce (See [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: The power deposition (heating) rate (in Bethes per second) due to neutrino absorption in the gain region between the shock and the inner core as a function of log10 time after bounce for a large collection of our recent 3D CCSN models, colored by compactness (ξ1.75) fr…

**Figure 5.** Figure 5: Snapshots of an x-y slice in entropy space (per baryon per Boltzmann’s constant) of the inner region (±1000 km) of the explosion of the solar-metallicity 19.56-M⊙ progenitor. These stills are taken at 1.0, 2.0, 3.0, and 3.767 seconds after bounce, the latter just befor…

**Figure 6.** Figure 6: Sample snapshots of x-y slices in entropy space (per baryon per Boltzmann’s constant) of the early “Fornax” phase of explosion of the solar-metallicity 19.56-M⊙ model on a much larger scale than [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

**Figure 7.** Figure 7: Entropy (per baryon per Boltzmann’s constant) stills for the 19.56-M⊙ model during the FLASH phase of the simulations. Within ∼1000 seconds after bounce, the majority of the fallback accretion has subsided and ∼one solar mass of material has accreted onto the compact o…

**Figure 8.** Figure 8: Sample snapshots of x-y slices in entropy space (per baryon per Boltzmann’s constant) of the later explosion of the 23-M⊙ solar-metallicity model for six different times after the model was mapped from Fornax (top two) to FLASH (bottom four). Within ∼1000 seconds after…

**Figure 9.** Figure 9: Two x-y slices of the velocity field during the explosion of the 23-M⊙ solar-metallicity model at 7.99 and 20.2 seconds after bounce. The red field depicts the region were the matter at these times have positive radial velocity, while the blue field has negative radial…

**Figure 10.** Figure 10: Sample snapshots of x-y slices in entropy space (per baryon per Boltzmann’s constant) of the early explosion of the tenth-solar-metallicity 100-M⊙ for four different times after bounce. Red is higher entropy and blue is the lower entropy of the progenitor matter into …

**Figure 11.** Figure 11: Sum of the solid-angle-integrated νe and ¯νe neutrino luminosities (in Bethes per second) for a large collection of our recent 3D CCSN simulations versus the log10 of the time after bounce (in seconds). Note that the plots start at 100 milliseconds. The dotted curves …

**Figure 12.** Figure 12: Gravitational wave strain due to matter motions for both + (left) and × (right) polarizations as a function of time after bounce (in seconds) for our BH models, along with those for two representative non-black-hole formers (9.25-and 18.5-M⊙). The increase in strength…

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