Collapsars - Gamma-Ray Bursts and Explosions in "Failed Supernovae"

A. MacFadyen; S. E. Woosley

REVIEW

Collapsars - Gamma-Ray Bursts and Explosions in "Failed Supernovae"

A. MacFadyen, S. E. Woosley

Astrophysics · Submitted 19 Oct 1998 · 2 references

Pith's verdict: The disk half of this paper is solid, cross-validated work; the jet half is a plausibility argument, and the authors are more candid about that than the abstract's numbers suggest.

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arXiv IDastro-ph/9810274 (version 1)

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CitationA. MacFadyen, S. E. Woosley. "Collapsars - Gamma-Ray Bursts and Explosions in "Failed Supernovae"." arXiv:astro-ph/9810274 (1998). https://pith.science/paper/LLFAOPZC

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Editor's note

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Bottom line: this is the paper that turned collapsars from a sketch into a quantitative model, and the disk physics holds up. The jet is a different story, and the authors mostly know it. Read it for the accretion history, not for the 1.5% beaming number. What is genuinely new: this is the first time-dependent two-dimensional follow of the collapse with real stellar initial conditions, resolved accretion shocks, and a realistic equation of state with photodisintegration folded in. Figure 6 is the part I trust most. The simulation matches the Popham-Woosley-Fryer slim-disk solution inside 200 km across density, temperature, scale height, and angular momentum. That is a real cross-check between two independent codes, and it earns them the right to extrapolate their inner boundary with PWF's neutrino tables. The accretion history, 0.07 solar masses per second with 30% fluctuations, and the 50 ms power peak tied to a photodisintegration-driven oscillation of the accretion shock, is the most interesting result in the paper and I do not think it has been adequately followed up. They also flag their own weaknesses plainly: the viscosity-driven wind is artificial, the jet goes superluminal and the run was stopped, neutrino propagation is straight-line. Where the soft spot actually is: the energetics chain. Section 4.1.7 interpolates in PWF tables, and PWF is listed as submitted, not published, while carrying the load-bearing numbers. Table 1 is threshold-like: at a = 0.95 the annihilation efficiency jumps from 0.81% to 8.2% between 0.05 and 0.063 solar masses per second, and the model's mean rate of 0.07 sits inside that transition. A 30% fluctuation moves the deposited energy by an order of magnitude, so the 1 to 14 times 10^51 erg bracket is not a smooth uncertainty, it is closer to a bimodal outcome. One correction to the reader's note, though: the claim that the conservative end sits 20 to 40 times below what Section 5 needs does not survive Table 1. The conservative entry at 0.1 solar masses per second and a = 0.95 is 1.3 times 10^51 erg per second, which is right at the 10^51 erg per second injected. The low integrated number comes from the early low-accretion phase where efficiency collapses. So the injection rate is defensible at late times; the uncomputed quantity is the duty cycle, how much of the 20 seconds actually spends above threshold. That is the number the prediction in abstract:s8 really needs. Who should read it: anyone working on long bursts, stripped-envelope supernovae, or black hole accretion at high rates. It deserves referees, and the disk sections will pass; the jet section needs the relativistic follow-up the authors say is in progress.

Referee report

Significance

This is a substantial and influential contribution. The disk calculation is genuinely cross-validated: Figure 6 shows the 2D equatorial profiles of density, temperature, scale height, angular frequency and specific angular momentum matching the steady-state slim-disk solution of Popham, Woosley & Fryer inside ~200 km, which is a meaningful independent check on both calculations. The parameter survey over alpha and specific angular momentum, the identification of the photodisintegration-driven accretion instability with power near 50 ms (Fig. 15), and the explicit falsifiable prediction linking long GRBs to stripped-envelope supernovae are all strengths. The paper is also candid about its limitations, stating in §5 that the non-relativistic jet calculation became unrealistic and must be redone with relativistic hydrodynamics, and in §4.1.7 that the neutrino treatment needs to be trusted more carefully. Those acknowledged limitations are not the basis of my concerns; the concerns below are about what the abstract claims relative to what was actually computed.

Major objections (4)

[§5 and abstract:s3] The abstract states that 'Simulated deposition of this energy in the polar regions results in strong relativistic outflow,' where 'this energy' is the (1–14)×10^51 erg bracket of abstract:s2. In fact §5 injects energy at a single rate, 5×10^50 erg s^-1 per pole (10^51 erg s^-1 total), and follows it for only 0.83 s. The conservative end of the bracket is far weaker: 0.5×10^51 erg over 20 s is about 2.5×10^49 erg s^-1, roughly 40 times below the rate §5 itself states is required to reverse the polar inflow ('energy deposition 5×10^50 erg s^-1 becomes capable of reversing the inflow'). The manuscript therefore does not demonstrate that the lower part of the quoted bracket produces a jet at all. Either a run at the conservative rate should be presented, or the abstract and §5 should state plainly that only the optimistic deposition rate was shown to drive an outflow.
[§5] The claim of 'strong relativistic outflow' is an extrapolation, not a simulation result. The code is non-relativistic, and the authors state that by 8.42 s 'the calculation had become unrealistic with speeds behind the jet head appreciably superluminal' and was stopped. The relativistic character is inferred from the energy per gram and from the argument that radiation and pair momentum are omitted. This is a reasonable inference, but the abstract should not present it as a computed outcome. Relatedly, the jet was followed only to about 7000 km, roughly 2% of the stellar radius, so the 5–10 s penetration time of abstract:s4 is an estimate (the text says 'we estimate that it will in roughly 5 seconds'), not a result of the calculation.
[§4.1.7 and Table 1] The neutrino luminosity and annihilation efficiency that set the entire energy budget are obtained by logarithmic interpolation in Table 1, which is 'extracted from' Popham, Woosley & Fryer (1998)—listed in the references as 'submitted to ApJ'—and 'amended by additional calculations performed by Popham & Fryer specifically for the collapsar model,' i.e. unpublished private communication. These are load-bearing numbers for the (1–14)×10^51 erg bracket, and a reader cannot reproduce or independently check them from the published literature. The manuscript should document the interpolation procedure and the provenance of the amended entries in enough detail that the bracket can be reconstructed, or the reliance on unpublished companion-paper tables should be stated explicitly where the bracket is quoted.
[§4.1.7, Table 1, §7] Table 1 is strongly threshold-like: at a=0.95 the annihilation efficiency rises from 0.81% at Mdot=0.05 to 8.2% at Mdot=0.0631, and the model's mean accretion rate of 0.07 M_sun s^-1 sits inside this transition. The paper acknowledges in §7 that the disk is 'poised on the knife edge of advective dominated and neutrino dominated.' The consequence is that the quoted bracket is not a smooth uncertainty but closer to a bimodal outcome: a 30% accretion fluctuation, which Fig. 11 shows is common, moves the deposited energy by roughly an order of magnitude. This bifurcation should be stated explicitly, and its implication—that whether a jet forms at all may be an all-or-nothing function of the accretion history—should be discussed rather than folded into a single multiplicative range.

Minor objections (8)

[Abstract vs §4.1.7] The abstract quotes a lower bound of 1×10^51 erg, but §4.1.7 states that 'for the most conservative case of an initially non-rotating black hole and restricted neutrino transport, the energy fell to 0.5×10^51 erg.' These two numbers should be reconciled.
[Abstract and §5] The beaming fraction of 'about 1.5% of the sky' should be tied explicitly to the quoted opening angle. A 10-degree half-angle corresponds to roughly 0.8% of 4π, so the reader needs the angle that yields 1.5%.
[Figure 6 caption vs text] The Figure 6 caption gives t=7.39 s while the surrounding text (§4.1.2) discusses 7.598 s and 7.60 s. The times quoted for the same comparison should be made consistent.
[§4.1.5] The plume energy is stated to differ by about a factor of two depending on whether nu = alpha c_s r or nu = alpha c_s H is adopted. Since the plumes are offered as a supernova-energy channel, the choice of prescription and its justification should be stated more prominently than a parenthetical remark.
[§3 and §4.1.5] The 9-isotope network was turned off and only photodisintegration to free nucleons was followed, so the 56Ni yields invoked for the supernova channel are inferred from NSE freeze-out rather than computed. This should be flagged where the 56Ni-powered light curve of SN 1998bw is discussed.
[§6.1.2] Two precession expressions are quoted (Hartle et al. and Larwood) that give periods differing by roughly a factor of five for the stated disk parameters. The text should say which is adopted for the claimed ~0.2–1 s precession period and why.
[References] The text cites 'Aloy et al. 1999' in §5 while the reference list gives 'Aloy, M. A., et al. 1998.' The year should be made consistent.
[Throughout] There are typographical errors that should be corrected, including 'F AILED SUPERNOV AE' in the title, 'coalligned' (§6.1.2), 'duarion' (§6.3), 'patern' (Fig. 14 caption), and 'experimented' (§4.3).

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The paper

The paper claims

A massive star that collapses straight to a black hole can fire a jet clean through itself and make both a long gamma-ray burst and a supernova.

The reading

Some massive stars may skip the usual supernova bounce: the iron core keeps collapsing and quietly becomes a black hole. This paper asks what happens next if the star was rotating, and argues the answer is a gamma-ray burst. Using a two-dimensional hydrodynamics code, the authors follow a $14$ solar mass helium core for twenty seconds after the black hole forms and find a compact accretion disk feeding the hole at about $0.07$ solar masses per second, while the polar directions drain almost unimpeded and leave a low-density channel along the rotation axis. They then deposit energy in that channel at a rate comparable to what neutrino annihilation in the disk should supply, and a tightly collimated outflow punches out through the star in $5$ to $10$ seconds. If this is right, long bursts and stripped-envelope supernovae are two views of one event, and short hard bursts must come from somewhere else.

What carries the argument

The load-bearing mechanism is the collapsar itself: the combination of a failed core-collapse, a neutrino-cooled alpha-viscosity accretion disk, and the density contrast between equator and pole. Three pieces of machinery carry the argument. First, the Shakura-Sunyaev viscosity prescription, with $H$ the density scale height and $c_s$ the sound speed, is implemented as a full stress tensor so the disk can transport angular momentum and dissipate heat; the authors compare an $0.1$ case against a low-viscosity case whose effective numerical alpha is about $0.001$. Second, photodisintegration of helium and heavier nuclei into free nucleons is folded into the equation of state, which sets the disk thickness, the temperature, and hence the neutrino loss rate. Third, the neutrino luminosity and the efficiency of neutrino annihilation are not computed on the grid but interpolated from the steady-state slim-disk tables of a companion paper, as functions of accretion rate and Kerr parameter at a fixed $3$ solar mass hole; that interpolation is what turns the accretion history into the polar energy deposition that drives the jet.

Extended reading notes

Core claim

The paper's central claim is that a rotating massive helium star whose core collapse fails to produce a shock, and instead forms a black hole of $2$ to $3$ solar masses, is not a failure but a collapsar: an engine that produces both a supernova-like explosion and a gamma-ray burst. The argument runs in stages. Infall along the rotation axis is initially unimpeded, so an evacuated hourglass channel opens within a few seconds while equatorial matter piles up in a centrifugally supported disk at a few hundred kilometres. That disk accretes at a sustained, strongly time-variable rate of roughly $0.07$ solar masses per second for at least $15$ seconds and spins the hole up to a Kerr parameter near $0.9$. Energy deposited along the axis, whether by neutrino annihilation or by magnetic processes in the disk, drives a jet collimated to about $10$ degrees half-angle that displaces the overlying star and breaks out in $5$ to $10$ seconds; only after breakout can highly relativistic flow begin. The authors state the observational consequence bluntly: while only a small fraction of supernovae make gamma-ray bursts, all bursts longer than a few seconds should make supernovae like SN 1998bw, and hard, energetic bursts shorter than a few seconds are difficult to make this way.

Load-bearing premise

The energy that drives the jet is not calculated self-consistently: the neutrino luminosity and annihilation efficiency are read off sparse steady-state tables from a companion paper assuming a fixed three solar mass hole and straight-line neutrino paths, and the jet is then switched on by hand at a chosen rate of $5$ times $10^{50}$ erg per second per pole, so if the true efficiency sits near the conservative end of the quoted bracket the polar inflow is never reversed and no jet forms.

Editorial extensions

If this is right

Every gamma-ray burst longer than a few seconds should be accompanied by a supernova spectroscopically similar to SN 1998bw, although for distant bright bursts the afterglow from jet deceleration may outshine it.
Short, hard bursts with durations near $0.3$ seconds cannot be produced by this engine and require a different progenitor, most plausibly merging neutron stars or a neutron star and a black hole.
The enormous spread between GRB 971214 and GRB 980425 reflects mostly how much energy was beamed toward the observer, not a comparably large difference in the total energy released.
Hard X-ray precursors are expected as the jet first breaks out of the stellar surface, arriving ahead of the main burst by roughly ten seconds at a radius of $3\times10^{15}$ cm.
Collapsars should trace star formation, may be favoured at low metallicity where massive helium cores and rapid rotation survive, and should occur at roughly a per-cent of the supernova rate.

Reading between the lines

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

Because the burst is beamed into about $1.5$ per cent of the sky, the model predicts a much larger population of off-axis collapsars visible as broad-lined Type Ic supernovae with weak or absent gamma-rays; finding those without a burst would be strong independent support.
The accretion rate sits deliberately near the boundary between advection-dominated and neutrino-cooled disks, so small changes in progenitor mass, angular momentum, or viscosity could shut the jet off while leaving the disk-driven supernova intact. That is a natural route to supernovae without bursts, and it makes the burst rate a steep function of progenitor properties.
The reported power at $50$ milliseconds and its overtone in the accretion history suggests a testable discriminant: time structure in a burst light curve on that scale would have to come from the engine, whereas structure on much shorter scales must come from shocks or circumstellar interaction.
The jet's energy is quoted as a bracket spanning roughly a factor of thirty. A single well-observed long burst with an independently estimated beaming-corrected energy at the low end of that bracket would strain the neutrino-annihilation channel and push the model toward magnetic extraction from the spinning hole.

Original abstract

Using a two-dimensional hydrodynamics code (PROMETHEUS), we study the continued evolution of rotating massive helium stars whose iron core collapse does not produce a successful outgoing shock, but instead forms a black hole. We study the formation of a disk, the associated flow patterns, and the accretion rate for disk viscosity parameter, alpha ~ 0.001 and 0.1. For the standard 14 solar mass model the average accretion rate for 15 s is 0.07 solar masses per second and the total energy deposited along the rotational axes by neutrino annihilation is (1 - 14) x 10**51 erg, depending upon the evolution of the Kerr parameter and uncertain neutrino efficiencies. Simulated deposition of this energy in the polar regions results in strong relativistic outflow - jets beamed to about 1.5% of the sky. The jets remain highly focused, and are capable of penetrating the star in 5 - 10 s. After the jet breaks through the surface of the star, highly relativistic flow can commence. Because of the sensitivity of the mass ejection and jets to accretion rate, angular momentum, and disk viscosity, and the variation of observational consequences with viewing angle, a large range of outcomes is possible ranging from bright GRBs like GRB 971214 to faint GRB-supernovae like SN 1998bw. X-ray precursors are also possible as the jet first breaks out of the star. While only a small fraction of supernovae make GRBs, we predict that all GRBs longer than a few seconds will make supernovae similar to SN 1998bw. However, hard, energetic GRBs shorter than a few seconds will be difficult to make in this model.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,841 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.90 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.20 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Using a two-dimensional hydrodynamics code (PROMETHEUS), we study the continued evolution of rotating massive helium stars whose iron core collapse does not produce a successful outgoing shock, but instead forms a black hole. We study the formation of a disk, the associated flow patterns, and the accretion rate for disk viscosity parameter, alpha ~ 0.001 and 0.1. For the standard 14 solar mass model the average accretion rate for 15 s is 0.07 solar masses per second and the total energy deposited along the rotational axes by neutrino annihilation is (1 - 14) x 10**51 erg, depending upon the evolution of the Kerr parameter and uncertain neutrino efficiencies. Simulated deposition of this energy in the polar regions results in strong relativistic outflow - jets beamed to about 1.5% of the sky. The jets remain highly focused, and are capable of penetrating the star in 5 - 10 s. After the jet breaks through the surface of the star, highly relativistic flow can commence. Because of the sensitivity of the mass ejection and jets to accretion rate, angular momentum, and disk viscosity, and the variation of observational consequences with viewing angle, a large range of outcomes is possible ranging from bright GRBs like GRB 971214 to faint GRB-supernovae like SN 1998bw. X-ray precursors are also possible as the jet first breaks out of the star. While only a small fraction of supernovae make GRBs, we predict that all GRBs longer than a few seconds will make supernovae similar to SN 1998bw. However, hard, energetic GRBs shorter than a few seconds will be difficult to make in this model.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Using a two-dimensional hydrodynamics code (PROMETHEUS), we study the continued evolution of rotating massive helium stars whose iron core collapse does not produce a successful outgoing shock, but instead forms a black hole.	contribution 0.58	0.95	0.07	asserted 0.97
s1	We study the formation of a disk, the associated flow patterns, and the accretion rate for disk viscosity parameter, alpha ~ 0.001 and 0.1.	contribution 0.78	0.93	0.02	asserted 0.74
s2	For the standard 14 solar mass model the average accretion rate for 15 s is 0.07 solar masses per second and the total energy deposited along the rotational axes by neutrino annihilation is (1 - 14) x 10**51 erg, depending upon the evolution of the Kerr parameter and uncertain neutrino efficiencies.	result 1.00	0.93	0.07	asserted 0.96
s3	Simulated deposition of this energy in the polar regions results in strong relativistic outflow - jets beamed to about 1.5% of the sky.	result 1.00	0.91	0.10	asserted 1.00
s4	The jets remain highly focused, and are capable of penetrating the star in 5 - 10 s.	result 1.00	0.89	0.06	asserted 0.91
s5	After the jet breaks through the surface of the star, highly relativistic flow can commence.	result 0.97	0.59	0.05	asserted 0.53
s6	Because of the sensitivity of the mass ejection and jets to accretion rate, angular momentum, and disk viscosity, and the variation of observational consequences with viewing angle, a large range of outcomes is possible ranging from bright GRBs like GRB 971214 to faint GRB-supernovae like SN 1998bw.	interpretation 0.84	0.47	0.23	hedged possibility 0.94
s7	X-ray precursors are also possible as the jet first breaks out of the star.	result 0.78	0.54	0.04	hedged possibility 1.00
s8	While only a small fraction of supernovae make GRBs, we predict that all GRBs longer than a few seconds will make supernovae similar to SN 1998bw.	interpretation 0.90	0.64	0.59	asserted 0.86
s9	However, hard, energetic GRBs shorter than a few seconds will be difficult to make in this model.	limitation 0.76	0.57	0.13	hedged possibility 0.54

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** — Angular momentum (j) distribution in a 20 M⊙ star evolved from an initially rigidly rotating main sequence star with equatorial velocity 200 km s−1 by Heger, Langer, & Woosley (1998). The solid line gives j on the main sequence; the dotted line is at hydrogen depletion; the dashed line, at helium depletion; and the dash-dotted line is the presupernova star. A decrease of the total stellar mass by mass loss during hydrogen and helium burning is apparent. The distribution of j in the presupernova star shows sharp decreases at the outer edges of convective shells and the helium core…

**Figure 2.** — Density, radial velocity, specific angular momentum, and enc

**Figure 3.** — The velocity field in Model 14A at 0.751 s showing early disc forma

**Figure 4.** — The velocity field at 0.751 s color coded by composition. The colo

**Figure 5.** — The mass accretion rate as a function of radius within 45 degr

**Figure 6.** — The simulation (crosses; density, temperature, radial velo

**Figure 7.** — The ratio of centrifugal force to gravity in Model 14A at a tim

**Figure 8.** — The density in the central regions of Model 14A 7.60 seconds

**Figure 9.** — A larger view of the density structure in Model 14A at a later t

**Figure 10.** — The radial Mach number, Mr, at 7.60 seconds in the standard run, Model 14A, This figure highlights regions of supersonic flow and the location of shocks, especially the one at the edge of the accretion disk at 350 km. The yellow arrows near the equator represent the gas which feeds the disc (the tan toiroidal region interior to 350 km). The red arrows indicate outflow due to centrifugal bounce and viscous heating

**Figure 11.** — Top panel: Mass accretion rate in Model 14A for the entire 2

**Figure 12.** — Mass accretion rate as a function of angle during the episod

**Figure 13.** — On a smaller scale the surface mass density (Σ, top panel) an

**Figure 14.** — The mass flux field, ρ times v at the same times as

**Figure 15.** — Fourier power spectrum of the accretion rate shown in Fig.

**Figure 16.** — Flow patterns in Model 14A at 9.48 s on a larger scale (50000 k

**Figure 17.** — Origin of the viscosity driven “wind” shown in Fig. 16. Regions o

**Figure 18.** — Upper panel: The total outward directed kinetic energy in t

**Figure 19.** — The hole mass and normalized Kerr parameter grow rapidly in t

**Figure 20.** — Energy deposition rate due to neutrino annihilation in the pola

**Figure 21.** — Time integrated neutrino annihilation energy. The top panel

**Figure 22.** — Density structure at 7.52 s in the low viscosity run, Model 14

**Figure 23.** — Despite its low viscosity, the accretion rate in Model 14B is ab

**Figure 24.** — Velocity vectors show the onset of a mild explosion produced

**Figure 25.** — Velocities in the equatorial plane for two runs that did (uppe

**Figure 26.** — Density, temperature, internal energy per gram, and pr

**Figure 27.** — Energy density in the jet and surrounding area 0.824 s afte

Figures reproduced from arXiv:astro-ph/9810274 by the authors.

References

Works cited (2)

[11]

The integrated accretion rate is given between the equator an d 22.5 degrees (dashed line); 45 degrees (solid line); and 90 degrees (dash-dotted line). Mo st of the accretion is through the disk and not from the polar accretion column. – 52 – Fig. 13.— On a smaller scale the surface mass density (Σ, top panel) an d radial velocity in the equatorial plane ...

View on Pith
[16]

grows with time. After 8 sec, material begins to leave the compu tational grid, but a total energy of 2 - 3 ×1051 erg is estimated to have been generated in 20 sec. Lower panel: Total energy dissipated in the disk exterior to 50 km integrated ove r time. A much larger amount of energy is dissipated interior to 50 km but is not included her e. The energy i...

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Gamma-Ray Bursts and Optical Brightness: Insights from Swift Satellite
astro-ph.HE 2026-09 conditional novelty 4.0 of 10

Survival analysis of Swift UVOT V-band data, including censored optical limits, finds no statistically significant association between gamma-ray burst properties and optical brightness.
Earliest simultaneous multi-color optical observations of GRB 230328B: from 41 seconds to the host-galaxy identification
astro-ph.HE 2026-06 unverdicted novelty 4.0 of 10

New early multi-wavelength data on GRB 230328B shows afterglow with early bump and late achromatic rebrightening at ~4000 s, modeled via MCMC as forward shock plus late energy injection in a dusty S0 host with AV~0.8 ...
On the Duration of Gamma-Ray Bursts
astro-ph.HE 2024-12 conditional novelty 4.0 of 10

GRB duration is shaped by the progenitor, the central engine, the emitter, and geometry, so short versus long duration is not a reliable direct indicator of what exploded or merged.
Short-duration gamma-ray bursts from Kerr-Newman black hole mergers
astro-ph.HE 2024-11 reject novelty 4.0 of 10

A Kerr-Newman black hole produced by a binary black hole merger, with a magnetized disk, can power a short gamma-ray burst via the Blandford-Znajek mechanism, and the model is applied to GW150914.
Constraining GRBs pseudo-redshift using different empirical correlations
astro-ph.HE 2019-09 conditional novelty 4.0 of 10

Using the Amati and the Guiriec luminosity-peak energy correlations on six Fermi bursts, the authors find consistent pseudo-redshifts for three bright bursts with known redshifts, but the two correlations differ by up...
Explosion Mechanisms of Core-Collapse Supernovae
astro-ph.SR 2012-06 accept novelty 3.0 of 10

Neutrino heating plus nonradial flows explains ordinary core-collapse supernovae but likely not hypernovae, which appear to need magnetorotational driving.
Correlation between X-ray and gamma data of Swift measurements
astro-ph.HE 2026-09 accept novelty 2.0 of 10

A larger-sample canonical correlation analysis confirms the strong link between gamma-ray fluence and early X-ray flux and finds a significant contribution from the HI column density.
GRB 250424A: A Case Study of Energy Injection with Multiwavelength Observations
astro-ph.HE 2026-06 unverdicted novelty 2.0 of 10

GRB 250424A afterglow shows simultaneous shallow decay in X-ray and optical bands modeled as continuous energy injection (q≈0.34) into a forward shock in constant-density medium, with E_K,iso ≈5.5×10^52 erg and no cle...
Interstellar dust production, destruction and effects of dust depletion in galaxies
astro-ph.GA 2025-06 unverdicted novelty 2.0 of 10

The paper reviews dust production, destruction and growth processes in galaxies, compiles literature data on comoving dust mass density, presents evidence for and against interstellar dust growth, and identifies the h...
Supernova nucleosynthesis: a review
astro-ph.HE 2026-09 unverdicted

A comprehensive review of supernova nucleosynthesis covering Type Ia, core-collapse, electron-capture, and pair-instability supernovae.
Gamma-ray bursts: what do we know today that we did not know 10 years ago?
astro-ph.HE 2024-12 unverdicted

A review of the past decade of gamma-ray burst research, highlighting structured jets, GR-MHD simulations, TeV detections, and the contested idea that many GRBs have moderate Lorentz factors.

How later papers used it

364 later papers cite it

Evidence: substantial. 361 of the citing papers share no author with it, and 9 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 476 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 1 used its method or tool and 1 used its data or values.

Uses its method or tool 1 of 2 papers with this label

Suppressed viscous heating and angular momentum transport in regions of mostly radial infall following a similar prescription from this paper.

Collapsar disk outflows I: Viscous hydrodynamic evolution in axisymmetry (2024) · 0.96 · paraphrased: the licence does not allow quoting

Uses its data or values 1 of 3 papers with this label

Used this paper's density of the baryonic accretion disk in the collapsar model of about 10^6±2 g/cm^3 as a comparison for the gas density.

Supersymmetric Partially Interacting Dark Matter (2014) · 0.96 · paraphrased: the licence does not allow quoting

How the literature uses it

90 arXiv papers cite this in 128 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 60 sentences without a confident label

Uses its method or tool 1 paper

To avoid numerical problems in regions of mostly radial infall, viscous heating and angular momentum transport are suppressed as $e^-|𝐯|/v_ϕ$ for $|𝐯| > v_ϕ≡j/(rsinθ)$, following a similar prescription from [ref] .

Collapsar disk outflows I: Viscous hydrodynamic evolution in axisymmetry · Evolution after BH formation · 0.96

Uses its data or values 2 papers

Unless noted otherwise, we take $Ṁ=0.02 M_⊙/s$ [ref] and $v_ej=0.05c$ [ref] .

Signature of Collapsars as Sources for High-energy Neutrinos and $r$-process Nuclei · Antineutrinos from $β$-decay · 1.00
In order for the density of the gas to be comparable to the density of the baryonic accretion disk in the collapsar model ($∼10^6±2 g/cm^3$ [ref] ) the Jeans mass of the gas must be[The Wolf-Rayet stars in Mrk 996 are $∼4.5$ Myr old ($z∼10^-4$) [ref] , therefore the relevant interacting dark matter temperature is that of the dark photon bath approximately today since the interacting dark matter is still coupled with the dark photon bath.] [equation]

Supersymmetric Partially Interacting Dark Matter · Gamma Ray Burst Phenomenology · 0.96

Compares with it 1 paper

For a simple comparison, it is much smaller than the values given for the initial radius in classic GRB literature [ref] , the values often chosen in simulations of GRBs [ref] , and those previously used in setting limits on Beyond-Standard-Model particles [ref] .

Reappraisal of the Constraints on Heavy Axion-like Particles from Gamma-Ray Bursts · Initial Launch Radius · 0.81

Cites it as support 4 papers

Meanwhile, the clear presence of a plateau in the higher redshift sample aligns with the expectation that collapsar progenitors of GRBs favor lower metallicity environments [ref] .

The GRB Intrinsic Duration Distribution: Progenitor Insights Across Cosmic Time · On the Plateau in the Redshift Separated Sub-samples · 0.96
Additionally, we considered the effect of a metallicity ceiling for progenitor stars; such a limit is motivated by GRB collapsar models which require mass loss over the progenitor Wolf Rayet stellar lifetime to be small [ref] .

The nature of HI absorbers in GRB afterglows: clues from hydrodynamic simulations · Sightline Generation · 0.97
This inference appears to be confirmed by numerical simulations, for NS-NS or NS-BH mergers [ref] as well as for collapsar models [ref] .

Gamma Ray Bursts and their links with Supernovae and Cosmology · Progenitors and Supernova Connection · 1.00

Cites it as background 57 papers

We will assume that the collapsar model [ref] , whereby the iron core of a progenitor star collapses into a black hole, describes some of the observed long gamma ray bursts and is followed by jet emission which is powered by the Blandford-Znajeck (BZ) mechanism [ref] .

Implications Of A Dark Sector U(1) For Gamma Ray Bursts · Introduction · 0.87
Collapsars, the collapse of rapidly rotating massive stars into black holes accompanied by energetic disk outflows, represent a potential prompt channel [ref] .

Distinct First-to-Second Peak Yield Ratios and Timescales Reveal a Sub-dominant Prompt Channel · Introduction · 0.91
The Collapsar model [ref] predicts that long-duration, soft spectrum, gamma-ray bursts (GRBs) would be accompanied by a supernova (SN) explosion.

From Gamma-Ray Bursts/Hypernovae To Black-Hole Binaries · Introduction · 0.89

Discussion

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[1] [11]

The integrated accretion rate is given between the equator an d 22.5 degrees (dashed line); 45 degrees (solid line); and 90 degrees (dash-dotted line). Mo st of the accretion is through the disk and not from the polar accretion column. – 52 – Fig. 13.— On a smaller scale the surface mass density (Σ, top panel) an d radial velocity in the equatorial plane ...

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[2] [16]

grows with time. After 8 sec, material begins to leave the compu tational grid, but a total energy of 2 - 3 ×1051 erg is estimated to have been generated in 20 sec. Lower panel: Total energy dissipated in the disk exterior to 50 km integrated ove r time. A much larger amount of energy is dissipated interior to 50 km but is not included her e. The energy i...

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