A Unified Picture of Short and Long Gamma-Ray Bursts from Compact Binary Mergers

The recent detections of the ∼10 s long γ-ray bursts (GRBs) 211211A and 230307A followed by softer temporally extended emission (EE) and kilonovae point to a new GRB class. Using state-of-the-art first-principles simulations, we introduce a unifying theoretical framework that connects binary neutron star (BNS) and black hole–NS (BH–NS) merger populations with the fundamental physics governing compact binary GRBs (cbGRBs). For binaries with large total masses, M tot ≳ 2.8 M ⊙, the compact remnant created by the merger promptly collapses into a BH surrounded by an accretion disk. The duration of the pre-magnetically arrested disk (MAD) phase sets the duration of the roughly constant power cbGRB and could be influenced by the disk mass, M d . We show that massive disks (M d ≳ 0.1 M ⊙), which form for large binary mass ratios q ≳ 1.2 in BNS or q ≲ 3 in BH–NS mergers, inevitably produce 211211A-like long cbGRBs. Once the disk becomes MAD, the jet power drops with the mass accretion rate as Ṁ∼t−2 , establishing the EE decay. Two scenarios are plausible for short cbGRBs. They can be powered by BHs with less massive disks, which form for other q values. Alternatively, for binaries with M tot ≲ 2.8 M ⊙, mergers should go through a hypermassive NS (HMNS) phase, as inferred for GW170817. Magnetized outflows from such HMNSs, which typically live for ≲1 s, offer an alternative progenitor for short cbGRBs. The first scenario is challenged by the bimodal GRB duration distribution and the fact that the Galactic BNS population peaks at sufficiently low masses that most mergers should go through an HMNS phase.


INTRODUCTION
Gamma-ray bursts (GRBs) can originate from at least two distinct astrophysical systems: the collapse of massive rotating stars ("collapsars"; Woosley 1993;MacFadyen & Woosley 1999) and compact binary mergers (Eichler et al. 1989;Paczynski 1991).These two event classes are commonly associated with long GRBs (lGRBs) and short GRBs (sGRBs), respectively.Their durations follow log-normal distributions, with mean values of ∼ 30 s for lGRBs and ∼ 0.5 s for sGRBs (Kouveliotou et al. 1993;McBreen et al. 1994).The overlap of the two distributions poses a challenge to a clear distinction between the classes (Bromberg et al. 2013), particularly for bursts lasting between ∼ 1 s and ∼ 30 s (Nakar 2007).A more accurate burst classification can be obtained when the GRB is followed by optical emission from the astrophysical site: supernova Ic-BL (Galama et al. 1998;Hjorth et al. 2003) or kilonova from a compact object merger (Li & Paczyński 1998;Metzger et al. 2010; ogottlieb@flatironinstitute.orgTanvir et al. 2013).Being the most luminous events in the sky, GRBs are detected out to large distances, and in part because of their bright synchrotron afterglows, are infrequently accompanied by detectable thermal optical counterparts.
The recent detection of optical/infrared kilonova signals following two ∼ 10 s-long bursts in GRB 211211A (Rastinejad et al. 2022;Troja et al. 2022;Yang et al. 2022) and GRB 230307A (Levan et al. 2023a;Sun et al. 2023;Yang et al. 2023) has reignited interest in the origin of long-duration GRBs that are not associated with collapsars (see also Gal-Yam et al. 2006;Della Valle et al. 2006;Bromberg et al. 2013;Lü et al. 2022;Levan et al. 2023b), but likely originating from compact binary mergers (cbGRBs).Such long durations would at least naively be unexpected in binary mergers insofar that the accretion timescales responsible for the jet launching are expected to be of order of seconds (e.g., Narayan et al. 1992).The long-duration cbGRB (lbGRBs) events may constitute a third type of GRB population.Indeed, a closer examination of the GRB duration distribution reveals that it is best fit with three log-normal distributions (Horváth & Tóth 2016;Tarnopolski 2016).These distribu-tions potentially correspond to three distinct populations: (i) collapsar lGRBs with T 90 ≳ 30 s, (ii) short-duration cbGRBs (sbGRBs) from binary mergers with T 90 ≲ 1 s, and (iii) lb-GRBs 211211A and GRB 230307A-like events from binary mergers, lasting T 90 ∼ 10 s.Below we adhere to the conventional assumption that sbGRBs are more common than lbGRBs (Yin et al. 2023).However, we note that three lognormal distribution fits suggest otherwise (Horváth & Tóth 2016), so we do not consider the rates to be a stringent constraint.
It is tempting to associate the two cbGRB classes with the two types of compact binary mergers: black hole (BH) and neutron star (NS), and binary NS (BNS) systems.Based on the two BH-NS mergers detected during the LVK O3b run, the BH-NS merger rate was constrained to be R BHNS = 45 +75 −33 Gpc −3 yr −1 if these two events are representative of the entire population, versus R BHNS = 130 +112 −69 Gpc −3 yr −1 for a broader BH-NS population (Abbott et al. 2020).In comparison, the rate of BNS mergers was found to be R BNS = 320 +490 −240 Gpc −3 yr −1 (Abbott et al. 2021).Therefore, if the two detected BH-NS events are representative, BH-NS mergers are likely to be significantly rarer than BNS mergers, similar to the scarcity of lbGRBs compared to sbGRBs.In the case of a broader BH-NS population, other merger properties such as larger mass ratios, significant spin-orbital misalignment, and low BH spins need to be considered (Belczynski et al. 2008), all of which would result in less massive disks and the associated challenges in launching a relativistic jet (e.g., Kyutoku et al. 2015).Regardless of the BH-NS merger rate, the fraction of this population that yields electromagnetic emission is thus likely to be negligible compared to BNS mergers (Fragione 2021;Sarin et al. 2022;Biscoveanu et al. 2023).
The main cbGRB emission phase is often accompanied by additional light curve components.For example, in lb-GRB 211211A, the variable hard burst that lasted ∼ 10 s was preceded by an oscillating precursor flare (Xiao et al. 2022), and followed by a smoother and softer γ/X-ray emission for ∼ 100 s (Gompertz et al. 2023), referred to as the "extended emission" (EE; Norris & Bonnell 2006;Perley et al. 2009).The prolonged EE, which is more commonly seen in association with lbGRBs (Norris et al. 2011;Kaneko et al. 2015), accompanies the main signal in ∼ 25% − 75% of cbGRBs (Norris & Gehrels 2008;Norris et al. 2010;Kisaka et al. 2017).It is generally characterized by two components: an initial roughly flat "hump" (Mangano et al. 2007;Perley et al. 2009), followed by a power-law decay ∼ t −2 (Giblin et al. 2002;Kaneko et al. 2015;Lien et al. 2016).Any cbGRB model linked to the underlying physics of binary mergers must therefore explain the entire emission signal, including precursor flares and EE phases.
In this paper, we review recent first-principles simulations, and how they constrain the origins of the different types and phases of cbGRB light curves.In particular, we present a framework for connecting the binary merger population with the entire spectrum of cbGRB observations.The paper is structured as follows.In §2 we argue that while lGRB jets are powered by magnetically arrested disks (MADs), BHpowered cbGRB jets are generated before the disk enters a MAD state.In §3 we show that the formation of a massive disk ( M d ≈ 0.1 M ⊙ ) around the post-merger BH inevitably powers lbGRBs such as GRB 211211A.In §4 we present two self-consistent models as the origin of sbGRBs: promptcollapse BHs forming low-mass disks and hypermassive NSs (HMNSs); we describe why we favor these two scenarios over alternatives, such as delayed-collapse BHs, supramassive NSs (SMNSs), white dwarf (WD) mergers/accretion induced collapse (AIC), and neutrino-driven jets.In §5 we discuss the origin of the precursor and EE of cbGRBs, compare the models with observables, and deduce that sbGRBs are likely powered by HMNSs, whereas lbGRBs are powered by BHs with massive disks.We summarize and conclude in §6.

COLLAPSAR GRBS VS. CBGRBS: TO BE MAD OR
NOT TO BE MAD Long GRBs and cbGRBs take place in very different astrophysical environments, leading to distinct conditions for their occurrence and potentially differing central engines that drive these events.A recent study by Gottlieb et al. (2023a) demonstrated that lGRB jets are launched from BHs once the accretion disk becomes MAD.The reason for this is that a successful jet launching requires the Alfvén velocity to surpass the free-fall velocity of the inflowing gas, allowing magnetohydrodynamic waves to escape from the BH ergosphere and form the emerging jet (Komissarov & Barkov 2009).In other words, a sufficiently powerful magnetic flux empowers a BH to launch jets in defiance of the inward motion of the surrounding stellar envelope.Numerical simulations (Gottlieb et al. 2022a) have confirmed that this process is sustained once the disk becomes MAD, occurring when the dimensionless magnetic flux on the BH reaches a threshold of ϕ ≡ Φ( Ṁr2 g c) −1/2 ≈ 50, where r g is the BH gravitational radius, Φ is the dimensional magnetic flux, and Ṁ is the mass accretion rate (e.g., Tchekhovskoy 2015).The BZ-jet power is determined by (Blandford & Znajek 1977;Tchekhovskoy et al. 2011): where r H is the radius of the BH horizon, and f (a) is the functional dependency on the BH spin.This relation can also be expressed in terms of the dimensionless magnetic flux ϕ: where the jet launching efficiencies are defined as: where η a is the maximum efficiency for a given BH spin calibrated by Lowell et al. (2023).In a MAD state η ϕ = 1, and thus Eq. ( 2) shows that the jet launching efficiency depends only on a.This implies that the lGRB timescale is governed either by the BH spin-down timescale, ȧ (Jacquemin-Ide et al. 2023), or by the accretion timescale (e.g., Gottlieb et al. 2022a).
In contrast to collapsars, where the newly-formed BH is embedded in a dense massive stellar core, binary mergers take place in a considerably less dense environment surrounding the central engine.Consequently, jets can emerge well before the disk reaches a MAD state at T MAD .Numerical simulations incorporating self-consistent models of binary mergers, capable of launching these jets, have verified this expectation (e.g., Hayashi et al. 2022Hayashi et al. , 2023)).These simulations show that the compactness of the post-merger disk allows for the dimensional magnetic flux to rapidly accumulate on the BH 1 , resulting in a constant jet power, P j (t < T MAD ) ∼ Φ ∼ const (Eq.( 1)).Due to the decaying mass accretion rate, the dynamical importance of the magnetic field (as measured by the dimensionless magnetic flux ϕ ∝ Φ Ṁ−1/2 ) grows with time.Once ϕ ≈ 50 is reached, the disk enters a MAD state, which saturates the jet launching efficiency η ϕ ≈ 1.Thereafter, the jet power follows the declining mass accretion rate, P j (t > T MAD ) ∝ Ṁ following Eq.(2).
Unlike collapsars, the disks formed from binary mergers do not have an external supply, resulting in their steady depletion and a continuous decrease in the BH mass accretion rate.In fact, at t ≳ 0.1 s, the mass accretion rate Ṁ follows a single power-law decay without a characteristic timescale relevant to cbGRBs (which in the collapsar case is set by the structure of the progenitor star).This implies that, in contrast to lGRBs where jet launching persists during the MAD phase of the disk and its timescale is set by Ṁ or ȧ, in mergers 2 it is the MAD transition at T MAD (dictated by M d and Φ) that eventually causes the jet power to decay, thus setting the cbGRB duration, as we now describe.
3. LBGRBS FROM BHS WITH MASSIVE DISKS Gottlieb et al. (2023b) presented first-principles simulations of a BH-NS merger with mass ratio q = 2, which results in a rapidly spinning BH with a ≃ 0.86.A substantial accretion disk of mass M d ≈ 0.15 M ⊙ formed around the BH, resulting in a high initial accretion rate Ṁ ∼ M ⊙ s −1 .We find a similar outcome here for simulations of a BNS merger of component masses 1.06 M ⊙ and 1.78 M ⊙ , initialized from the endpoint of the merger simulations of Foucart et al. (2023).In that system, the remnant promptly collapses to a BH with a = 0.68, surrounded by a disk with M d ≈ 0.1 M ⊙ (see Appendix §A for the full numerical results of the BNS merger simulations).
Eq. (2) shows that the jet power depends on both the mass accretion rate and the magnetic flux on the BH, Φ. Binary compact mergers produce small accretion disks that promptly feed the available magnetic flux onto the BH3 .Because Φ hardly changes thereafter during the subsequent accretion phase, this results in a constant jet power P j ∼ const with a magnitude that depends on the disk's poloidal field strength.This is demonstrated in Figure 1, which depicts the jet power as a function of time for different values of Φ and If the initial plasma beta in the disk is low (leading to large Φ), then the jet launching efficiency is high, and the jet starts with too much power compared to sbGRB luminosities.In such cases, the dimensionless magnetic flux on the BH quickly saturates and the disk becomes MAD, ending the  (Gottlieb et al. 2023b) and the 5 BNS merger simulations presented here, all of which generate massive disks M d ≈ 0.1 M ⊙ .The purple line delineates the logarithmic average of these mass accretion rates, which constitutes the maximum jet power assuming η a = 1 corresponding to a BH spin a ≈ 0.87 (left vertical axis).Turquoise lines illustrate schematically the jet power evolution for different assumptions about the dimensional magnetic flux threading the BH, Φ, and the corresponding total jet energy, E j .Since the magnetic flux on the BH is likely accumulated early and hence remains nearly constant before the disk transitions to MAD, the jet power, P j , is also predicted to be roughly constant at these times.However, once the dimensionless magnetic flux saturates in the MAD state, the jet power saturates at P j = Ṁc 2 and thus follows the mass-accretion rate Ṁ ∝ t −2 thereafter (we have extrapolated P j by a dashed line to later times).The yellow (blue) region outlines the estimated average jet power and duration T 90 (T 50 ) of the sbGRB (lbGRB) population based on prompt emission and afterglow observations (see text).While the jets from such massive disks are either too powerful, or operate for too long, compared to the sbGRB population, BH accretion from such massive disks nicely matches the observed properties of lbGRBs.
constant jet power phase.This translates to a relatively short and exceedingly luminous cbGRB (see e.g. the top turquoise line in Fig. 1).This outcome challenges the model of Gao et al. (2022), which suggests that a strong magnetic field can halt accretion to prolong the cbGRB duration.
If instead, the initial plasma beta in the disk is high (low Φ) or the initial magnetic field configuration is predominantly toroidal (see e.g., Appendix §A), then the jet launching efficiency is low and the jet can generate a luminosity characteristic of sbGRBs.Over time, the efficiency increases due to the development of a global poloidal magnetic field and the decrease in the mass accretion rate that follows 4 Ṁ ∼ t −2 , 4 Energy injection from alpha-particle recombination can also act to steepen the mass accretion power-law, after neutrino cooling is no longer important, at t ≳ 1 s (Metzger et al. 2008a;Haddadi et al. 2023).
as was also found in other numerical simulations (Fernández et al. 2015(Fernández et al. , 2017(Fernández et al. , 2019b;;Christie et al. 2019;Metzger & Fernández 2021;Hayashi et al. 2022), where the normalization of the mass accretion rate is set by M d .When the disk finally becomes MAD at T MAD , the efficiency stabilizes at η ϕ ≈ const, and Eq. ( 2) reads P j ∼ Ṁ ∼ t −2 (see e.g. the bottom turquoise lines in Fig. 1).The two phases of P j (t < T MAD ) ∼ P 0 and P j (t > T MAD ) ∼ t −2 are generic for BH-powered cbGRB jets.This motivates future analytic and numerical models to consider such temporal evolution of the jet power, with two free parameters: T MAD , determined by the values of ϕ, and P 0 , determined by Φ.
We stress that a roughly constant jet power does not imply a constant γ-ray luminosity.Firstly, as shown in Fig. 4(d) in Appendix A, the jet power itself exhibits temporal variability, particularly for the initially toroidal configurations, owing to the stochastic nature of the dynamo process.Secondly, different portions of the jet undergo different levels of mixing and mass entrainment by the surrounding environment, leading to fluctuations in the baryon loading, magnetization, and Lorentz factor.These variations likely translate to a range of radiative efficiencies.This implies that even though the jet power remains roughly constant on average (consistent with the observed lack of temporal evolution in the statistical properties of GRB light curves throughout the burst; e.g., McBreen et al. 2002), different light curves can exhibit different shapes and variability, depending on the specifics of the merger.

Constraints from cbGRB observations
To compare the predictions of numerical simulations with observational data, we need to deduce the true jet properties from observations.The observed duration of the γ-ray emission from cbGRB, T 90 , varies depending on the detectors used (Bromberg et al. 2013), and whether the GRB duration distribution is modeled assuming 2 (lGRB and cbGRB) or 3 (lGRBs, sbGRBs, and lbGRBs) populations.To estimate the range of T 90 for sbGRBs, we refer to the lowest and highest T 90 values found among 2 and 3 Gaussian fits to Fermi and BATSE duration distributions in Tarnopolski ( 2016) and find: 0.38 s ≤ T 90 ≤ 0.85 s.For lbGRBs, we take the prompt emission durations of recent events GRB 211211A and GRB 230307A as boundaries: where T 50 = 12.1 s (Tamura et al. 2021) and T 50 = 9.2 s (Svinkin et al. 2023), respectively.The use of T 50 instead of T 90 , in this case, is motivated by the comparable radiated energies of the prompt burst and EE phases (Kaneko et al. 2015;Zhu et al. 2022), rendering T 50 a more accurate estimate for the prompt duration.
The characteristic jet power of cbGRBs can be estimated as: where E iso,γ is the isotropic equivalent γ-ray energy, f b is the beaming fraction, and ϵ γ is the radiative efficiency, of the γ-ray emission.We take E iso,γ ≈ 2 × 10 51 erg for sbGRB (Fong et al. 2015), while for lbGRB we adopt values E iso,γ ≈ 5.3 × 10 51 erg (Yang et al. 2022) and E iso,γ ≈ 1.5 × 10 52 erg (Levan et al. 2023a) measured for GRB 211211A and GRB 230307A, respectively.We adopt a range of beaming factors 0.01 ≤ f b ≤ 0.11 (Fong et al. 2015), corresponding to a true γ-ray jet energy for sbGRB of E obs,γ ≈ 2×10 49 −2×10 50 erg (Fong et al. 2015).Early estimates of the γ-ray efficiency in lGRBs found ϵ γ ≈ 0.5 (Panaitescu & Kumar 2002), but later analyses by Beniamini et al. (2015Beniamini et al. ( , 2016) ) suggested a lower value of ϵ γ ≈ 0.15.Berger (2014) found that the ratio of cbGRB prompt to afterglow energy is higher by an orderof-magnitude compared to lGRBs, indicating a potentially higher ϵ γ for cbGRBs.Nevertheless, this discrepancy might be attributed to the brighter afterglow emission arising from the denser large-scale environments surrounding the massive star progenitors of lGRBs.It thus remains unclear whether the difference between lGRBs and cbGRBs results from variations in the external medium, or is intrinsic (i.e., attributed to higher ϵ γ in cbGRBs) due to e.g.substantial wobbling jet motion in collapsar jets (Gottlieb et al. 2022b).We thus consider a range of 0.15 ≤ ϵ γ ≤ 0.5 in our estimates.
Figure 1 compares theoretical and numerical estimates of the jet power with cbGRB observations.The right vertical axis shows the characteristic evolution of the BH accretion rate as a function of time after the merger (purple line), which we have obtained by averaging the results of BH-NS merger simulations by Gottlieb et al. (2023b) and the BNS merger simulations presented here (gray lines), all of which produce massive disks with M d ≈ 0.1 M ⊙ .The jet power, displayed on the left vertical axis, is expected to be roughly constant at early times, insofar that most of the magnetic flux Φ accumulates on the BH quickly.However, as the accretion rate drops, the dimensionless magnetic flux ϕ ∝ Ṁ−1/2 increases with time, until the disk enters a MAD state and the jet efficiency η ϕ ≈ 1 saturates.After this point, the jet power P j ≈ η a Ṁc 2 (Eq.( 2)) tracks the decaying mass-accretion rate P j ∝ t −2 , marking the cbGRB characteristic timescale as that at which the disk goes MAD.
In order to achieve the characteristic jet powers required to explain sbGRBs (yellow region), the magnetic flux needs to be Φ ∼ 10 27.5 G cm 2 (bottom turquoise lines).However, for such a flux, the accretion disk can only enter a MAD state after several seconds, significantly longer than the sbGRB duration, T MAD ≫ T 90 .On the other hand, flux at roughly this same level Φ ≲ 10 27 G cm 2 leads to a jet which naturally achieves both the correct power and duration of the lbGRB class (blue region).
We conclude that for relatively large disk masses M d ≳ 0.1 M ⊙ (consistent with that required to produce the kilonova ejecta in GW170817; e.g., Perego et al. 2017;Siegel & Metzger 2017), the resultant jets exhibit either excessively high power (if the seed magnetic flux threading the disk is large) or lower power with extended duration of activity (if the seed flux is weaker).The former is ruled out observationally, implying that massive disks must give rise to lbGRBs.Therefore, if the jet in GW170817 was powered by a BH surrounded by a massive disk, then the inferred jet energy, E j ≈ 10 49 − 10 50 erg (Mooley et al. 2018) indicates that the jet was not a luminous cbGRB but rather a lbGRB (e.g., the bottom turquoise line in Fig. 1).Unfortunately, because the jet was ∼ 20 • off-axis (Mooley et al. 2018), the bulk of the gamma-ray emission was beamed away from Earth, precluding a direct measurement of the jet duration.

Disfavored solutions
Here we explore potential caveats to the conclusions of the previous subsection.However, finding reasons to disfavor each, we shall ultimately conclude that BHs surrounded by massive disks remain the most likely explanation for lb-GRBs.

Lower post-merger BH spins
According to Eq. ( 2), one potential way to reduce the jet power is to decrease the maximum efficiency η a by considering a lower post-merger BH spin for an otherwise similar magnetic flux.For example, a BH spin of a ≈ 0.4 yields maximum efficiency of only η a ≈ 0.1 (Lowell et al. 2023).This would allow BHs with massive disks to power sbGRBs provided the BH spin obeyed a ≲ 0.4.However, this requirement conflicts with the results of numerical relativity simulations, which find post-merger BH spins 0.6 ≲ a ≲ 0.8 (Kiuchi et al. 2009;Kastaun & Galeazzi 2015;Sekiguchi et al. 2016;Dietrich et al. 2017) for BNS mergers, corresponding to 0.3 ≲ η a ≲ 0.7.BH-NS mergers result in comparable or slightly higher remnant BH spins, at least for systems leading to the formation of massive accretion disks (Foucart et al. 2011(Foucart et al. , 2013(Foucart et al. , 2014(Foucart et al. , 2017(Foucart et al. , 2019;;Kyutoku et al. 2011Kyutoku et al. , 2015;;Kawaguchi et al. 2015).Appealing to a lower BH spin can thus only reduce the jet energy by a factor of ≈ 2 compared to our estimates assuming η a ≈ 1.

Delayed jet launching
As the magnetic field in post-merger accretion disks is anticipated to be predominantly toroidal (e.g., Ruiz et al. 2018), a jet of significant power may only be launched after a dynamo process in the disk generates a sufficiently strong global poloidal field.If the seed magnetic field is weak, the jet onset might be delayed for several seconds (see e.g., Hayashi et al. 2023), thus operating for only a brief period before the disk transitions into a MAD state.This would make it possible for a BH with a massive disk to produce a sbGRB.Nevertheless, it is unlikely that this scenario can serve as a generic explanation for sbGRBs, as fine-tuning is required to launch the jet only briefly after ∼ 10 s, just before the disk reaches a MAD state, in order to achieve T 90 ≲ 1 s.

Misestimating the cbGRB duration
Another possible caveat worth exploring is whether the jet duration could be inferred incorrectly from observations.Such an erroneous estimation could occur while (i) converting from the engine activity duration to T 90 , or (ii) due to uncertainties in observations: (i) If the interaction of the jet with the external medium is sufficiently strong to decelerate the jet head to sub-relativistic velocities, the radial extent of the jet can become significantly shorter than T MAD /c, leading to an observed GRB duration considerably shorter than the MAD timescale over which the jet is launched.However, for typical properties of merger ejecta and cbGRB jet energies, the jet head exhibits at least mildly relativistic motion from the onset (Gottlieb & Nakar 2022), supporting the usual assumption that the GRB duration follows the activity time of the jet (i.e., T 90 ∼ T MAD ).
(ii) In collapsars, the physics of jet propagation (Bromberg et al. 2011) and the observed GRB duration distribution (Bromberg et al. 2012) support a substantial fraction of jets being choked inside the star (see also Gottlieb et al. 2022a).Some jets may operate just long enough to break out of the star and power a short-duration GRB (Ahumada et al. 2021;Rossi et al. 2022).If collapsar jets outnumber those originating from binary mergers within the sGRB population, this could in principle lead to underestimates of the typical duration of binary merger jets.However, while such an increase in the inferred T 90 of binary merger jets could potentially alleviate the tension in accounting for sbGRB from massive BH disks, it provides no natural explanation for the bimodal distribution of GRB durations.

Prompt-collapse Black Holes
When the total mass of a BNS exceeds a critical threshold M tot ≳ 2.8 M ⊙ , the remnant created by the merger promptly collapses into a BH surrounded by an accretion disk (Bauswein et al. 2013), the mass of which depends sensitively on the binary mass ratio.For unequal mass ratios (q ≳ 1.2), as characterized by our BNS merger simulations, the lighter NS is disrupted, resulting in a massive accretion disk, M d ≈ 0.1 M ⊙ .By contrast, prompt-collapse mergers with q ≈ 1 generate significantly smaller disk masses, M d ≲ 10 −2 M ⊙ (see Shibata & Hotokezaka 2019, for a review).Assuming the mass accretion rate to scale linearly with the disk mass, and Φ to be largely independent of M d , then disk masses of M d ≲ 10 −2 M ⊙ could power jets consistent with sbGRB observations.This implies that sbGRB can in principle be powered through massive BNS mergers with M tot ≳ 2.8 M ⊙ and q ≈ 1.In BH-NS mergers, similarly low disk masses of M d ≲ 10 −2 M ⊙ are possible for high binary mass ratios, q ≫ 1, low pre-merger BH spin, or large spin-orbit misalignment (Foucart et al. 2018).
The region M tot > 2.8 M ⊙ in Figure 2 overviews this scenario.Low disk masses, such as those produced by equal mass BNS mergers that undergo prompt BH formation (bottom yellow region) or high mass ratio BH-NS mergers (top right yellow region)5 , giving rise to sbGRBs.The opposite case of mergers forming massive BH disks then power lb-GRBs (blue region).If BHs power all cbGRB jets, then it is expected that the cbGRB duration spectrum will be continuous via the disk mass distribution.This seems to be in tension with the observed bimodal distribution.This scenario also poses an additional requirement on the rates given that most cbGRBs arise from BNS mergers.If sbGRBs are more common than lbGRBs, this would require that q ≈ 1 BNS mergers (sbGRBs) should be more common than unequal mass ratio BNS mergers (lbGRBs).While consistent with the mass ratio distribution of the Galactic BNS population being narrowly concentrated around q ≲ 1.2 (Vigna-Gómez et al. 2018;Farrow et al. 2019), this picture is in tension with the BNS masses being below the expected prompt collapse threshold ≈ 2.8 M ⊙ , as we now discuss.

Long-lived HMNSs
Observations of Galactic BNSs indicate an average NS mass of M NS ≈ 1.33 M ⊙ (Özel et al. 2012;Kiziltan et al. 2013;Özel & Freire 2016;Farrow et al. 2019).If representative of the extragalactic merger population as a whole, this relatively low mass suggests that most mergers will not undergo a prompt collapse into a BH given current constraints on the NS Equation of State (EoS) (e.g., Margalit & Metzger 2019).Furthermore, larger Fe cores are generally expected to result in both more energetic explosions and greater NS natal kicks, resulting in a correlation between these two properties (Tauris et al. 2017).Since large kicks tend to unbind the binary, this makes less massive BNS systems more likely to eventually merge compared to their more massive counterparts.
The merger of BNS systems with M tot ≲ 2.8 M ⊙ results in the formation of a highly magnetized differentially rotating HMNS, which only collapses into a BH after some de-lay (e.g., Shibata & Taniguchi 2006;Kastaun & Galeazzi 2015;Hanauske et al. 2017).As a result of amplification of the magnetic field via differential rotational and instabilities, such HMNSs have the potential to produce energetic jets that could be the source of sbGRBs (Kluźniak & Ruderman 1998).One challenge to this scenario is that the polar outflows from HMNS are subject to baryon contamination of ∼ 10 −4 M ⊙ str −1 driven by strong neutrino heating from the atmosphere just above the surface (Thompson et al. 2001;Dessart et al. 2009;Metzger et al. 2018), which for jets of sbGRB energies limits their bulk Lorentz factors to Γ ≲ 10 ( Metzger et al. 2008b).While relatively low, such Lorentz factors might be nevertheless compatible with constraints based on compactness arguments in cbGRBs (Nakar 2007) 6 .
Comparing the observed properties of cbGRBs with the energy output and lifetime of HMNSs is challenging due to the sensitivity of the latter to several theoretically uncertain properties of the post-merger system.The lifetime of the HMNS is governed by various physical processes, including neutrino cooling and angular momentum transport, the timescales for which in turn depend on factors such as the strength of the remnant's large-scale magnetic field, the saturation level of various magnetohydrodynamic instabilities giving rise to turbulent transport, and the initial distribution of angular momentum and temperature (Margalit et al. 2022).The complexity of incorporating all of these physical processes into long-term simulations, on top of uncertainties in the EoS, renders the lifetimes of HMNSs highly uncertain (Hotokezaka et al. 2013a;Dietrich et al. 2017).
More massive binaries in general produce HMNSs with shorter lifetimes (Shibata & Taniguchi 2006;Bauswein et al. 2013).For binaries with M tot ≈ 2.7 M ⊙ the HMNS lifetime is primarily governed by angular momentum transport and the specific EoS (Hanauske et al. 2017).For less massive HMNSs, the collapse is dictated by either angular momentum transport with a timescale of T HMNS ∼ 0.1 s, or if the HMNS is partially thermally supported (Hotokezaka et al. 2013a;Kaplan et al. 2014), by neutrino cooling with a timescale of T HMNS ∼ 1 s (Sekiguchi et al. 2011).The binary mass ratio also plays a role, with greater asymmetry resulting in a longer HMNS lifetime due to increased angular momentum support (Dietrich et al. 2017).

Short cbGRB
No Disks

BNS
No Binaries

Long cbGRB
Figure 2. The outcomes of compact object mergers and their ability to power various cbGRBs sub-classes as a function of the binary mass ratio and total mass.lbGRBs occur in high M tot and high q BNS mergers that form a massive BH disk, or in high pre-merger BH spin and low mass ratio BH-NS mergers (blue region).sbGRBs may arise either from equal mass ratio BNS mergers (bottom yellow region) and low pre-merger BH spin/high mass ratio BH-NS mergers (top yellow region), or by HMNS formed in BNS mergers with M tot ≲ 2.8 M ⊙ (left yellow region).The absence of evidence for distinct sub-classes of sbGRBs suggests that either BHs or HMNSs are likely to be the sole origin of these events, i.e.only one of the proposed sbGRB scenarios is correct.The Galactic BNS mass distribution, the bimodal GRB duration distribution, and GW170817 observations favor HMNSs as the engine of sbGRB jets.
Siegel 2023; Kiuchi et al. 2023).On the other hand, Most & Quataert (2023) found for a similar magnetic field and binary mass that the jet emission is lower by several orders of magnitude compared to other simulations.Furthermore, the HMNS lifetime varies greatly among those simulations, from T HMNS ∼ 10 ms to T HMNS ≳ 1 s, demonstrating the uncertainty in the HMNS lifetime, even when similar magnetic fields and M tot are considered (Ruiz et al. 2016(Ruiz et al. , 2020;;Ciolfi et al. 2019;Ciolfi 2020;Aguilera-Miret et al. 2023;Most & Quataert 2023;Kiuchi et al. 2023).The specific properties of the binary and the EoS, thus play a crucial role in determining the characteristics of HMNSs.
Perhaps the tightest constraint on the properties of HMNSs comes through the interpretation of the first multi-messenger BNS system, GW170817, characterized by M tot ≈ 2.75 M ⊙ and q ≲ 1.3 (Abbott et al. 2019).GW170817 provided valuable insights into the EoS of dense matter (Radice et al. 2018b), and supported the existence of a transient HMNS phase (Margalit & Metzger 2017;Shibata et al. 2017;Rezzolla et al. 2018).The large quantity of slow-moving ejecta inferred from the kilonova, argues against a prompt collapse of the BH but is consistent with the expectation of disk outflows from a merger accompanied by a HMNS phase.The low inferred abundance of lanthanides in the ejecta (e.g., Kasen et al. 2017) supports strong neutrino irradiation of the disk by the HMNS (e.g., Metzger & Fernández 2014;Kasen et al. 2015;Lippuner et al. 2017).These findings thus point towards the requirement of a sufficiently stiff EoS, capable of supporting the formation of an HMNS from the GW170817 merger with M tot ≈ 2.75 M ⊙ .The HMNS could have persisted for the Alfvén crossing timescale of ∼ 1 s (Metzger et al. 2018), sufficiently long to power a sbGRB.Based on a suite of merger simulations targeted towards GW170817, Radice et al. (2018a) found that the remnant indeed most likely possessed enough angular momentum to prevent a collapse and to form a long-lived HMNS, even for M tot ≈ 2.75 M ⊙ .
The region M tot < 2.8 M ⊙ in Figure 2 summarizes this alternative scenario, in which sbGRBs arise from transient jets powered by moderately long-lived HMNSs formed from relatively low-mass binaries (left yellow region).In this scenario, all prompt-collapse BHs give rise to lbGRBs, where dimensional analysis suggests that M d determines the jet power ( §5.2).

Delayed-collapse Black Holes
In BNS mergers where the combined mass is M tot ≲ 2.8 M ⊙ , the collapse of the HMNS into a BH may introduce a delayed launching of BZ-jets, which could potentially contribute to the cbGRB populations.When the BH formation is preceded by a transient phase of a HMNS, the disk mass depends on T HMNS .If the HMNS collapses within a few ms, the system evolves in a similar way to promptcollapse BHs.A longer-lasting HMNS with T HMNS ≳ 10 ms allows for a greater opportunity for the post-collapse disk to grow through angular momentum transport to M d ≈ 0.1 M ⊙ (e.g., Hotokezaka et al. 2013a).However, a longer-lived HMNS also provides an opportunity for the disk to lose mass prior to the BH formation.The disk continuously expands due to viscous angular momentum transport by the differentially rotating HMNS and viscous heating by magnetorotational instabilities (MRI) in the disk.Once neutrino cooling becomes subdominant to viscous heating, the disk expels winds, thereby reducing its mass (see, e.g., Siegel & Metzger 2018;Fernández et al. 2019b).In cases where vigorous viscous heating prompts rapid expansion, a substantial portion of the disk mass might be lost within T HMNS (Fujibayashi et al. 2018(Fujibayashi et al. , 2020)).
The post-HMNS collapse disk mass remains elusive due to uncertainties pertaining to variables such as the magnetic field and effective viscosity in the disk, T HMNS , and other contributing factors.Given the significant impact of the disk mass on determining the cbGRB type, the role of delayedcollapse BHs remains uncertain7 .Two possibilities exist: (i) If the disk mass is appreciably reduced by viscous heating prior to BH formation, then the BZ-jet might be less luminous compared to the preceding HMNS-powered jet that generated the sbGRB.In such instances, the jets launched by delayed-collapse BHs could serve as sources of EE once they transition into the MAD state.(ii) If the viscous heating is insufficiently strong to remove the bulk of the disk mass on T HMNS timescale, the BH forms with a massive disk.As outlined in §4.1, such disks are likely to give rise to lb-GRBs.If this configuration characterizes the standard picture of HMNSs, the lbGRBs would supersede the observational imprint of HMNS-powered jets, indicating that all cbGRBs are powered by BHs.Interestingly, this perspective forecasts that BNS mergers with M tot ≲ 2.8 M ⊙ lead to lbGRBs, implying that lbGRBs are more common than sbGRBs.

Long-lived SMNSs
For particularly low-mass binaries M tot ≲ 2.4 M ⊙ , a very long-lived rigidly rotating SMNS with M d ≈ 0.1 M ⊙ can form (Giacomazzo & Perna 2013;Foucart et al. 2016).Similar to the HMNS case, the early stages after the formation of a SMNS can in principle give rise to moderately relativistic outflows with Γ ∼ 10 (e.g., Metzger et al. 2008b).However, SMNSs can live for t ≫ 1 s before collapsing, and thus may generate a relativistic wind that reaches Γ ≳ 100 as the rate of neutrino-driven mass-ablation from the SMNS surface decays (e.g., Thompson et al. 2004;Metzger et al. 2008b).Relativistic magnetohydrodynamic (MHD) (Bucciantini et al. 2012) and numerical relativity (Ciolfi et al. 2017;Ciolfi 2020;Ruiz et al. 2020) simulations have demonstrated that longlived magnetars are potentially capable of powering cbGRB jets.Such jets could be compatible with energy injection into cbGRB afterglows (Zhang & Mészáros 2001), and the latetime spin-down luminosity of the magnetar obeys ∼ t −2 , also consistent with the observed decay evolution of the EE (Metzger et al. 2008b;Bucciantini et al. 2012;Gompertz et al. 2013).
The kilonovae which accompanied the two recent lb-GRBs, GRB 211211A and GRB 230307A, support relatively slow outflows ( v ej ≲ 0.1c) containing high-opacity material consistent with significant lanthanide/actinide enrichment (Rastinejad et al. 2022;Levan et al. 2023a;Barnes & Metzger 2023).While both these properties are consistent with the disk outflows from a BH accretion disk (e.g., Siegel & Metzger 2017;Fernández et al. 2019b), the ejecta velocities are too low compared to those expected following substantial energy injection from the magnetar wind (Bucciantini et al. 2012).Sustained neutrino irradiation of the disk outflows from the hot stable neutron star remnant, also precludes significant heavy r-process material (e.g., Metzger & Fernández 2014;Kasen et al. 2015;Lippuner et al. 2017).
Additional arguments which disfavor SMNSs as the progenitors of the majority of the cbGRBs include: (i) lack of evidence for a significant injection of rotational energy from the magnetar based on the late radio afterglow emission (Metzger & Bower 2014;Horesh et al. 2016;Schroeder et al. 2020;Beniamini & Lu 2021); (ii) the BNS mass distribution favors HMNSs as the common remnant of a BNS merger, and recent results by Margalit et al. (2022) show that accretion can shorten the SMNS lifetime such that it is closer to T HMNS , reducing the parameter space capable of generating long-lived magnetars.In light of the viability of the massive BH disk scenario, the above arguments disfavor the model suggested by Metzger et al. (2008b), Sun et al. (2023), in which lbGRBs with EE are powered by long-lived magnetars.

Binary WD merger and AIC
The formation of a magnetized NS does not require a merger that involves a pre-existing NS.Instead, it may originate from the gravitational collapse of a WD in a binary system (Taam & van den Heuvel 1986).The secondary star for AIC can either be a merging WD companion, or a nondegenerate donor (e.g., Duncan & Thompson 1992;Usov 1992;Yoon et al. 2007).The resulting newly formed NS can be a magnetar if the magnetic field of the progenitor WD is very strong and is amplified by flux freezing during the collapse (see e.g., Burrows et al. 2007) or after the collapse through magnetic winding or other dynamo action after the merger/collapse.Magnetars formed from AIC may potentially act as central engines for cbGRBs (Usov 1992;Metzger et al. 2008b).
Accreting WDs are generally considered to lose much of their angular momentum during their evolution (e.g., through classical nova eruptions), ultimately becoming slow rotators (Berger et al. 2005).In the case of binary WD mergers, the angular momentum budget is much higher initially; however, the most massive mergers capable of undergoing AIC ultimately produce an NS with a mild rotation period of ∼ 10 ms, due to angular momentum redistribution during the postmerger phase prior to collapse (Schwab 2021).Such slowly rotating magnetars have a limited energy reservoir and would not be accompanied by an appreciable accretion disk.
AIC occurs when a massive oxygen-neon WD accretes matter from a companion star until it reaches the Chandrasekhar limit and collapses into an NS (e.g., Nomoto & Kondo 1991; however, see Jones et al. 2016).During the collapse process, conservation of angular momentum may lead to the formation of a rapidly spinning NS surrounded by a disk (Bailyn & Grindlay 1990).Additionally, the fast and differential rotation in the newly formed NS results in a substantial amplification of the magnetic field (Dessart et al. 2007), which may result in a millisecond magnetar.However, the AIC faces similar challenges as the SMNS scenario ( §4.4).For example, neutrino irradiation from the long-lived magnetar will increase the electron fraction in the disk outflows (e.g., Metzger et al. 2009;Darbha et al. 2010), leading to inconsistencies with the lanthanide-rich ejecta inferred from the kilonova emission from GRB 211211A and GRB 230307A.
Another scenario involving WDs is an NS-WD merger (Fryer et al. 1999;King et al. 2007), which was proposed as origins of GRB 211211A (Yang et al. 2022) and possibly GRB 230307A (Sun et al. 2023).It is argued that the burst duration scales with the accretion timescale, which in turn scales inversely with the density of the companion star for an accretion-powered engine, favoring a WD.However, as we have shown in §3, the burst timescale depends on the disk mass and the magnetic flux threading the BH and does not necessarily require a low-density WD to prolong the accretion timescale.In fact, we find that after t ∼ 100 ms, the mass accretion rate follows a single power-law profile, indicating that there is no accretion timescale relevant to cb-GRBs.Additionally, proton-rich matter accreted from the disrupted WD is unlikely to reach high enough densities to produce neutron-rich outflows capable of generating any significant r-process material, much less the relatively heavy lanthanides (Metzger 2012;see Fernández et al. 2019a for simulations of the post-merger disk evolution and nucleosynthesis).The NS-WD merger scenario thus faces difficulties in explaining the observed kilonova emission (see Barnes & Metzger 2023, and references therein).

Neutrino annihilation
The high accretion rates anticipated in post-merger disks give rise to strong neutrino emission.Efficient annihilation of neutrinos and anti-neutrinos can generate relativistic jets that may power cbGRBs (e.g., Woosley 1993).These jets are expected to operate as long as the accretion rate is Ṁ ≳ 10 −2 M ⊙ (Popham et al. 1999).This requirement implies that massive disks are necessary (e.g., Leng & Giannios 2014) to enable jet launching for T 90 ≲ 1 s.If the initial magnetic field in the disk is predominantly toroidal, then BZ-jet may follow the neutrino-driven jet after t ≳ 1 s (e.g., Christie et al. 2019;Gottlieb et al. 2023b), and power the late EE (Barkov & Pozanenko 2011).This scenario cannot explain lbGRBs, and as we now argue, is also disfavored as the origin of sb-GRBs.
The main limitation of neutrino-driven jets lies in their available energy (Leng & Giannios 2014;Just et al. 2016).In BNS mergers, where a significant amount of ejecta is expected along the polar axis, these low-energy jets would fail to break out and generate a cbGRB (Just et al. 2016).Furthermore, the mass distribution of the Galactic BNS population suggests that most post-merger remnants are HMNSs.The large amount of mass in the HMNS atmosphere ( §4.2) would load neutrino-driven jets with baryons, hindering their ability to achieve relativistic velocities (Dessart et al. 2009).Consequently, such jets would be incapable of producing cbGRBs.

ORIGIN OF THE PRECURSOR FLARE AND EXTENDED EMISSION, AND COMPARISON OF BH-POWERED AND HMNS-POWERED JETS
Figure 3 utilizes the light curves of lbGRB 211211A (black) and sbGRB 930131A (gray) to illustrate the connection between the underlying physics of the compact object (orange labels) and the various phases observed in the cb-GRB light curve (yellow for sbGRBs, blue for lbGRBs, and green for preceding and succeeding phases).A sbGRB can be powered by either a BH with a light accretion disk or a long-lived HMNS before it eventually collapses into a BH.A lbGRB is fueled by a BH surrounded by a massive accretion disk, as the dimensionless magnetic flux threading the BH steadily accumulates.The origin of the precursor flare and the EE are discussed below.
Up to this point, we have presented both HMNS-powered and BH-powered jets as potential contributors to sbGRBs.However, there is no evidence indicating the existence of two distinct sub-populations among sbGRBs, suggesting that only one of these engines is responsible for producing the majority of sbGRBs.Table 1 summarizes the origin of sb-GRBs and lbGRBs, as well as the outcomes of the different types of mergers, as predicted in both scenarios.We denote the scenario in which HMNSs power sbGRBs and BHs power lbGRBs by the "hybrid" scenario.The scenario in which all cbGRBs are powered by BHs, with the GRB duration increasing with the disk mass, is denoted by "all-BH" scenario.Both scenarios predict the formation of a lb-GRBs when the BH is surrounded by a massive disk.When a less massive disk is present (in nearly-equal mass ratio BNS mergers with M tot ≳ 2.8 M ⊙ , or in BH-NS mergers with either high q or low a), the all-BH scenario predicts a sbGRB signal, whereas the hybrid scenario predicts a lbGRB signal.When M tot ≲ 2.8 M ⊙ , the cbGRB duration in the all-BH scenario depends on the uncertain post-HMNS collapse disk mass (see §4.3).
In the all-BH scenario, the cbGRB duration spans a continuous spectrum, whereas, in the hybrid scenario, the BHpowered lbGRBs comprise a separate class.Therefore, the hybrid scenario offers a natural distinction between sbGRBs Event type Scenario: Table 1.Summary of the mapping between the Hybrid and All-BH scenarios and associated cbGRB classes.
powered by HMNSs and lbGRBs powered by BHs.Furthermore, the hybrid scenario finds support from the bimodal cbGRB duration distribution, the mass distribution of BNS systems, as well as from observations and simulations of GW170817.In the following subsections, we show that the hybrid scenario is also more compatible than the all-BH scenario with all phases of the cbGRB light curve.

Precursor flare
Each of the proposed hybrid and all-BH scenarios postulates a different physical origin for the precursor flare before the rise of the main burst.In the hybrid scenario, Most & Quataert (2023) demonstrated how the differentially rotating HMNS builds loops with footpoints at different latitudes on its surface.The resultant twist in the loop causes it to become unstable, inflate and buoyantly rise, forming a bubble that is entirely detached from the HMNS surface, and erupting after reconnecting (e.g., Carrasco et al. 2019;Mahlmann et al. 2023;Most & Quataert 2023).This behavior powers quasi-periodic flares prior to the jet formation.
For BH-powered jets, Gottlieb et al. (2023b) showed that if the seed magnetic field in the disk is toroidal, as expected in binary systems, then the stochastic accumulation of incoherent magnetic loops on the horizon can lead to a short burst of energy (see model T s in their figure 1(d)), which may constitute the precursor flare.As more flux reaches the BH, the stochastic field cancels out by virtue of contribution of loops of different polarity.Consequently, the total flux drops to zero, before starting to build a large-scale poloidal field through the dynamo process and power the cbGRB emission.Due to the stochastic nature of the accumulated flux, the flare energy is expected to be very weak, and the resultant outflow may not be able to punch through the optically thick disk wind and/or dynamical ejecta (Gottlieb et al. 2023b).Therefore, the emergence of such precursor flares in the all-BH scenario may require fine-tuning.Nevertheless, it is possible that the precursor in the all-BH scenario is also powered by a short-lived HMNS before it collapses into a BH on a ∼ 10 ms timescale.

Main cbGRB burst
Dimensional analysis suggests that Φ ∼ √ M d , thus M d ∼ Φ 2 ∼ P 2 j , while the dimensionless magnetic flux ϕ is independent of M d .This is also supported by the fact that the saturation level of the amplified ordered field in the disk seems to scale with the turbulent disk pressure, which in turn likely scales with Ṁ.This implies that reducing the disk mass results in a lower jet power, rather than shortening the cbGRB duration, which scales with the dimensionless magnetic flux (see §3).Therefore, unless there is an intrinsic correlation be-tween M d and ϕ, the variation in M d does not naturally yield the variation in the cbGRB duration.This favors BHs with less massive disks to power weaker lbGRBs, and sbGRBs as a distinct cbGRB population, which emerges from HMNSs.

Extended emission
Following the main hard burst, the softer EE phase commences.In both hybrid and all-BH scenarios, an accretion disk forms and is present at the time of the EE.Once the disk enters the MAD state, the jet power evolves in accordance with the mass accretion rate, P j ∼ t −2 , similar to the observed temporal evolution of the EE decay.The preceding flat EE hump is thus generated by the constant power jet, just before the disk transitions to a MAD state.The EE may end once the disk is overheated after ∼ 100 s, and evaporates on this timescale (Lu & Quataert 2023).This evolution of a constant jet power followed by a t −2 decay for another order-of-magnitude in time naturally results in a comparable energy content between the cbGRB prompt emission and the EE, as suggested by observations (Kaneko et al. 2015).
Any cbGRB model must account for two observational constraints related to EE: (i) the EE is observed in ∼ 25% − 75% of cbGRBs and is commonly found in lbGRBs (Norris et al. 2011;Kaneko et al. 2015;Kisaka et al. 2017).Considering that all disks eventually transition to a MAD state where P j ∼ t −2 , this correlation might be attributed to an observational bias if lbGRBs exhibit brighter EE. (ii) The EE likely emerges ∼ 10 s after the onset of the prompt emission.This implies that if the EE follows a sbGRB where T 90 ≪ 10 s, there must be a quiescent period between the prompt and the EE phases (e.g., Perley et al. 2009).
The all-BH scenario, which posits that both cbGRB types are powered by BHs, encounters difficulties in explaining either of the constraints mentioned above: (i) If sbGRBs are powered by BHs, then the cbGRB duration would be determined by the disk mass, while the jet power would depend on the magnetic flux.Consequently, there would be no obvious correlation between the cbGRB duration and jet power, and thus with the EE power.Therefore, the all-BH scenario does not explain the observed correlation between lbGRBs and the EE.(ii) As described in §3, BHs launch jets with a constant power followed immediately by the EE decay once the disk transitions to a MAD state.Therefore, no quiescent times would be expected to emerge between the prompt emission and the EE phase.
If sbGRBs are powered by HMNSs, both observational constraints can be accounted for, provided that at the time of BH formation the disk mass is M d ≲ 10 −2 M ⊙ (see §4.3).In this scenario, HMNSs power the sbGRB while the postcollapse BZ-jet generates the EE hump followed by the EE decay.(i) Low-mass disks contain a reduced energy reservoir available for the post-HMNS collapse BZ-jet.As a result, a significant fraction of sbGRB-associated EE may fall below the detection threshold, increasing the likelihood of detecting an EE associated with lbGRBs.(ii) Following the HMNS collapse and before the launch of the BZ-jet, a quiescent time between the prompt emission and the EE emerges.

CONCLUSIONS
The discoveries of ∼ 10-s long prompt emission in lbGRBs 211211A (Rastinejad et al. 2022) and 230307A (Levan et al. 2023a), followed by softer EE signals, suggest that the cb-GRB population can be divided into two classes: sbGRBs (T 90 ≲ 1 s) and lbGRBs (T 50 ∼ 10 s).However, the underlying physics that differentiates these classes and the origin of the prolonged EE are poorly understood.Moreover, drawing inferences about the astrophysical properties of binary mergers from cbGRB observables poses a formidable challenge.In this paper, we have developed a novel theoretical framework that connects different binary merger types to the distinct sub-populations of cbGRB and to the different components in their light curves.
In collapsars, the presence of a dense stellar core surrounding the BH hinders the launching of jets when the accretion disk is not in a MAD state.This implies that for lGRBs, the jet operates in a MAD state at all times, and the characteristic lGRB duration can be set by either the mass accretion rate or by the BH spin-down timescale.By contrast, in binary systems where the environment is less dense, the conditions allow for the launching of the jet before the disk enters the MAD state.Due to the compactness of the disk, the dimensional magnetic flux, Φ, quickly accumulates on the BH, resulting in a roughly constant jet power before the transition to MAD occurs.After the accretion disk enters the MAD state, the jet power follows the mass accretion rate of P j ∼ Ṁ ∼ t −2 , signaling the end of the prompt emission phase.This behavior is consistently observed in all first-principles simulations and should be considered when modeling cbGRB jets.In this jet power evolution model, there are two free parameters: (i) the time of the transition to a MAD state, T MAD , which determines the cbGRB duration and is influenced by ϕ; (ii) the magnitude of the constant jet power, which is governed by Φ.
BNS mergers with an unequal binary mass ratio and BH-NS mergers with a moderate mass ratio and high pre-merger BH spin can lead to the formation of a massive accretion disk with a mass of M d ≳ 0.1 M ⊙ , as was inferred from GW170817 observations (e.g., Perego et al. 2017;Siegel & Metzger 2017).Depending on Φ (as illustrated in Fig. 1), such a massive disk can give rise to either extremely bright sbGRB, or lbGRB.Analyzing the sbGRB and lbGRB observational data, we conclude that these massive disks inevitably power long-duration signals, and thus are most likely the progenitors of lbGRBs such as GRB 211211A and GRB 230307A.
The nature of the resultant central engine is determined by the total mass of the binary system.In the case of a BH-NS merger, or a BNS merger with M tot ≳ 2.8 M ⊙ , the immediate merger product is a BH (e.g., Bauswein et al. 2013).As mentioned, the mergers of BNS with a high mass ratio, and of BH-NS with a moderate mass ratio and a high premerger BH spin, form a massive accretion disk and therefore are the progenitors of lbGRBs.In other mergers, the resultant BH disk is less massive, and if Φ is weakly dependent on M d , a sbGRB jet can be generated.Regardless of the disk mass, the disk ultimately becomes MAD.Before the transition is complete, the constant jet power may give rise to the EE hump.When the MAD state commences, the jet power follows P j ∼ t −2 and thus aligns with the observed temporal evolution of the EE decay (Giblin et al. 2002;Lien et al. 2016).While this interpretation of cbGRBs powered by BHs provides an explanation for sbGRBs and lbGRBs, it faces challenges in explaining various observational features in cbGRB light curves, including flares observed before the prompt emission, the correlation between the EE and lbGRBs, and the quiescent time observed between the prompt emission and the EE.Most importantly, the Galactic BNS population suggests that most binary systems have M tot ≲ 2.75 M ⊙ (e.g., Özel et al. 2012;Kiziltan et al. 2013), where a prompt collapse into a BH is not anticipated.
In BNS mergers with M tot ≲ 2.8 M ⊙ , the product of the merger is a HMNS (e.g., Margalit & Metzger 2019).Both analytic and numerical studies demonstrated that HMNSs are capable of generating relativistic jets that power cb-GRBs (e.g., Metzger et al. 2008b;Kiuchi et al. 2023).The best-studied event in this mass range is the multi-messenger GW170817 with M tot ≈ 2.75 M ⊙ .The associated kilonova signal observed in GW170817 supports the formation of a long-lived ( T HMNS ≲ 1 s) HMNS (Metzger et al. 2018;Radice et al. 2018b).This timescale is sufficiently long to power sbGRBs.Unlike BHs, HMNSs can naturally produce precursor flares (Most & Quataert 2023), and account for the quiescent time between the prompt and the EE by virtue of the transition from HMNS-powered to BH-powered jets.It can also explain why sbGRBs are infrequently followed by EE (Norris et al. 2011).The reason is that if the accretion disk has lost mass through disk winds such that at the time of BH formation it is less massive, then the BZ-jets that form after the HMNS collapse are likely weaker compared to lb-GRBs powered by prompt-collapse BHs.Therefore, the EE in sbGRB events is fainter, such that EE are commonly observed following lbGRBs.
Various constraints, from kilonova observations to radio constraints on late-time rotational energy injection, favor prompt-collapse BH-powered jets and HMNS-powered jets over models that include long-lived magnetars, WDs, or neutrino-driven jets.While we thus find it likely that BHs with massive disks are responsible for lbGRBs, we are less certain about the origin of the shorter sbGRB population.A priori, both BH-powered jets (BH-NS mergers or BNS mergers with M tot ≳ 2.8 M ⊙ and q ≲ 1.2) and HMNSpowered jets ( M tot ≲ 2.8 M ⊙ ) remain viable possibilities (Fig. 2).However, the lack of evidence for two distinct sub-classes among the sbGRB population, suggests that one of these channels dominates.We find several reasons to prefer transient HMNSs over low-disk mass BHs in this case.
A key distinction between the all-BH and hybrid scenarios lies in the cbGRB duration distribution.BH-powered jets should exhibit a continuous spectrum from sbGRBs to lbGRBs, scaling with the binary mass ratio.Conversely, if HMNSs are the progenitors of sbGRBs, they differ intrinsically from BH-powered lbGRBs, proposing two distinct cb-GRB classes.The recent joint detections of cbGRBs with kilonovae provide an exciting opportunity to assemble a sizable sample of confirmed cbGRB events.Analyzing this collection could shed light on whether kilonova-associated sbGRBs and lbGRBs form a continuous spectrum or represent distinct classes.This, in turn, may enable us to deduce whether HMNSs, BHs, or both, serve as the primary progenitors of sbGRBs.

Figure 1 .
Figure1.The jet power evolution of post-merger accretion disks for varying levels of magnetic flux ranging from non-MAD to MAD.Gray lines show the post-merger mass accretion rate evolution (right vertical axis) obtained for 4 BH-NS merger simulations(Gottlieb et al. 2023b) and the 5 BNS merger simulations presented here, all of which generate massive disks M d ≈ 0.1 M ⊙ .The purple line delineates the logarithmic average of these mass accretion rates, which constitutes the maximum jet power assuming η a = 1 corresponding to a BH spin a ≈ 0.87 (left vertical axis).Turquoise lines illustrate schematically the jet power evolution for different assumptions about the dimensional magnetic flux threading the BH, Φ, and the corresponding total jet energy, E j .Since the magnetic flux on the BH is likely accumulated early and hence remains nearly constant before the disk transitions to MAD, the jet power, P j , is also predicted to be roughly constant at these times.However, once the dimensionless magnetic flux saturates in the MAD state, the jet power saturates at P j = Ṁc 2 and thus follows the mass-accretion rate Ṁ ∝ t −2 thereafter (we have extrapolated P j by a dashed line to later times).The yellow (blue) region outlines the estimated average jet power and duration T 90 (T 50 ) of the sbGRB (lbGRB) population based on prompt emission and afterglow observations (see text).While the jets from such massive disks are either too powerful, or operate for too long, compared to the sbGRB population, BH accretion from such massive disks nicely matches the observed properties of lbGRBs.

Figure 3 .
Figure3.An illustration of how the underlying physics of the merger product (orange) in the hybrid and all-BH scenarios (red) translates into different phases in the cbGRB light curves: sbGRB (yellow), lbGRBs (blue) and preceding and succeeding phases (green).Representations of the light curves of the lbGRB 211211A(Rastinejad et al. 2022) and sbGRB 930131A(Kouveliotou et al. 1994) are shown in black and gray, respectively, in a log-log scale.