GRB 221009A with an unconventional precursor: a typical two-stage collapsar scenario?

As the brightest Gamma-Ray burst (GRB) ever detected, GRB 221009A may offer a chance that reveals some interesting features which are hidden in those bursts that are not so bright. There seems a very weak emission with a flux of $10^{-8}\sim10^{-7}$ erg cm$^{-2}$ s$^{-1}$ between the first pulse ($T_0\sim T_0+50$~s, $T_0$ is the trigger time) and the main burst (appears from $T_0+180$ s). Thus the gap time between them is not really quiescent, and the first pulse could be taken as an unconventional precursor, which may provide a peculiar case study for the GRB-precursor phenomena. A two-stage collapsar scenario is proposed as the most likely origin for this burst. In this model, the jet for the precursor is produced during the initial core-collapse phase, and should be weak enough not to disrupt the star when it breaks out of the envelope, so that the fallback accretion process and the forming of the disk could continue. We present an approach in which the duration and flux both provide constraints on the luminosity ($L_{\rm j}$) and the Lorentz factor at the breakout time ($\Gamma_{\rm b}$) of this weak jet. The estimated $L_{\rm j}\lesssim 10^{49}$ erg s$^{-1}$ and $\Gamma_{\rm b}$ has an order of ten, which are well consistent with the theoretical prediction. Besides, the weak emission in the gap time could be interpreted as a MHD outflow due to a magnetically driven wind during the period from the proto-neutron star phase to forming the accretion disk in this scenario.


Introduction
Precursors are usual for bright, long gamma-ray bursts (GRBs; ∼20%; e.g., Lazzati 2005) and the emission types and jet compositions of their precursors and main bursts are listed in Table 1.A quasi-thermal (QT) component could be observed in precursors, as shown in Types 2, 3, and 4, while most of the precursors are found to be nonthermal (NT; e.g., Li & Mao 2022).There are some models or mechanisms for precursors of long bursts.Fireball-internal shock (IS) models (e.g., Mészáros & Rees 2000;Ramirez-Ruiz et al. 2002;Wang & Mészáros 2007) and jet-cocoon interaction (e.g., Nakar & Piran 2017) both predict a precursor with a QT component, as shown in Types 2, 3, and 4 in Table 1; the quiescent time for the former is estimated to be about 10 s.The jet-cocoon interaction mechanism and the "twostage" model (e.g., Cheng & Dai 2001;Wang & Mészáros 2007) both correspond to a scenario of a collapsar.In the "two-stage" scenario, the precursor is from a weak jet that may be produced by a collapsed core (e.g., a LeBlanc & Wilson jet; LeBlanc & Wilson 1970) or by a rotating proto-neutron star (PNS) during the initial core-collapse phase, while the quiescent time ∼100 s is the timescale of fallback and the forming of a proto-compact star with an accretion disk; the central engine of the main burst is a black hole (BH) or neutron star (NS).The process of the "two-stage" model is shown in Figure 1.In the "magnetar-switch" model (Bernardini et al. 2013), the precursor and the main burst arise from the accretion of matter onto the surface of the magnetar; the accretion process can be halted by the centrifugal drag exerted by the rotating magnetosphere onto the infalling matter, allowing for multiple precursors and very long quiescent times.Lipunov's works (e.g., Lipunov & Gorbovskoy 2007;Lipunova et al. 2009) suggest a collapsing "spinar" similar to the "two-stage" model, without any accretion in the process.The origins for precursors are still under debate in some works (e.g., Lazzati 2005;Burlon et al. 2009;Bi et al. 2018;Li & Mao 2022), and it is of importance to perform precursor research to understand the physical mechanisms of the GRB central engine.
In this analysis, the so-called precursor in GRB 221009A is not conventional, because the "quiescent" time is not really quiescent.Note that in former works (e.g., Burlon et al. 2009), a time interval during which the background (BG)-subtracted light curve is consistent with zero is defined as a "quiescent" time.For GRB 221009A, there exist some weak emissions between the first pulse (T 0 ∼ T 0 + 50 s; T 0 is the trigger time) and the main burst beginning at T 0 + 180 s, as shown in Figures 2(a) and (b).However, we still could use the mechanisms for precursors to interpret its origin.
The paper is organized as follows.In Section 2, we extract the observational properties of the first pulse (T 0 ∼ T 0 + 50 s) and the followed weak emissions (T 0 + 50 s ∼T 0 + 170 s).In Section 3, several scenarios for the precursor and jet launching are discussed.In Section 4, a conclusion and summary are given based on the discussion.

The Observational Properties of the First Pulse and Weak Emissions
BG estimation for the extremely long GRB 221009A is important.We use the data from a nearby orbit as BG for the GBM Na I 8 detector and a polynomial with 0-2 orders for the GBM bismuth germanate (BGO) 0 detector above 385 keV.The details are shown in the Appendix.As shown in Figures 2(a) and (b), some weak emissions exist between the first pulse and the main burst, and are mainly from the lower-energy band (100 keV).The first pulse lasts ∼50 s.After a very weak emission with a duration of around 70 s, a long bump of 60 s comes before the main burst, as shown in Figure 2(c).
2.1.The First Pulse from T 0 to T 0 + 50 s Fittings with BAND, an exponential cutoff power law (CPL), and a power-law (PL) function3 are performed on the time-integrated spectrum from T 0 to T 0 +10 s, which contains 80% photons.The Markov Chain Monte Carlo fitting is performed to find the parameters with the maximum Poisson likelihood.The BAND model is determined to be the best model by the method of the Bayesian information criterion (BIC; Wei et al. 2016), requiring ΔBIC to be at least 6 (please refer to the footnote). 4With the contribution from the HXMT/CsI detectors, which have a large effective area in the high-energy region (Song et al. 2022a), the low-energy photon index (α), the high-energy photon index (β), and the peak energy (E p ) of the νF ν spectrum are determined to be α = −1.55 ± 0.03, β = − 2.02 ± 0.02, and E p = 242.9± 113.0 keV, as shown in Figure 2(d), with a flux of -+ -2.00 10 0.17 0.34 6 erg cm −2 s −1 .The low photon energy index α < − 2/3 (the so-called "line of death"; Preece et al. 1998), which is well consistent with the synchrotron mechanism.In comparison, Lesage et al. (2023) 1.98 10 0.03 0.03 6 erg cm −2 s −1 , and E p ∼ 4 MeV with GBM and LAT data; the slightly different value of α and the much higher E p may be due to the different modeling used in Lesage et al. (2023).We note that our E p is consistent with that (E p = 281.8± 13.8 keV) obtained with the GBM and HEBS data in Yang et al. (2023).The constant-cadence (Burgess 2014) method and Bayesian blocks (BBlocks; Scargle et al. 2013) method with a false alarm probability p 0 = 0.01 are used for binning in time-resolved analysis.We also require a signal-to-noise ratio (S/N) 30 at least in one detector, so we combine some adjacent bins.The time bins are [0., 1.2], [1.2, 2.4], [2.4,3.9], [3.9, 6.7], and [6.7, 10] s.The evolution of α is shown in Figure 2(e).Generally, the double-tracking trend of the α-flux and E p -flux, is observed in the first 10 s, which is well consistent with that of the onezone synchrotron model (e.g., Uhm & Zhang 2014;Li et al. 2019).Note that α < −1 for the first pulse, implying that NT emission is dominant.The internal-collision-induced magnetic reconnection and turbulence mechanism (ICMART; Zhang & Yan 2011) is preferred as the one-zone synchrotron model for this NT emission mainly.

The Weak Emissions between the First Pulse and the Main Burst
The emission from T 0 + 50 s to T 0 + 115 s has S/N ∼ 10 in the Na I 8 detector.Therefore, it is difficult to describe the shape of spectrum.The observed flux is estimated to be ∼10 −8 erg cm −2 s −1 with the PL model, as shown in Figure 2(f).The long bump from T 0 + 115 s to T 0 + 172 s is best described by the CPL function with α = − 1.00 ± 0.15 and E p = 78.5 ± 8.0 keV.The flux is ∼10 −7 erg cm −2 s −1 , as shown in Figure 2(g).Lesage et al. (2023) suggested the possible existence of a photospheric component in this weak emission; however, we consider that this emission is too weak to justify an additional thermal component in the modeling.Conservatively, the order of magnitude of the flux is used in the following analysis, which does not affect our conclusion.

The Possible Origin of the First Pulse
There are some common characteristics between the first pulse in GRB 221009A and the conventional precursor: it is much weaker than the main burst and there is a gap time from the main burst.Thus, several models or mechanisms for precursors could be used to interpret the origins of the first pulse as well.Fireball-IS models and jet-cocoon interaction are excluded first, because there does not seem to be any evident QT component in the emission of the precursor, as discussed in Section 2.1.
Besides, the gap time between the precursor and the main burst is too long (∼100 s) for the fireball-IS model.In the fireball-IS model, the gap time is contributed by three parts (e.g., Wang & Mészáros 2007).The first part (t 1 ) is the time that the rarefaction wave takes to arrive at the reverse shock.Once the jet head reaches the stellar surface, the pressure in front of the jet head decreases suddenly, and a rarefaction wave will form and propagate back into the shocked jet material at the speed of sound ( = c c 3 s ).The width of the shocked jet is less than the distance from the core to the envelope (r), thus t 1  r/c s ; 6r 11 s.The second part (t 2 ) is from the time that the unshocked jet passes through the envelope, t 2 = r/c = 3r 11 s.
The IS dissipation occurs at about R d as the beginning of the main burst, and the third part (t 3 ) is the delay between the main burst and the precursor, 2 .The gap time is the sum of t 1 , t 2 , and t 3 and has an order of 10 s.
It seems that the "two-stage," "magnetar-switch," and spinar models could be consistent with the NT emission for the precursor and long gap time.Here we define two quantities: (1) the Lorentz factor Γ b at the breakout time of the jet for the precursor, which is the Lorentz factor when the jet breaks out of the envelope and can be taken as the maximum Lorentz factor of the jet passing through the envelope;5 and (2) the luminosity of the jet (L j ) for the precursor.In the "magnetarswitch" and spinar models, Γ b and L j are not constrained especially, while for the two-stage model, the jet for the precursor should be weak enough not to disrupt the star, so that the fallback accretion process and the forming of the disk can continue.In detail, a mild Γ b < 100 and the released energy 10 50 erg are both required (Wang & Mészáros 2007).Therefore, the estimation of L j and Γ b for the first pulse is important.The "two-stage" model can be excluded if a weak jet is not consistent with the data.The first pulse of GRB 221009A has a long duration of tens of seconds (80% of photons are in ∼10 s).Thus, t b  10 s, where t b is the time taken by the jet head to move from the interior of the star to the surface.
Assuming the jet acceleration is saturated, we have Equation (12) in Wang & Mészáros (2007) to describe the relation among Γ b , L j , and t b : 1 4 b,10 3 4 where r ∼ 10 11 cm is the distance from the core to the envelope; CGS6 units are used here.The flux in the first 10 s is ∼2 × 10 −6 erg cm −2 s −1 (L iso,γ ∼ 10 50 erg s −1 with redshift z = 0.151, from de Ugarte Postigo et al. (2022); here, L iso,γ denotes E iso,γ /T and T is the duration time in the rest frame of the central engine; T = T obs /(1 + z) with T obs is that in the rest frame of the observer, thus, the isotropic-equivalent luminosity L iso could be 10 50 ∼ 10 51 erg s −1 (L iso = L iso,γ /ò γ with radiative efficiency ò γ ∼ 50%-90% for the ICMART mechanism; Zhang & Yan 2011).Considering the opening angle (θ b ) at the breakout time ∼1/Γ b and q L L 2 j i s o b 2 , we have Here, we present an approach to limit L j and Γ b .By combining the above equation and constraint, the region for the possible values for L j and Γ b is the overlap of these two, as shown in Figure 3 in dark blue.The range of L j corresponds to 10 48 erg s −1 , and Γ b has an order of 10, which is well consistent with the weak-jet assumption.Note that this estimation is approximate with the orders of magnitude of these quantities, e.g., r 11 ∼ 1 and L iso,51 ∼ 1.For specific values, the orders of magnitude of the results will not be changed much.If we use the full time of the first pulse, t b  50 s, the edge of the violet shadow in Figure 3 that denotes the lower limit of the Γ b will move to the lower range according to Constraint (1); L iso,γ ∼ 2.5 × 10 49 erg s −1 is smaller, thus the possible Γ b and L j become much smaller that those with t b  10 s.
For the unsaturated acceleration case, as already calculated in Equation (11) in Wang & Mészáros (2007) for t b  10 s, Γ b  10.In this case, the upper limit of is still weak with luminosity of 10 48 ∼ 10 49 erg s −1 , since L iso ∼ 10 50 -10 51 erg s −1 .
Therefore, from the above discussion, the observed flux and duration of this pulse both provide constraints on L j  10 49 erg s −1 in this case.Otherwise, a shorter duration or larger luminosity could result in a larger Γ b or L j , so that the assumption of a weak jet fails.Note that the estimated θ b is not small and the weak jet from the initial collapsar is an axial jet (e.g., LeBlanc & Wilson 1970); the strong jet of the main burst launched by, e.g., the Blandford-Znajek (BZ) mechanism (Blandford & Znajek 1977), is also in the axial direction of rotation, thus we still could see the burst with the first pulse, though the latter is highly collimated with a much smaller opening angle.
Another constraint for the origin is the weak emission between the first pulse and the huge main burst.As estimated in Section 2.1, the flux of the weak emission has an order of 10 −8 ∼ 10 −7 erg cm −2 s −1 , which is one to two magnitudes smaller than that of the first pulse (∼10 −6 erg cm −2 s −1 ).In a collapsar scenario of the "two-stage" model, the "quiescent" time is the timescale of the period from the PNS phase to forming an accretion disk.During this time, the newborn NS would launch a strong neutrino-driven wind, or a magnetically driven wind due to the differential rotation of the NS.A semianalytical spindown formula (Siegel et al. 2014) for a magnetically driven wind gives a luminosity of ( ) where B is the surface magnetic field strength at the polar cap region, R is the radius of the NS, and P is the period.It seems that this spindown mechanism could produce an MHD outflow with luminosity of one to two magnitudes smaller than that of the first pulse (∼10 49 erg s −1 ) if the values of B, R, and P are in reasonable ranges.
For the "magnetar-switch" model, the longer the waiting time, the higher the stored energy available for the next emission episode.The "quiescent" time for GRB 221009A is long, and the main burst is extremely bright, which seems consistent with the prediction of "magnetar-switch."There are three mechanisms of energy extraction for a magnetar as a central engine for a GRB, including: (1) spindown controlled by magnetic dipole radiation; (2) extracting the differential rotational energy of the NS through erupting magnetic bubbles by winding up the poloidal magnetic field into the a toroidal configuration (Kluźniak & Ruderman 1998); and (3) accretion.In the propeller mechanism, the accretion process can be halted by the centrifugal drag exerted by the rotating magnetosphere onto the infalling matter, and during the halting time, there should be no evident emission emitted.The weak emission of 60 s before the main burst is not predicted in this model.If "magnetar-switch" works, it is necessary to interpret the long bump of 60 s before the main burst, at least.If we assume it is not from the beginning of the re-accretion, it must be from the magnetic dipole radiation or the erupting magnetic bubbles.The former should exist during the burst and does not begin at T 0 + 112 s; the latter occurs at a hot PNS phase, and the released energy (∼10 51 erg) seems too high for the bump.If it is the beginning of the re-accretion, it is not reasonable that it lasts ∼60 s with a very low luminosity (∼10 49 erg s −1 , corresponding to ∼10 −7 erg cm −2 s −1 at the distance of this GRB) as the next emission episode with high energy.Moreover, the "magnetar-switch" scenario offers a good explanation for these GRBs, whose precursors have spectral and temporal properties similar to the main prompt emission and smaller, but comparable, energetics (Bernardini et al. 2013), because the origins for precursors and main bursts are the same in this model.It is significant that the energies released in the precursor and the main emission are not comparable for GRB 221009A.Therefore, considering these inconsistencies, the "magnetar-switch" model may be not the best interpretation for GRB 221009A.
In the scenario of the spinar model, the details for a weak jet corresponding to the precursor are not predicted or constrained.It also occurs in a collapsar scenario, thus we think the production of the long bump may be similar to that in the twostage model.There is not enough information for us to rule out or accept it.Table 2 is a summary of the consistency between the mechanisms for GRB precursors and the observational properties of GRB 221009A.If one property could be interpreted or predicted by the mechanism, the corresponding blank in the table is filled with "Yes"; otherwise, "No" is filled for the inconsistency and "…" is for the case of no prediction.For example, the weak jet is not predicted in the spinar model, thus the blank is filled with "…." In general, from the analysis of the first pulse or precursor and the "quiescent" time, it is proposed that the properties of the first pulse are well consistent with the prediction by the mechanism for the precursor in the "two-stage" model in the collapsar scenario.Moreover, the first pulse is different from the traditional definition of the precursor because of the weak emission in the gap time.

Discussion and Summary
We present an approach to infer the possible ranges of Γ b and L j of the jet for the first pulse with constraints from the duration and flux in a collapsar scenario.Furthermore, this approach could be used to speculate on the origins of the precursors of GRBs in a future study.
The first pulse of GRB 221009A is NT, which is the difference between GRB 221009A and GRB 160625B (e.g., Zhang et al. 2018); the first precursor of the latter is dominated by a thermal component.In the scenario of GRB 160625B, the precursor occurs after the formation of the accretion disk.As a comparison, we consider that for GRB 221009A the precursor is from the weak jet produced by a rotating PNS during the initial core-collapse phase, rather than the initial prompt accretion phase, as shown in Figure 1.Considering the estimated luminosity (10 49 erg s −1 ) with a duration of tens of seconds, the total energy (∼10 50 erg) the jet carried is well consistent with that predicted by, e.g., LeBlanc & Wilson (1970) and Wheeler et al. (2000).In summary, the origin for the first pulse is discussed conservatively in this analysis, and a weak jet from the initial core-collapse phase in the "two-stage" scenario is taken as the most likely origin, while the other origin for the precursor, the spinar model, is not ruled out.
As the brightest GRB ever detected, GRB 221009A may provide a case that reveals some interesting features that are hidden in those bursts that are not so bright.If the source of the burst had a high z, or the observations were not so head-on, the weak emission in the gap time might be missed in the detection.In that case, the gap time seems quiescent and the first pulse should seem similar to the precursors detected before.However, in GRB 221009A, a weak emission during the gap time is observed that enriches the GRB precursor phenomena, and is important for us to understand the physical mechanisms of the GRB central engine.
S. thanks Dr Ming-Yu Ge and Dr Yuan You for the suggestions on the BG estimation.

Appendix About BG Estimation
The BG estimation for the extremely long GRB 221009A is important.Figure 4 shows the event data from the nearby orbits, which help us to know the shape of the BG.The shift time (∼5720 s) is determined by the smallest sum of squares of the difference between the two light curves from T 0 − 1000 s to T 0 from GRB 221009A and the nearby orbits.Figure 5 shows the light curves and event data from the nearby orbits as BG in different energy bands.The BG could be well described by the data from the nearby orbits for the Na I 7 and 8 detectors.However, from Figures 4(c) and 5(c) for BGO data, the nearby data are not very consistent with those from the trigger of GRB 221009A.From above 385 keV, we find that the GRB event ends at ∼600 s.Therefore, we could use a polynomial to describe T 0 +[−1100, −5] s and [900, 2400] s, so that the peaking structure could be well described.The contribution below 385.2 keV in BGO 0 (channels 0-5) is ignored in the fitting procedure.

Figure 2 .
Figure 2. (a) The light curve and BG shape from the data of Na I 8.(b) The BG-subtracted light curves in different energy bands of Na I 8. (c) The light curve from T 0 to T 0 + 200 s.(d) The spectrum of the first pulse.(e) The light curves from the GBM Na I 8 detector and HXMT, α, and E p values of the precursor.(f) The spectrum of T 0 + 50 s to T 0 + 115 s.(g) The spectrum of T 0 + 115 s to T 0 + 172 s.

Figure 3 .
Figure 3.The relation between Γ b and L j in Equation (2) in red dotted lines of different L iso .The violet shadow denotes the possible Γ b − L j only with Constraint (1) if t b  10 s.The dark blue shadow denotes the region of possible Γ b and L j .

Figure 4 . Zhang Figure 5 .
Figure 4.The light curves of BGO, Na I 7, and Na I 8 from T 0 − 1100 s to T 0 + 2500 s and nearby orbits.

Table 1
The Emission Types of Long GRBs with Precursors Figure 1.A scenario for the "two-stage" model of precursors.