11institutetext:  Department of Physics and Earth Science, University of
Ferrara, via Saragat 1, I–44122, Ferrara, Italy22institutetext: INAF –
Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero
Gobetti 101, I-40129 Bologna, Italy33institutetext: INFN – Sezione di Ferrara,
via Saragat 1, I–44122, Ferrara, Italy44institutetext: INAF, Osservatorio
Astronomico d’Abruzzo, via Mentore Maggini snc, 64100 Teramo,
Italy55institutetext: Department of Physics, University of Cagliari, SP
Monserrato-Sestu, km 0.7, 09042 Monserrato, Italy66institutetext: Ioffe
Institute, Politekhnicheskaya 26, 194021 St. Petersburg,
Russia77institutetext: Astronomical Observatory of the Autonomous Region of
the Aosta Valley (OAVdA), Loc. Lignan 39, I-11020, Nus (Aosta Valley), Italy

# Distribution of the number of peaks within a long gamma-ray burst: The full
Fermi/GBM catalogue

R. Maccary , mccrnl[at]unife[dot]it1122 0000-0002-8799-2510 M. Maistrello 1122
0009-0000-4422-4151 C. Guidorzi 112233 0000-0001-6869-0835 M. Sartori 11
0009-0007-3573-5305 L. Amati 22 0000-0001-5355-7388 L. Bazzanini 1122
0000-0003-0727-0137 M. Bulla 113344 0000-0002-8255-5127 A. E. Camisasca 77
0000-0002-4200-1947 L. Ferro 1122 0009-0006-1140-6913 F. Frontera 1122
0000-0003-2284-571X A. Tsvetkova 552266 0000-0003-0292-6221

(Received 9 May 2024 / Accepted 5 July 2024)

###### Abstract

Context. The dissipation process responsible for the long gamma-ray burst
(GRB) prompt emission and the kind of dynamics that drives the release of
energy as a function of time are still key open issues. We recently found that
the distribution of the number of peaks per GRB is described by a mixture of
two exponentials, suggesting the existence of two behaviours that turn up as
peak-rich and peak-poor time profiles.

Aims. Our aims are to study the distribution of the number of peaks per GRB of
the entire catalogue of about 3000 GRBs observed by the Fermi Gamma-ray Burst
Monitor (GBM) and to make a comparison with previous results obtained from
other catalogues.

Methods. We identified GRB peaks using the mepsa code and modelled the
resulting distribution following the same procedure that was adopted in the
previous analogous investigation.

Results. We confirm that only a mixture of two exponentials can model the
distribution satisfactorily, with model parameters that fully agree with those
found from previous analyses. In particular, we confirm that $(21\pm 4)$% of
the observed GRBs are peak-rich ($8\pm 1$ peaks per GRB on average), while the
remaining 80% are peak-poor ($2.12\pm 0.10$ peaks per GRB on average).

Conclusions. We confirm the existence of two different components, peak-poor
and peak-rich GRBs, that make up the observed GRB populations. Together with
previous analogous results from other GRB catalogues, these results provide
compelling evidence that GRB prompt emission is governed by two distinct
regimes.

###### Key Words.:

Gamma-ray burst: general – Methods: statistical

##  1 Introduction

Long-lasting gamma-ray bursts (GRBs) are thought to be produced by the
collapse of the core of some hydrogen-stripped massive stars, in which a
relativistic jet is launched by the newborn compact object, either a neutron
star (NS) or a black hole (BH), and makes it to the stellar photosphere
(Woosley, 1993; Paczyński, 1998; MacFadyen & Woosley, 1999; Yoon & Langer,
2005). Today, almost 30 years since the first discoveries of the long-lasting
multiwavelength counterpart (from gamma rays, X-rays, and optical light to
radio waves) following the initial gamma-ray emission (so-called afterglow),
the wealth of knowledge of the GRB phenomenon, such as the energetics, the jet
structure, its Lorentz factor, the density of surrounding environment, and the
properties of the progenitor stars has grown remarkably (see e.g. van Eerten
2018; Salafia & Ghirlanda 2022; Levan et al. 2016 for reviews). However, the
kind of mechanism and energy reservoir powering the GRB prompt emission, the
nature of the dissipation process into gamma-rays, and the distance from the
progenitor star at which it takes place, remain highly debated and hot topics
(see Pe’er 2015; Zhang 2018 for reviews).

Even inexperienced eyes are caught by the variety of prompt emission light
curves (LCs), which range from simple and smooth single pulses all the way up
to very complex spiky profiles including many peaks and occasionally quiescent
times in between, during which the signal can temporarily drop below
instrumental sensitivity. Ever since, attempts to interpret the variability
and apparent lack of systematic temporal evolution of the most variable LCs
have resulted in mechanisms based on internal dissipation of some kind of
energy (either kinetic or magnetic) into gamma-rays through shocks within a
wind of relativistic shells (see e.g. Kumar & Zhang 2015 for a review).
However, the rich wealth of information hidden in the observed complexity of
GRB LCs remains mostly unintelligible. In particular, an open question is
whether this variety could be the result of a common stochastic process. If
positive, a precise characterisation of this process would reveal how GRB
inner engines work, shedding light on the nature of the powering mechanism and
on the nature of the engines themselves. Under this assumption, a way to gain
clues is by studying the distributions of a number of properties, such as the
duration, energy, and luminosity of individual peaks that make up GRB LCs, as
well as their waiting times. Possible evidence for self-organised criticality
was found and discussed in analogy with other astrophysical transient sources,
such as solar flares or magnetar bursts, which might also be ruled by similar
kinds of instabilities (Wang & Dai, 2013; Lyu et al., 2020; Li et al., 2023;
Li & Yang, 2023; Maccary et al., 2024).

The distribution of the number of peaks within long GRB LCs has been studied
and modelled in detail for the first time only recently (Guidorzi et al.,
2024, hereafter G24). This distribution was studied in four different
experiments: the Burst And Transient Source Experiment (BATSE; Paciesas et al.
1999), on board the Compton Gamma-Ray Observatory; the Burst Alert Telescope
(BAT; Barthelmy et al. 2005) on board the Neil Gehrels Swift Observatory; the
BeppoSAX Gamma-Ray Burst Monitor (GRBM; Frontera et al. 1997); and the
Insight-HXMT High Energy instrument (HE; Liu et al. 2020). The result, which
emerged from the analysis of these four independent catalogues, is that the
distribution of the number of peaks is modelled by a mixture of two
exponentials (M2E). The two components are characterised by two different
average numbers of peaks per GRB: $2.1\pm 0.1$ and $8.3\pm 1.0$, nicknamed
‘peak-poor’ and ‘peak-rich’, respectively. The result was unexpected, given
also the diversity of the four experiments in terms of energy passbands and
effective areas. The existence of two distinct components was interpreted as
evidence of two correspondingly different dynamical regimes, through which
long GRB inner engines work.

In their work, G24 could not extend the same analysis to the entire GRB
catalogue of the Fermi Gamma-ray Burst Monitor (GBM; Meegan et al. 2009), but
reported an analogous preliminary result obtained over a sample of nearly 400
GRBs. In the present work we report the same kind of analysis applied to the
full GRB catalogue of GBM currently available. The importance of this
additional investigation cannot be overstated: not only does it represent a
further test on independent data, but it is also statistically very sensitive,
given that the GBM data set outnumbers the data sets previously analysed by
G24. In addition, since GBM and BAT share the largest number of GRBs, it is
possible to further explore to what extent the number of peaks of any given
GRB depends on the detector.

The paper is organised as follows. Section 2 describes the data sample and
reduction. Section 3 presents the results of the statistical analysis, whose
discussion and conclusions are reported in Section 4.

##  2 Data analysis

###  2.1 Data set

The GBM is composed of $12$ NaI scintillators sensitive in the $8$–$1000$ keV
energy range and of two BGO scintillators, sensitive to the high energy tail
of a typical GRB spectrum ($150$ keV–$30$ MeV), overlapping with NaI detectors
at low energies. We started from $3091$ long GRBs detected by GBM from 14 July
2008 to 4 February 2024. We excluded short GRBs by discarding those with
$T_{\rm{90}}<2$ s, where $T_{\rm{90}}$ is the time interval encompassing from
5% to 95% of the total fluence, as well as those with clear evidence of a
compact merger origin, such as 211121A and 230307A111191019A should also
appear in this list, but it was not seen by the GBM. (Levan et al., 2023;
Troja et al., 2022; Gompertz et al., 2023; Levan et al., 2024). Very bright
GRBs that saturated the GBM detectors, such as 130427A and 221009A (Preece et
al., 2014; Burns et al., 2023), were also left out. From the remaining GRBs,
$154$ have a known (spectroscopic) redshift, and $410$ are in common with BAT.

Gamma-ray bursts affected by the simultaneous occurrence of a solar flare were
discarded. Solar flares were identified by observing the relative intensity
between the flare and the GRB on different units and on different energy
ranges, taking into account the direction of the Sun. Being spectrally softer
than GRBs, most solar flares are barely visible above 40 keV.

We finally rejected all the GRBs whose LC was lacking data points within the
$T_{90}$ interval. Eventually, we ended up with 2971 GRBs, which is hereafter
referred to as the GRB sample used for the analysis.

###  2.2 Background subtraction

Gamma-ray burst LCs were extracted in the full NaI energy range ($8-1000$
keV), using a $64$ ms bin time. We subtracted the background using the GBM
data
tools222https://fermi.gsfc.nasa.gov/ssc/data/analysis/gbm/gbm_data_tools/gdt-
docs/.

(Goldstein et al., 2022) following standard prescriptions: we selected one
time window preceding the burst and another one following, both having
comparable or longer duration than that of the interval containing the
burst,333This requirement ensures that all the harmonics that significantly
contribute to the background in the burst interval can be adequately modelled
in the selected adjacent windows. and interpolated the background with a
polynomial function of order up to 3. For each GRB we looked into the ‘scat
detector mask’ entry on the HEASARC
catalogue444https://heasarc.gsfc.nasa.gov/db-
perl/W3Browse/w3table.pl?tablehead=name%3Dfermigbrst&Action=More+Options to
identify the detectors used by the GBM team. We used the TTE (Time Tagged
Event) data whenever they covered the whole GRB, from the start of its
$T_{90}$ interval to the end.

We removed the spikes caused by charged particles hitting the detectors as
follows: all the bins whose counts exceeded the neighbouring counts by $\geq
9\sigma$ were tagged as spike candidates. Once visual inspection of different
GBM units confirmed the particle, and thus the spurious nature of a given
spike candidate, its counts were replaced with the mean of the neighbouring
bins.

The quality of the background subtraction was assessed by computing mean and
standard deviation of the normalised residuals555They are defined as the
difference between counts and model, divided by the corresponding uncertainty
(see Maccary et al. 2024). of the time windows used for background
interpolation. In particular, we made sure that the background-subtracted
counts satisfied the uncorrelated Gaussian noise assumption required by mepsa
(Guidorzi 2015; see Section 2.3) first by carrying out a normality test on the
normalised residuals (Kolmogorov-Smirnov), to ensure that the noise was
Gaussian, and then by examining the autocorrelation function (ACF) of the
normalised residuals and by carrying out a runs test, to ensure they were
uncorrelated.

###  2.3 Identification of peaks

In line with G24, all the 64 ms background-subtracted LCs were sifted with
mepsa, a well-calibrated code tailored to identify statistically significant
GRB peaks in uniformly sampled time series affected by Gaussian uncorrelated
noise. We discarded peaks with signal-to-noise ratio S/N$<5$. We ended up with
9625 peaks from 2954 GRBs having at least one significant peak. In parallel,
we repeated the same selection by imposing two further thresholds on S/N: 8822
peaks from 2790 GRBs for S/N$>7$; 7371 from 2388 GRBs for S/N$>9$.

##  3 Results

###  3.1 Fermi-GBM sample

We computed the distribution of the number of peaks per GRB, following the
procedure by G24, and tested the various models considered therein (simple
exponential, simple and broken power law, and stretched exponential). As did
G24, we found that the data can only be satisfactorily fitted by a M2E model
given by

${f(n)\ =\ k\ ({e^{-n/n_{1}}\ +\ \xi\,e^{-n/n_{2}}})\;},$ (1)

where $k$ is a normalisation constant, $n_{i}$ is the characteristic number of
peaks per GRB of the $i$-th component ($i=1,2$), and $\xi$ is a relative
normalisation parameter. The expected number of peaks per GRB of the $i$-th
component is given by

$\langle n^{(i)}\rangle\ =\
\frac{\sum_{n=1}^{+\infty}ne^{-n/n_{i}}}{\sum_{n=1}^{+\infty}e^{-n/n_{i}}}\
=\frac{1}{1-e^{-1/n_{i}}}\;,$ (2)

and the fraction of GRBs contributing to the second component is given by

$\bar{w}_{2}\ =\ k\ \xi\sum_{n=1}^{+\infty}e^{-n/n_{2}}\;.$ (3)

The observed distribution along with the best fit model are shown in Figure 1,
while Table 1 reports the best fit values of the model parameters and the
corresponding $p$-value of the $\chi^{2}$ test.

The M2E model fits the data very well (e.g. $p$-value of the two-tail
$\chi^{2}$ test of $0.80$), while other models were unable to describe it
(e.g. a fit with a stretched exponential yielded a $p$-value of 0.0026), thus
confirming the previous results. The mean number of peaks for the peak-poor
and for the peak-rich component is $\langle
n^{(1)}\rangle=2.10^{+0.10}_{-0.10}$ and $\langle
n^{(2)}\rangle=7.61^{+0.97}_{-0.84}$, respectively. The fraction of peak-rich
GRBs is $\bar{w}_{2}=0.21^{+0.04}_{-0.04}$.

Figure 1: Distribution of the number of peaks per GRB for the Fermi/GBM catalogue. The observed and expected counts are displayed in orange and blue, respectively. The histogram bins were grouped to ensure a minimum number of 15 expected counts per bin. The dashed black line shows the best-fitting model of mixture of two exponentials. The blue and grey regions respectively show the 50% and 90% model confidence interval obtained from sampling the posterior distribution of the model parameters computed through Markov chain Monte Carlo simulations. S/N | $N$ | $N_{p}$ | $k$ | $n_{1}$ | $\langle n^{(1)}\rangle$ | $n_{2}$ | $\langle n^{(2)}\rangle$ | $\xi$ | $\bar{w}_{2}$ |  $\chi^{2}$ test
---|---|---|---|---|---|---|---|---|---|---
Threshold |  |  |  |  |  |  |  |  |  |  $p$-value
$5$ | $2954$ | $9625$ | $0.71^{+0.05}_{-0.05}$ | $1.55^{+0.11}_{-0.11}$ | $2.10^{+0.11}_{-0.11}$ | $7.07^{+0.99}_{-0.82}$ | $7.61^{+0.97}_{-0.84}$ | $0.04^{+0.01}_{-0.01}$ | $0.21^{+0.04}_{-0.04}$ | $0.80$
$7$ | $2790$ | $8822$ | $0.82^{+0.06}_{-0.06}$ | $1.39^{+0.11}_{-0.10}$ | $1.95^{+0.10}_{-0.10}$ | $6.78^{+0.93}_{-0.77}$ | $7.53^{+0.90}_{-0.77}$ | $0.04^{+0.01}_{-0.01}$ | $0.23^{+0.04}_{-0.04}$ | $0.78$
$9$ | $2388$ | $7371$ | $0.93^{+0.08}_{-0.08}$ | $1.26^{+0.10}_{-0.10}$ | $1.83^{+0.10}_{-0.10}$ | $6.70^{+0.93}_{-0.75}$ | $7.23^{+0.90}_{-0.77}$ | $0.039^{+0.012}_{-0.010}$ | $0.23^{+0.04}_{-0.04}$ | $0.43$
Table 1: Best-fit values and 90% confidence intervals of the parameters of the
model of the mixture of two exponentials applied to the Fermi/GBM data set.
All these parameters are defined in Section 3.

###  3.2 Swift-BAT/Fermi-GBM common sample

Fermi/GBM shares 410 GRBs with Swift/BAT, 361 of which were covered by BAT in
burst mode. As G24 did for the common sample between CGRO/BATSE and
BeppoSAX/GRBM, here we used the BAT-GBM common sample to study how the number
of peaks of any given GRB depends on the detector; the ultimate goal was to
test the robustness of our result.

Following G24, we considered the difference $\Delta
n=n_{\rm{GBM}}-n_{\rm{BAT}}$ between the number of peaks detected by GBM and
that of BAT for each common GRB. We replicated the same analysis assuming the
three different thresholds on S/N: S/N $>5$; S/N$>7$; and S/N$>9$. Figure 2
shows the distributions of $\Delta n$ for the three different thresholds on
S/N. The median value of $\Delta n$ is zero for all S/N thresholds. The
interval $|\Delta n|\leq 2$ collects from 85 to 88% of the complete common
samples, whereas from 92 to 94% common GRBs have $|\Delta n|\leq 3$. These
values prove that both experiments are equivalently sensitive to the number of
peaks, in spite of their different energy passbands. As noted by G24, $\Delta
n$ for most GRBs is significantly smaller than the difference between the mean
values of peak-rich and peak-poor GRBs, $\langle n^{(2)}\rangle-\langle
n^{(1)}\rangle=5.5^{+0.9}_{-0.7}$ (90% confidence), which makes the
identification of the two families of long GRBs robust and essentially
detector-independent.

###  3.3 Combined sample

We merged the results of the five catalogues and treated them as if they were
a single result. The GBM result reported in the present work, is clearly
dominant as its 2954 GRBs outnumber those from the the other catalogues (which
included 1457, 1277, 820, and 202 GRBs). We obtained an acceptable fit
($p$-value of 0.06) with the same but more accurate value for the fraction of
peak-rich GRBs: $\bar{w}_{2}\leavevmode\nobreak\
(\rm{all})=0.20^{+0.02}_{-0.02}$, and similar values for the mean number of
peaks for the peak-poor and peak-rich component $\langle
n^{(1)}\rangle=2.25^{+0.08}_{-0.07}$ and $\langle
n^{(2)}\rangle=9.08^{+0.72}_{-0.66}$, respectively.

Figure 2: Distribution of $\Delta n$ for three different thresholds on S/N: 5,
7, and 9.

###  3.4 Impact of selection effects and the Malmquist bias

The number of peaks per GRB clearly depends on the S/N of each peak. As such,
the selection of GRBs with suitable peaks as well as their classification of
peak-poor versus peak-rich depends on S/N, too. Any given GRB that would have
been observed at higher-than-actual redshift, could have been either tagged
with fewer peaks or missed altogether. Consequently, our results are
potentially affected by a significant Malmquist bias. As we also did in G24,
repeating the analysis for a range of different S/N thresholds, and thus
mimicking the effect of moving given GRBs further away, our aim was to explore
the robustness of our results against any distance-related bias. Two
interesting facts emerge from this analysis:

  1. 1.

The fraction $\bar{w}_{2}$ of peak-rich GRBs essentially remains constant for
all catalogues and for the different S/N thresholds, and therefore appears to
be a robust property that is least affected by anything that depends on peak
brightness. In the following, we delve further into this aspect, which seems
to clash with the Malmquist bias;

  2. 2.

The average number of peaks per GRB changes only slightly for different
thresholds on S/N: from $2.1$ (S/N¿5) to $1.8$ (S/N¿9) for the peak-poor
class, and, correspondingly, from $7.6$ to $7.2$ for the peak-rich class
(Table 1). This is understood by the following argument: not only does the
number of peaks decrease by increasing the threshold on S/N of any given GRB
(mimicking the consequence of moving it to higher redshifts), but the number
of GRBs featuring at least one significant peak also decreases. As a result,
the average number of peaks per surviving GRB decreases less abruptly than the
overall number of peaks.

In principle, a direct way to understand the impact of the Malmquist bias is
by focusing on a sample of GRBs with measured redshift. Unfortunately, this
sample is currently too small to make a statistically sound analysis feasible.
Nonetheless, we explored in more detail the reasons for the first
consideration above as follows. We addressed two questions: By moving a peak-
rich GRB to progressively higher redshifts, we wanted to know (a) at what
relative distance it becomes peak-poor, thus contributing to altering the true
distribution, and (b) at what relative distance the GRB disappears, an event
coinciding with the brightest peak sinking below threshold?

The answer to (b) depends on the intensity of the brightest peak, while we
assume that the answer to (a) depends on the intensities of the third or
fourth brightest peaks, once we take three or four as a reasonable proxy of
the number of peaks for discriminating between peak-poor and peak-rich GRBs.

For each of the peak-rich GRBs with at least 6 S/N$>5$ peaks, we took the four
brightest ones. We ended up with 399 GRBs. For each GRB we calculated the
three following ratios: $r_{21}\geq r_{31}\geq r_{41}$, respectively
corresponding to the ratio of the intensities of the second, of the third, and
of the fourth brightest peaks to the intensity of the brightest peak.

As a result, on average it is $r_{41}\sim 2/3$, with $0.56$–$0.77$ as
interquartile, so the range of intensities of the four brightest peaks is
relatively narrow. Specifically, from the disappearing of the fourth peak to
the disappearing of the brightest peak, the threshold on S/N increases only by
$\sim$50% on average. Translating the relative change of the S/N threshold in
terms of the relative change in the maximum volume within which a given peak
can be detected, the volume increases by a factor of $(2/3)^{-3/2}\approx
1.8$, so 80% (we used the scaling $V\propto p^{-3/2}$ of volume $V$ on peak
flux $p$). This is a relatively short range compared with the range of
redshifts spanned by the GRB populations that make up the observed catalogues
and the GBM catalogue in particular. Replacing the fourth with the third
brightest peak, the relative volume change shrinks to 60%, so the previous
conclusion holds true a fortiori. This property of most peak-rich GRBs may
explain why the Malmquist bias does not strongly affect the result of a
constant peak-rich fraction throughout the different catalogues and GRB
populations.

##  4 Discussion and conclusions

Guidorzi et al. (2024) modelled for the first time the distribution of the
number of peaks in long GRB LCs through the analysis of four independent
catalogues (CGRO/BATSE, Swift/BAT, BeppoSAX/GRBM, and Insight-HXMT/HE), which
differ from each other in terms of energy passbands and effective areas. Only
a mixture of two exponentials was found to model all four distributions,
supporting the existence of two families, called peak-poor and peak-rich,
characterised by an average number of peaks per GRB of around $2.1\pm 0.1$ and
$8.3\pm 1.0$, respectively. It was also found that peak-poor GRBs make up
about 80% of the GRB populations observed by past and present experiments.

In the present work we carried out the analogous investigation over the
Fermi/GBM GRB catalogue, which currently includes about 3000 GRBs and
therefore offers a further opportunity to test the previous results with a
high degree of statistical accuracy. Remarkably, not only did we confirm that
the distribution can only be modelled by a mixture of two exponentials, but we
also found that the best-fitting parameter values are fully consistent with
what was found by G24 from different and independent data sets. Specifically,
the expected numbers of peaks for the two families of peak-poor and of peak-
rich GRBs are remarkably similar to the G24 results. Analogously, the fraction
of peak-rich GRBs is found to be $0.21\pm 0.04$, fully consistent with what
was found by G24. Although they were ignored in the present analysis, long-
merger candidates would belong to the hard tail of the peak-rich family:
211211A has 48 peaks and 230307A has 53 peaks. Should peak richness be
confirmed in future analogous events, it would provide a clue to the way the
inner engines of these mergers work.

Figure 3 shows a visual comparison between the GBM results reported here and
the results obtained by G24. Interestingly, while the fraction of peak-poor
GRBs is basically the same for all the five catalogues, the average numbers of
peaks per each GRB for both families of the only BATSE is somewhat higher. As
discussed in G24, this is ascribed to the larger effective area of BATSE
compared with the other instruments, including GBM.

Figure 3: This figure describes our present results compared with those of
G24. Top panels, left to right: Violin plots of the posterior distributions of
the three parameters $\langle n^{(1)}\rangle$, $\langle n^{(2)}\rangle$, and
$\bar{w}_{2}$, respectively representing the expected number of peaks per GRB
of the peak-poor and the peak-rich classes, and the fraction of peak-rich GRBs
obtained for the GBM sample. The horizontal bars span 5 to 95% quantiles.
Bottom panels, left to right: Comparison between the results obtained for the
same parameters in this work, with those obtained by G24 from other
catalogues.

In conclusion, we confirmed that the existence of these two families is a
robust result that is not sensitive to the experiments and their energy
passbands. As discussed by G24, these two different dynamics ruling long GRB
prompt emission might point to either two different families of engines left
over by the collapse of the core, either a NS or a BH, or two different
regimes in which GRB engines release their energy. As noted in G24, the
distinctive property of peak-rich GRBs is the presence of sub-second
variability that adds to the slow-varying component, which is instead observed
in both kinds of GRBs.

The existence of two distinct dynamics in the observed population of GRBs can
be interpreted within different models of how dissipation into gamma-rays
takes place (see G24 for a detailed discussion). Consequently, it does not
directly help to discriminate between different interpretations. Nevertheless,
it provides a solid clue to how GRB engines work, with the possibility that
they could operate close to a critical regime. In this way, a completely
different dynamical behaviour can result from a small difference in some key
properties, such as the degree of magnetisation of the relativistic ejecta, as
discussed in G24. Should the peak richness of GRBs be found preferentially
associated with other key properties in future investigations, the
implications would help to narrow down the identity of GRB engines and the
nature of the dissipation process that governs the prompt emission.

###### Acknowledgements.

We thank the anonymous reviewer for providing insightful comments that
improved the manuscript. R.M. and M.M. acknowledge the University of Ferrara
for the financial support of their PhD scholarships. R.M. acknowledges the
Fermi team for covering flight costs for attending the Fermi summer school
2023. A.T. acknowledges financial support from ASI-INAF Accordo Attuativo
HERMES Pathfinder operazioni n. 2022-25-HH.0 and the basic funding program of
the Ioffe Institute FFUG-2024-0002. L.A. acknowledges support from INAF Mini-
grant programme 2022. A.C. is partially supported by the 2023/24 “Research and
Education” grant from Fondazione CRT. The OAVdA is managed by the Fondazione
Clément Fillietroz-ONLUS, which is supported by the Regional Governement of
the Aosta Valley, the Town Municipality of Nus and the ”Unité des Communes
valdotaines Mont-Emilius”.

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