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

Xin-Ying Song Key Laboratory of Particle Astrophysics, Institute of High
Energy Physics, Chinese Academy of Sciences, Beijing 100049, China  University
of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049,
China  Shuang-Nan Zhang  Key Laboratory of Particle Astrophysics, Institute of
High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
University of Chinese Academy of Sciences, Chinese Academy of Sciences,
Beijing 100049, China

###### Abstract

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
$10^{-8}\sim 10^{-7}$ 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.

gamma-ray bursts:individual–radiation mechanisms: non-thermal

##  1 Introduction

Precursors are usual for bright, long GRBs ($\sim 20\%$, e.g., Lazzati, 2005)
and the emission types and jet compositions of their precursors and main
bursts are listed in Table 1. 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 non-thermal (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 quasi-thermal (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. Jet-
cocoon interaction mechanism and the ‘two-stage’ 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 which may be
produced by a collapsed core ( e.g., LeBlanc & Wilson jet, LeBlanc & Wilson,
1970) or by a rotating proto-neutron star (PNS) during the initial core-
collapse phase, while the quiescent time $\sim$100 s is the timescale of
fallback and forming 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 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 the
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 the former
works (e.g. Burlon et al., 2009), a time interval during which the background
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
($T_{0}\sim T_{0}+50$ s, $T_{0}$ is the trigger time) and the main burst
beginning at $T_{0}+180$ s, as shown in Figure 2 (a) and (b). However, we
still could use the mechanisms for precursors to interpret its origin.

‘two-stage’ model

Figure 1: A scenario for the ‘two-stage’ model of precursors.

GRB 221009A was detected by many missions, such as Fermi/GBM (GCN 31565,
Lesage & Fermi Gamma-ray Burst Monitor Team, 2022), Fermi-LAT (GCN 32637,
Bissaldi et al., 2022), Swift/BAT/XRT (GCN 32632, Dichiara et al., 2022),
Konus-Wind (GCN 31604, Svinkin et al., 2022), Insight-HXMT (ATel 155660, Tan
et al., 2022), HEBS (GCN 32751, Liu et al., 2022) and LHAASO (GCN 32677, Huang
et al., 2022). For GRB 221009A, the prompt emission has a long duration $\sim
1000$ s. The isotropic-equivalent radiated energy $E_{\rm iso,\gamma}\sim
10^{55}$ erg has been reported in some works (e.g., Frederiks et al., 2023; An
et al., 2023). Note that the jet of the main burst is highly collimated with a
small opening angle $\theta\sim 1.0^{\circ}$ (Ren et al., 2022; An et al.,
2023), thus, the outflow has a total energy of $f_{\rm b}E_{\rm iso}\sim
10^{51\sim 52}$ erg with $f_{\rm b}\sim\theta^{2}/2$ and $E_{\rm iso}=E_{\rm
iso,\gamma}+E_{\rm iso,\rm k}$, where $E_{\rm iso,\rm k}$ is the isotropic-
equivalent kinematic energy and has an order of $10^{55}$ erg. This is a
typical released energy for a collapsar to form a BH or a magnetar (e.g.,
MacFadyen et al., 2001), though GRB 221009A is the brightest ever detected in
terms of $E_{\rm iso,\gamma}$.

The paper is organized as follows. In Section 2, we extract the observational
properties of the first pulse ($T_{0}\sim T_{0}+50$ s) and the followed weak
emissions ($T_{0}+50$ s $\sim$ $T_{0}+170$ 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.

Table 1: The emission types of long GRBs with precursors. QT: quasi-thermal; NT: non-thermal. Type No. | 1 | 2 | 3 | 4 | 5
---|---|---|---|---|---
precursor | NT | QT | QT+NT | QT | NT
main burst(or following episodes) | NT | NT | NT | QT+NT | QT+NT

##  2 The observational properties of the first pulse and weak emissions

Background (BG) estimation for extremely long GRB 221009A is important. We use
the data from nearby orbit as BG for GBM NaI 8 detector, and polynomial with
0-2 orders for GBM BGO 0 detector above 385 keV. The details are shown in
Appendix A. As shown in Figure 2 (a) and (b), some weak emissions exist
between the first pulse and the main burst, and are mainly from the lower
energy band ($\lesssim 100$ keV). The first pulse lasts $\sim 50$ s. After a
very weak emission with duration of around 70 s, a long bump of 60 s comes
before the main burst as shown in Figure 2 (c).

(a) NaI 8
(b) NaI 8

Figure 2:  (a) The light curve and BG shape from the data of NaI 8. (b) The BG
subtracted light curves in different energy bands of NaI 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 GBM NaI 8 detector and HXMT, $\alpha$ and $E_{\rm p}$
values of 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.

(c)
(d) $T_{0}$ to $T_{0}+10$ s (e)

(f) $T_{0}+50$ s to $T_{0}+115$ s(g) $T_{0}+115$ s to $T_{0}+172$ s
Figure. 2— Continued.

###  2.1 The first pulse from $T_{0}$ to $T_{0}+50$ s

Fittings with BAND, exponential cut-off power law (CPL), and power law (PL)
function111 The formulae for spectral models, BAND, CPL, PL could be found in
the Appendix in Song et al. (2022a). are performed on the time-integrated
spectrum from $T_{0}$ to $T_{0}$+10 s which contains $80\%$ photons. The
Markov Chain Monte Carlo (MCMC) 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 bayesian information criterion (BIC, Wei et al.,
2016), and require $\Delta$BIC is at least 6222$\Delta$BIC$\geq 10$, the
preference is very strong; $10>\Delta$BIC$\geq 6$, strong; $6>\Delta$BIC$\geq
2$, positive. . If with the contribution from HXMT/CsI detectors which have
large effective area in high energy region (Song et al., 2022b), the low
energy photon index ($\alpha$), the high energy photon index ($\beta$) and the
peak energy ($E_{\rm p}$) of $\nu F_{\nu}$ spectrum is determined to be
$\alpha=-1.55\pm 0.03$, $\beta=-2.02\pm 0.02$ and $E_{\rm p}=242.9\pm 113.0$
keV as shown in Figure 2 (d). The low photon energy index $\alpha<-2/3$ (the
so-called ‘line of death’, Preece et al., 1998), which is consistent well with
the synchrotron mechanism.

The constant cadence (CC, 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 the signal-to-
noise ratio (S$/$N) $\geq$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], [6.7, 10] s. The evolution of $\alpha$ is shown in Figure 2 (e).
Generally, the double-tracking trend of $\alpha$-flux and $E_{\rm p}$-flux, is
observed in the first 10 s, which is consistent well with that of one-zone
synchrotron model (e.g., Uhm & Zhang, 2014; Li et al., 2019). Note that
$\alpha<-1$ for the first pulse, implies non-thermal (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.

###  2.2 The weak emissions between the the first pulse and the main burst

The emission from $T_{0}+50$ s to $T_{0}+115$ s has S/N$\sim 10$ in NaI 8
detector. Therefore, it is difficult to describe the shape of spectrum. The
observed flux is estimated to be $\sim 10^{-8}$ erg cm-2 s-1 with 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 CPL function with $\alpha=-1.00\pm 0.15$ and $E_{\rm
p}=78.5\pm 8.0$ keV. The flux is $\sim 10^{-7}$ erg cm-2 s-1 as shown in
Figure 2 (g).

##  3 the possible origin of the first pulse

There are some common characteristics between the first pulse in GRB 221009A
and the conventional precursor: much weaker than the main burst and a gap time
from the main burst. Thus, several models or mechanisms for precursors could
be used to interpret origins of the first pulse as well. Fireball-internal
shock (IS) models and jet-cocoon interaction are excluded first, because there
seems not 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
($\sim 100$ 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 ($c_{\rm
s}=c/\sqrt{3}$). The width of the shocked jet is less than the distance from
the core to the envelope ($r$), thus $t_{1}\lesssim r/c_{\rm s}\simeq 6r_{11}$
s. The second part ($t_{2}$) is from the time that the unshocked jet pass
through the envelop, $t_{2}=r/c=3r_{11}$ s. The internal shock dissipation
occurs at about $R_{d}$ as the beginning of the main burst, and the third part
($t_{3}$) is the delay of the main burst to the precursor,
$t_{3}=R_{d}/2\Gamma^{2}c=1.7R_{d,15}\Gamma^{-2}_{2}$ s. 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 $\Gamma_{\rm b}$ 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;333Note that $\Gamma_{\rm b}$ may be not
the maximum Lorentz Factor of the jet ($\Gamma$) and $\Gamma_{\rm b}<\Gamma$;
(2) the luminosity of the jet ($L_{\rm j}$) for the precursor. In the
‘magnetar-switch’ and spinar model, $\Gamma_{\rm b}$ and $L_{\rm j}$ 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 could continue. In details, a
mild $\Gamma_{\rm b}<100$ and the released energy $\lesssim 10^{50}$ erg are
both required (Wang & Mészáros, 2007). Therefore, the estimation of $L_{\rm
j}$ and $\Gamma_{\rm b}$ 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 ($80\%$ photons
are in $\sim$10 s). Thus, $t_{b}\lesssim 10$ 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 $\Gamma_{\rm b}$, $L_{\rm j}$
and $t_{\rm b}$,

$\Gamma_{\rm b}\gtrsim 10r_{11}^{1/2}L_{\rm j,49}^{-1/4}t_{\rm b,10}^{-3/4},$
(1)

where $r\sim 10^{11}$ cm is the distance from core to envelope; CGS444the
convention $Q=10^{n}Q_{n}$ is adopted for CGS units. units are used here. The
flux in the first 10 s is $\sim 2\times 10^{-6}$ erg cm-2 s-1 ($L_{\rm
iso,\gamma}\sim 10^{50}$ erg s-1 with redshift $z=0.151$ from de Ugarte
Postigo et al. (2022); here $L_{\rm iso,\gamma}$ denotes $E_{\rm
iso,\gamma}/T$, $T$ is the duration time in the rest frame of central engine;
$T=T_{\rm obs}/(1+z)$ with $T_{\rm obs}$ is that in the rest frame of the
observer), thus, the isotropic-equivalent luminosity $L_{\rm iso}$ could be
$\gtrsim 10^{50}\sim 10^{51}$ erg s-1 ($L_{\rm iso}=L_{\rm
iso,\gamma}/\epsilon_{\gamma}$ with radiative efficiency
$\epsilon_{\gamma}\sim 50\%-90\%$ for ICMART mechanism, Zhang & Yan, 2011).
Considering the opening angle ($\theta_{\rm b}$) at the breakout time $\sim
1/\Gamma_{\rm b}$ and $L_{\rm j}\sim L_{\rm iso}\theta_{\rm b}^{2}/2$, we have

$\Gamma_{b}\sim(2L_{\rm j}/L_{\rm iso})^{-1/2}.$ (2)

Here, we present an approach to limit $L_{\rm j}$ and $\Gamma_{\rm b}$. By
combining the above equation and constraint, the region for the possible
values for $L_{\rm j}$ and $\Gamma_{\rm b}$ is the overlap of these two as
shown in Figure 3 in dark blue. The range of $L_{\rm j}$ corresponds to
$\lesssim 10^{48}$ erg s-1, and $\Gamma_{b}$ has an order of 10, which is
consistent well with the weak jet assumption. Note that this estimation is
approximate with the orders of magnitudes of these quantities, e.g.,
$r_{11}\sim 1$ and $L_{\rm iso,51}\sim 1$. For specific values, the order of
magnitudes of the results will not be changed much. If we use the full time of
the first pulse, $t_{b}\lesssim 50$ s, the edge of the violet shadow in Figure
3 which denotes the lower limit of the $\Gamma_{\rm b}$ will move to the lower
range according to Constraint (1); $L_{\rm iso,\gamma}\sim 2.5\times 10^{49}$
erg s-1 is smaller, thus the possible $\Gamma_{\rm b}$ and $L_{\rm j}$ become
much smaller that those with $t_{b}\lesssim 10$ s.

$t_{\rm b}\lesssim 10s$

Figure 3: The relation between $\Gamma_{\rm b}$ and $L_{\rm j}$ in Equation
(2) in red dotted lines of different $L_{\rm iso}$. The violet shadow denotes
the possible $\Gamma_{\rm b}-L_{\rm j}$ only with the Constraint (1) if
$t_{\rm b}\lesssim 10$ s. The dark blue shadow denotes the region of possible
$\Gamma_{\rm b}$ and $L_{\rm j}$.

For the unsaturated acceleration case, as already calculated in Equation (11)
in Wang & Mészáros (2007) for $t_{\rm b}\lesssim 10$ s, $\Gamma_{\rm b}\gtrsim
10$. In this case, the upper limit of $\theta_{\rm b}\lesssim 0.1$, so that
$L_{\rm j}\sim L_{\rm iso}\theta_{\rm b}^{2}/2$ is still weak with luminosity
of $10^{48}\sim 10^{49}$ erg s-1, since $L_{\rm iso}\sim 10^{50}-10^{51}$ erg
s-1.

Therefore, from the above discussion, the observed flux and duration of this
pulse both provide constraints on $L_{\rm j}\lesssim 10^{49}$ erg s-1 in this
case. Otherwise, a shorter duration or larger luminosity could result in a
larger $\Gamma_{\rm b}$ or $L_{\rm j}$, so that the assumption of a weak jet
fails. Note that the estimated $\theta_{\rm b}$ 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.

One question arises that there may be a possible jet-cocoon interaction during
the jet passing through the envelop. If $\Gamma_{\rm b}$ is large enough, the
mixing between the two components (the jet material and a stellar material
shocked by the expanding high pressure cocoon) could be ignored. As simulated
numerically in Nakar & Piran (2017), a relativistic cocoon may produce a short
(a few seconds) extremely bright QT burst (with the observed temperature of
$10\mbox{--}$100 keV) as the precursor. Otherwise, if $\Gamma_{\rm b}$ is
small enough, the partial mixing occurs (Nakar & Piran, 2017). As a result,
optical/UV emission should appear with temperature of $\sim 10^{4}$ K, beyond
the observed precursor phase; unfortunately, the optical/UV observations
started much later and can not offer more information on this. There is no
evident thermal component observed in the precursor, furthermore, most of
emission in the precursor is NT at least. This might be also evidence that the
jet responsible for the precursor is weak with a mild Lorentz Factor.

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 $10^{-8}\sim 10^{-7}$ erg cm-2 s-1, which is one to
two magnitudes smaller than that of the first pulse ($\sim 10^{-6}$ erg cm-2
s-1). In a collapsar scenario of the ‘two-stage’ model, the ‘quiescent’ time
is the time scale 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 semi-analytical spindown formula (Siegel et al., 2014) for a
magnetically driven wind gives a luminosity of

$L\simeq 10^{48}B^{2}_{14}R^{3}_{6}P^{-1}_{-4}{\rm erg\,s}^{-1},$ (3)

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 a MHD outflow with luminosity of one to two magnitudes
smaller than that of the first pulse ($\sim 10^{49}$ 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) spin down controlled by magnetic dipole radiation, 2) extracting
differential rotational energy of the NS through an 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 ($\sim 10^{51}$ erg)
seems too high for the bump. If it is the beginning of the re-accretion, it is
not reasonable that it lasts $\sim 60$ s with a very low luminosity ($\sim
10^{49}$ erg s-1, corresponding to $\sim 10^{-7}$ 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 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 two-stage 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 ‘?’.

Table 2: The consistency between the mechanisms for precursors and GRB 221009A. GRB 221009A/mechanisms for precursors | fireball-IS | jet-cocoon interaction | two-stage | magnetar-switch | spinar
---|---|---|---|---|---
Long gap time($\sim 100$ s) | No | Yes | Yes | Yes | Yes
NT precursor | No | No | Yes | Yes | Yes
The jet corresponding to precursor is weak enough | No | No | Yes | No | ?
The long bump ($\sim 60$ s, $10^{-7}$ erg cm-2 s-1) before the main burst | No | No | Yes | No | ?

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 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.

##  4 discussion and summary

We present an approach to infer the possible ranges of $\Gamma_{\rm b}$ and
$L_{\rm j}$ of the jet for the first pulse with the constraints from the
duration and flux in a collapsar scenario. Furthermore, this approach could be
used to speculate the origins of the precursors of GRBs in the future study.

The first pulse of GRB 221009A is non-thermal, 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 ($\lesssim 10^{49}$ erg s-1) with duration of tens of
seconds, the total energy ($\sim 10^{50}$ erg) the jet carried is well
consistent with that predicted by e.g. LeBlanc & Wilson (1970); 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 which 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 which enriches the
GRB-precursor phenomena, and is important for us to understand the physical
mechanisms of the GRB central engine.

The authors thank supports from the National Program on Key Research and
Development Project (2021YFA0718500). This work was partially supported by
International Partnership Program of Chinese Academy of Sciences (Grant
No.113111KYSB20190020). The authors are very grateful to the GRB data of
Fermi/GBM, HXMT and HEBS and konus-Wind. We are very grateful for the comments
and suggestions of the anonymous referees. Dr. Xin-Ying Song thanks Dr Ming-Yu
Ge and Dr Yuan You for the suggestions on the background estimation.

##  Appendix A About background estimation

The background (BG) estimation for extremely long GRB 221009A is important.
Figure 4 shows the events data from the nearby orbits, which helps us know the
shape of BG. The shift time ($\sim 5720$ 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 nearby orbit. Figure 5 shows the light curves
and events data from the nearby orbit as BG in different energy bands. The BG
could be well described by the data from nearby orbits for NaI 7 and 8
detectors. However, from Figure 4 (c) and 5 (c) for BGO data, the nearby data
are not very consistent with those from trigger of GRB 221009A. From above 385
keV, we find the the GRB events ends at $\sim$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.

(a)
(b)
(c)

Figure 4: The light curves of BGO, NaI 7 and NaI 8 from $T_{0}-1100$ s to
$T_{0}+2500$ s and nearby orbits.

(a) NaI 7 (b) NaI 8

Figure 5: The light curves of NaI 7, 8 and BGO 0 from $T_{0}-1100$ s to
$T_{0}+2500$ s and nearby orbits in different energy bands.

(c) BGO 0Figure. 5— Continued.

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