# The peculiar short-duration GRB 200826A and its supernova111Based on data
obtained with the LBT programs: LBT-2019B-18 (PI A. Rossi), DDT-2019B-9 (PI P.
D’Avanzo), and LD-2020B-0100 (PI. B. Rothberg); and the TNG programme
A41_TAC15 (PI V. D’Elia).

A. Rossi INAF - Osservatorio di Astrofisica e Scienza dello Spazio, via Piero
Gobetti 93/3, 40129 Bologna, Italy  B. Rothberg LBT Observatory, University of
Arizona, 933 N.Cherry Ave,Tucson AZ 85721, USA  George Mason University,
Department of Physics & Astronomy, MS 3F3, 4400 University Drive, Fairfax, VA
22030, USA  E. Palazzi INAF - Osservatorio di Astrofisica e Scienza dello
Spazio, via Piero Gobetti 93/3, 40129 Bologna, Italy  D. A. Kann Instituto de
Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, S/N, 18008
Granada, Spain  P. D’Avanzo  INAF - Osservatorio Astronomico di Brera, Via E.
Bianchi 46, I-23807, Merate (LC), Italy  L. Amati  INAF - Osservatorio di
Astrofisica e Scienza dello Spazio, via Piero Gobetti 93/3, 40129 Bologna,
Italy  S. Klose Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778
Tautenburg, Germany  A. Perego Dipartimento di Fisica, Universitá di Trento,
Via Sommarive 14, 38123 Trento, Italy  INFN-TIFPA, Trento Institute for
Fundamental Physics and Applications, via Sommarive 14, I-38123 Trento, Italy
E. Pian  INAF - Osservatorio di Astrofisica e Scienza dello Spazio, via Piero
Gobetti 93/3, 40129 Bologna, Italy  C. Guidorzi  Department of Physics and
Earth Science, University of Ferrara, via Saragat 1, I-44122, Ferrara, Italy
INFN – Sezione di Ferrara, Via Saragat 1, 44122 Ferrara, Italy  INAF -
Osservatorio di Astrofisica e Scienza dello Spazio, via Piero Gobetti 93/3,
40129 Bologna, Italy  A. S. Pozanenko  Space Research Institute of the Russian
Academy of Sciences (IKI), 84/32 Profsoyuznaya Str, Moscow 117997, Russia
Moscow Institute of Physics and Technology (MIPT), 9 Institutskiy per.,
Dolgoprudny, Moscow Oblast 141701, Russia  National Research University Higher
School of Economics, Moscow 101000, Russia  S. Savaglio  Physics Department,
University of Calabria, 87036 Arcavacata diRende, Italy  G. Stratta  INAF -
Osservatorio di Astrofisica e Scienza dello Spazio, via Piero Gobetti 93/3,
40129 Bologna, Italy  INAF - Istituto di Astrofisica e Planetologia Spaziali,
via Fosso del Cavaliere 100, I-00133 Roma, Italy  G. Agapito INAF -
Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125-Firenze, Italy
S. Covino  INAF - Osservatorio Astronomico di Brera, Via E. Bianchi 46,
I-23807, Merate (LC), Italy  F. Cusano  INAF - Osservatorio di Astrofisica e
Scienza dello Spazio, via Piero Gobetti 93/3, 40129 Bologna, Italy  V. D’Elia
Space Science Data Center (SSDC) - Agenzia Spaziale Italiana (ASI), I-00133
Roma, Italy  INAF - Osservatorio Astronomico di Roma, via Frascati 33, 00040
Monte Porzio Catone, Italy  M. De Pasquale  University of Messina, MIFT
Department, Polo Papardo, Viale F.S. D’Alcontres 31, 98166 Messina, Italy
Department of Astronomy and Space Sciences, Faculty of Science, Istanbul
University, 34119 Istanbul, Turkey  M. Della Valle  INAF, Osservatorio
Astronomico di Capodimonte, Salita Moiariello 16, 80131 Naples, Italy  O. Kuhn
LBT Observatory, University of Arizona, 933 N.Cherry Ave,Tucson AZ 85721, USA
L. Izzo  DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 128,
2200 Copenhagen, Denmark  E. Loffredo  Gran Sasso Science Institute, Viale F.
Crispi 7, I-67100, L’Aquila (AQ), Italy  INFN - Laboratori Nazionali del Gran
Sasso, I-67100, L’Aquila (AQ), Italy  N. Masetti INAF - Osservatorio di
Astrofisica e Scienza dello Spazio, via Piero Gobetti 93/3, 40129 Bologna,
Italy  Departamento de Ciencias Físicas, Universidad Andrés Bello, Fernández
Concha 700, Las Condes, Santiago, Chile  A. Melandri  INAF - Osservatorio
Astronomico di Brera, Via E. Bianchi 46, I-23807, Merate (LC), Italy  P. Y.
Minaev  Space Research Institute of the Russian Academy of Sciences (IKI),
84/32 Profsoyuznaya Str, Moscow 117997, Russia  Moscow Institute of Physics
and Technology (MIPT), 9 Institutskiy per., Dolgoprudny, Moscow Oblast 141701,
Russia  P. N. Lebedev Physical Institute of the Russian Academy of Sciences,
Leninskii pr. 53, Moscow, 119991, Russia  A. Nicuesa Guelbenzu Thüringer
Landessternwarte Tautenburg, Sternwarte 5, 07778 Tautenburg, Germany  D. Paris
INAF - Osservatorio Astronomico di Roma, via Frascati 33, 00040 Monte Porzio
Catone, Italy  S. Paiano  INAF - Osservatorio Astronomico di Roma, via
Frascati 33, 00040 Monte Porzio Catone, Italy  INAF - Istituto di Astrofisica
Spaziale e Fisica Cosmica di Palermo, via Ugo La Malfa, 153, 90146 Palermo,
Italy  INAF - Istituto di Astrofisica Spaziale e Fisica cosmica di Milano, via
Alfonso Corti 12, 20133 Milano, Italy  C. Plantet INAF - Osservatorio
Astrofisico di Arcetri, Largo E. Fermi 5, 50125-Firenze, Italy  F. Rossi INAF
- Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125-Firenze, Italy
R. Salvaterra  INAF - Istituto di Astrofisica Spaziale e Fisica cosmica di
Milano, via Alfonso Corti 12, 20133 Milano, Italy  S. Schulze  The Oskar Klein
Centre, Physics Department of Physics, Stockholm University, Albanova
University Center, SE 106 91 Stockholm, Sweden  C. Veillet  LBT Observatory,
University of Arizona, 933 N.Cherry Ave,Tucson AZ 85721, USA  A. A. Volnova
Space Research Institute of the Russian Academy of Sciences (IKI), 84/32
Profsoyuznaya Str, Moscow 117997, Russia<EMAIL_ADDRESS>
###### Abstract

Gamma-ray bursts (GRBs) are classified as long and short events. Long GRBs
(LGRBs) are associated with the end states of very massive stars, while short
GRBs (SGRBs) are linked to the merger of compact objects. GRB 200826A was a
peculiar event, because by definition it was a SGRB, with a rest-frame
duration of $\sim 0.5$ s. However, this event was energetic and soft, which is
consistent with LGRBs. The relatively low redshift ($z=0.7486$) motivated a
comprehensive, multi-wavelength follow-up campaign to characterize its host,
search for a possible associated supernova (SN), and thus understand the
origin of this burst. To this aim we obtained a combination of deep near-
infrared (NIR) and optical imaging together with spectroscopy. Our analysis
reveals an optical and NIR bump in the light curve whose luminosity and
evolution is in agreement with several LGRB-SNe. Analysis of the prompt GRB
shows that this event follows the $E_{\rm p,i}-E_{\rm iso}$ relation found for
LGRBs. The host galaxy is a low-mass star-forming galaxy, typical for LGRBs,
but with one of the highest star-formation rates (SFR), especially with
respect to its mass ($\log M_{\ast}/M_{\odot}=8.6$, SFR $\sim
4.0\,M_{\odot}$/yr). We conclude that GRB 200826A is a typical collapsar event
in the low tail of the duration distribution of LGRBs.

These findings support theoretical predictions that events produced by
collapsars can be as short as 0.5 s in the host frame and further confirm that
duration alone is not an efficient discriminator for the progenitor class of a
GRB.

Gamma-ray bursts (629) — Supernovae (304) — Core-collapse supernovae (1668)

††facilities: Swift(XRT), LBT, TNG, MAO††software: IRAF (Tody, 1993), PyRAF
(Science Software Branch at STScI, 2012), DRAGONS (Labrie et al., 2019),
HOTPANTS (Becker, 2015), Le PHARE (Arnouts et al., 1999; Ilbert et al., 2006),
WCSTools (Mink, 2019)

##  1 Introduction

Traditionally, gamma-ray bursts (GRBs) are divided in two classes based on
their duration and their spectral hardness in the gamma energy range. The
majority of observed GRBs have durations longer than $2$ s, a soft high-energy
spectrum and are termed “long GRBs” (LGRBs), as opposed to “short GRBs”
(SGRBs) with a usually sub-second duration and a harder high-energy spectrum
(Mazets et al., 1981; Kouveliotou et al., 1993). However, there is a
substantial overlap between the distributions of the durations of the two GRB
classes (Kouveliotou et al. 1993, Bromberg et al. 2013, Horváth & Tóth 2016).

Long GRBs are typically associated with highly energetic broad-lined type Ic
supernovae (SNe) and have therefore been associated confidently with the
deaths of very massive stars (e.g., Woosley & Bloom, 2006; Cano et al.,
2017a). On the other hand, short GRBs are thought to be connected with the
merger of compact objects, as was firmly demonstrated in spectacular fashion
by the SGRB 170817A which was accompanied by the binary neutron star (NS)
merger gravitational-wave source GW170817 detected by the LIGO and Virgo
interferometers as well as by the kilonova (KN) AT2017gfo (e.g., Abbott et
al., 2017a, b, c; Pian et al., 2017; Smartt et al., 2017).

Improving our understanding of the connection between LGRBs and SNe has been
one of the most intense areas of research in the field of GRBs for over 20
years. More than 1400 bursts have been discovered by the Neil Gehrels Swift
Observatory (Swift hereafter) in the last 16 years, among which only $40-50$
GRBs have an associated SN identified by the late bumps in their optical
afterglow light curves, and to date, just 28 have been spectroscopically
confirmed (Rossi et al. 2022, in prep., Izzo et al. 2019; Melandri et al.
2021, Cano et al. 2017a and references therein, Klose et al. 2019; Cano et al.
2017b; Ashall et al. 2019a; Melandri et al. 2019; Hu et al. 2021). The burst
duration for all these events lasted for more than 2 s, therefore they are
considered LGRBs. While these results show a simple and clear correlation
between SNe and LGRBs, the reality may be more murky.

A first break in the LGRB-SN association was already found in 2006 with the
discovery of the LGRBs 060505 and 060614222GRBs 060505 and 060614 have
durations (T90) of $4\pm 1$s (Hullinger et al., 2006) and $\sim 102\pm 5$ s
(Barthelmy et al., 2006), respectively.. Their relatively low redshifts
($z=0.089$ and $z=0.125$, respectively) allowed for the search of the possibly
associated SNe, but despite achieving deep photometric limits no SN component
as luminous as those observed in the case of other long GRBs was detected
(Della Valle et al., 2006; Gal-Yam et al., 2006; Fynbo et al., 2006; Ofek et
al., 2007; McBreen et al., 2008; Xu et al., 2009)333 More recently, KNe have
been claimed to have been detected in the afterglows of GRB 060614 (Yang et
al., 2015; Jin et al., 2015) and GRB 060505 (Jin et al., 2021). This would
imply they are actually merger events (see Kann et al. 2011 for more
discussion).. Later, LGRB 111005A at $z=0.0133$ (Tanga et al., 2018;
Michałowski et al., 2018) also joined this group. On the other hand, in the
case of GRB 040924, classified as short for its rest-frame duration ($\sim 1$
s), an associated SN was detected (Wiersema et al., 2008; Soderberg et al.,
2006) thus identifying its origin as being the collapse of a massive star.
Another peculiar case is GRB 090426, which has a duration shorter than 2 s,
but with a high-energy spectrum and afterglow brightness typical of long GRBs
(Antonelli et al. 2009; Thöne et al. 2011; Nicuesa Guelbenzu et al. 2011,
2012; Kann et al. 2022, in prep.). Indeed, although classifying a burst by its
duration as either long or short is still the most simple and adopted
approach, the above results show that this is not enough to reveal the nature
of the GRB progenitor. Even considering the spectral hardness often may not
help in the classification (e.g., Minaev & Pozanenko, 2020a; Agüí Fernández et
al., 2021), and thus understanding the origin of the burst. Indeed, the most
secure way is to determine whether the event is associated with a supernova
(SN) and is a LGRB, or with a KN and is a SGRB.

We here present follow-up observations and analysis of GRB 200826A, including
the search for an associated SN and characterization of the host galaxy. This
very intense, but short-duration burst was detected by several space-based GRB
detectors (see Hurley et al., 2020), including Konus-_Wind_ (Ridnaia et al.,
2020; Svinkin et al., 2020), _Fermi_ /GBM (Mangan et al., 2020), _AGILE_ /MCAL
(Pittori et al., 2020) and _AstroSat_ /CZTI (Gupta et al., 2020). Stemming
from its observed short duration (GBM $T_{90}=1.14$ s, Mangan et al. 2020;
Konus-_Wind_ $T_{90}=0.772$ s, Svinkin et al. 2020), it was initially thought
to be a genuine SGRB. The ZTF survey project (Bellm et al., 2019) launched an
observing campaign to search for the optical counterpart (Sagues Carracedo et
al., 2020) within the large error circle of _Fermi_ /GBM. Among the several
candidates detected, ZTF20abwysqy was confirmed to be the afterglow of GRB
200826A (Ahumada et al., 2020a; Belkin et al., 2020a; Dichiara et al., 2020).
An X-ray afterglow was also detected by _Swift_ /XRT (D’Ai et al., 2020). The
GRB spectroscopic redshift ($z=0.748$) was obtained thanks to LBT/MODS
observations (Rothberg et al., 2020a). The provided distance was used to
calculate the real luminosities and energy values, which showed that GRB
200826A was a very energetic event with an isotropic energy release and a peak
energy more consistent with classical LGRBs than with typical SGRBs (Svinkin
et al., 2020). A SN bump in the afterglow light curve was finally reported by
Ahumada et al. (2020c). Additional optical observations of the afterglow and
the SN have been reported in Ahumada et al. (2021); Zhang et al. (2021).

Throughout this work, the flux density of the afterglow is described as
$F_{\nu}(t)\propto t^{-\alpha}\nu^{-\beta}$, and a $\Lambda$CDM world model
with $\Omega_{M}=0.308$, $\Omega_{\Lambda}=0.692$, and $H_{0}=67.8$ km s-1
Mpc-1 (Planck Collaboration et al., 2016) has been assumed. All data are in
observer frame, unless differently specified.

Figure 1: Left:  $1\arcmin\times 1\arcmin$ field-of-view (FoV) finding chart
derived from the TNG $r^{\prime}$-band imaging obtained on 2020-09-27 UT. The
star used for AO observations with SOUL and the LBT/LUCI camera is
highlighted. The rectangular region is centered on the location of the
afterglow, and its angular size is the same as the panels on the right. Right:
Results of the $H$-band follow-up using the second generation SOUL Adaptive
Optics with LUCI-1 at the Large Binocular Telescope. The top row shows the
location of the host and the GRB (see the region in the left panel). For
comparison, the bottom row shows the location of a star in the field. From
left to right: A) the LUCI-1 AO $H$-band imaging obtained on UT 02-10-2020
(i.e., close to the peak of the SN); B) LUCI-1 AO $H$-band image obtained four
months later when only the host is visible; and C) the subtraction between
these two epochs, where the transient is highlighted with a circle (top) and
the field star is cleanly subtracted (bottom). The FoV of each panel is
$2\farcs 6\times 2\farcs 0$. The LUCI-1 AO FoV is $30\arcsec\times 30\arcsec$.
In each panel North is up, East is to the left. The transient lies at a
projected distance of 0.75 kpc from the center of its host galaxy as discussed
in §3.5.

##  2 Observations and data analysis

###  2.1 Optical Spectroscopy

Optical spectroscopy of GRB 200826A was obtained with the Large Binocular
Telescope (LBT) on Mt. Graham, Arizona, USA, on August 28, 2020 at UT 09:06:45
(MJD 59089.379692) using both optical Multi-Object Double Spectrographs (MODS,
Pogge et al., 2010). Each MODS was configured using a 1″wide slit (R $\sim
1500$). MODS-1 was configured with the red grating
($0.58\,\mu\textnormal{m}-1.0\,\mu$m coverage) due to issues at the time with
the blue channel, and MODS-2 was configured with the dual grating
($0.32\,\mu\textnormal{m}-1.05\,\mu$m coverage). Observations consisted of
$4\times 900$ second exposures for the three channels, which yielded an
effective exposure time of 7200 seconds for
$0.58\,\mu\textnormal{m}-1.0\,\mu$m (the red channels). A position angle
$\textnormal{(PA)}=17.0^{\circ}$ was used in order to cover both the reported
location of the GRB 200826A afterglow and a nearby galaxy $15\arcsec$ NE.
Observations were obtained at or near transit with an effective airmass of
1.0005. The seeing for the spectroscopic observations ranged from $0\farcs
7-1\farcs 0$ and conditions were photometric.

The MODS data were reduced first with modsCCDRed version 2.04 to remove the
bias and flat-field the data. Next, custom IRAF scripts were used to: extract
along the central slit using a stellar trace; wavelength calibrate and rectify
the tilt in both X and Y directions using arc-lamp lines; flux calibrate the
data using the spectro-photometric standard star G191-B2B; and remove telluric
features from the red channels using the spectro-photometric standard. The
data from the three channels were combined into a single spectrum and re-
binned to a common scale of $\Delta\lambda=0.85$ Å pixel-1. An afterglow
spectral energy distribution (SED; §3) was then subtracted from the spectrum
and the absolute flux calibration was fine-tuned using the late-time
$g^{\prime}$, $r^{\prime}$, $\it i^{\prime}$, $\it z^{\prime}$ MODS and the
Large Binocular Cameras (LBCs; Giallongo et al., 2008) photometry (Table 1),
which is free from SN and afterglow emission (see §2.4).

###  2.2 Optical and Near-Infrared Imaging

The optical follow-up was performed with LBT in the Sloan filters $g^{\prime}$
and $r^{\prime}$ bands using the two twin MODS instruments, and in the Sloan
$r^{\prime}$ filter with the Device Optimized for the Low Resolution (DOLoRes)
optical imager and spectrograph mounted on the Telescopio Nazionale Galileo
(TNG) on La Palma (Canary Islands, Spain). We have also observed GRB 200826A
twice with AZT-22 1.5m telescope equipped with the SNUCAM CCD camera (Im et
al., 2010) at the Maidanak Astronomical Observatory (MAO, Uzbekistan).

All MODS observations were taken under good seeing conditions ($0\farcs
5-1\farcs 0$). Due to the binocular capabilities of LBT, the observations in
$g^{\prime}$ and $r^{\prime}$ were obtained simultaneously with both MODS
instruments. During summer of 2021, with the aim of expanding our host-galaxy
photometry data set, we obtained further $Ur^{\prime}i^{\prime}z^{\prime}$ and
$R_{C}$ imaging with the LBCs under variable seeing conditions ($0\farcs
9-1\farcs 5$), followed by further MAO observations in the $R_{C}$ band.
LBT/MODS and LBC imaging data were reduced using the data reduction pipeline
developed at INAF - Osservatorio Astronomico di Roma (Fontana et al., 2014)
which includes bias subtraction and flat-fielding, bad pixel and cosmic ray
masking, astrometric calibration, and coaddition. We have also downloaded the
Gemini/GMOS data at 28 and 46 d reported in Ahumada et al. (2021)444 PI L.
Singer, program GN-2020B-DD-104., and afterwards reduced them using the
dedicated Gemini pipeline DRAGONS (Labrie et al., 2019). Finally, we have
downloaded the $r^{\prime}$-band Gran Telescopio Canarias (GTC) data at $3.99$
d reported in Zhang et al. (2021)555 PI A. J. Castro-Tirado, program
GTCMULTIPLE4B-20A. TNG/DOLoRes, GTC and MAO images were reduced in a standard
manner using PyRAF/IRAF tasks (Tody, 1993).

The first $H$-band observations were obtained using the LBT Utility Camera in
the Infrared (LUCI, Seifert et al., 2003) imager and spectrograph in
conjunction with the Single conjugate adaptive Optics Upgrade for LBT (SOUL;
Pinna et al., 2021), the 2nd generation adaptive optics (AO) system at LBT.
Data were obtained 37.1 d after the GRB, close to the expected maximum light
of the possible associated SN. Compared to $J$ and $K$ bands, the $H$ band was
preferred for three reasons: 1) lower sky and thermal background with respect
to the $K$ band; 2) the AO performance is better than in $J$, allowing the
system to achieve a full-width at half-maximum (FWHM) $<0\farcs 1$; 3) there
are no strong emission lines from non-stellar sources or from star-formation
regions (like H$\alpha$ in the $J$-band at the redshift of our target), and
the host continuum is dominated by light from old, late-type stars. A
relatively bright foreground star ($R=15.06$ mag) $11\farcs 4$ away from the
GRB location (and within the field-of-view) was used as the “AO Reference
star” for the AO system. The AO system achieved an average FWHM of the point-
spread function (PSF) $\sim 0\farcs 13$. Subsequent observations were able to
achieve a FWHM $\sim 0\farcs 08-0\farcs 13$ (see §2.3 for more details). The
observations were repeated on December 1st (2020) and February 7th (2021), 97
and 158 d respectively, after the GRB event.

In September 2021 we also obtained $J$-band imaging of the host with LBT/LUCI.
All NIR data have been reduced using the same data reduction pipeline as for
LBT MODS data (§2.2), which in case of LUCI includes dark subtraction, flat-
fielding, bad pixel and cosmic ray masking, and sky subtraction. Finally, the
images were aligned to match the position of the AO reference star and co-
added using IRAF tasks. The astrometry was calibrated against field stars in
the GAIA DR2 catalogue (Gaia Collaboration et al., 2018) and has an
astrometric precision of 0$\farcs$15.

All data were analyzed by performing aperture photometry using DAOPHOT and
APPHOT under PyRAF/IRAF. For the optical data, the photometric calibration was
performed using a set of field stars observed during the fifth MODS epoch
(which had photometric conditions) and calibrated against the SDSS DR12
catalog magnitudes of brighter nearby stars (Alam et al., 2015). NIR
photometry was calibrated against the AO reference star and a pair of 2MASS
stars observed immediately after the GRB field during the first epoch. The
photometric calibration has a standard deviation of $0.02$ mags. To err on the
side of caution, $2\times$ this value was used as the photometric uncertainty.

Table 1: Photometry of the Transient and Host Galaxy.

$\Delta$ta | Magnitude | Filter | Telescope | Ref.c
---|---|---|---|---
(d) | ABb |  |  |
0.2112 | $20.86\pm 0.04$ | $g^{\prime}$ | ZTF | [1]
0.2304 | $20.70\pm 0.05$ | $r^{\prime}$ | ZTF | ”
0.2779 | $20.96\pm 0.16$ | $g^{\prime}$ | ZTF | ”
0.7663 | $>20.2$ | $R_{C}$ | Kitab | [2]
1.1458 | $22.75\pm 0.26$ | $g^{\prime}$ | ZTF | [1]
1.2125 | $>21.3$ | $r^{\prime}$ | ZTF | ”
1.2875 | $>21.2$ | $g^{\prime}$ | ZTF | ”
1.7351 | $>20.4$ | $R_{C}$ | Kitab | [2]
2.183d | $23.39\pm 0.16$ | $r^{\prime}$ | LBT/MODS | [3]
2.183d | $24.08\pm 0.19$ | $g^{\prime}$ | LBT/MODS | ”
2.27 | $>23.3$ | $r^{\prime}$ | FTN+LCO | [1]
2.28 | $>23.4$ | $g^{\prime}$ | FTN+LCO | ”
3.23 | $24.46\pm 0.12$ | $r^{\prime}$ | Lowell | ”
3.99 | $24.51\pm 0.14$ | $r^{\prime}$ | GTC | [3,4]
7.21 | $>23.5$ | $r^{\prime}$ | LBT/MODS | [3]
7.21 | $>23.6$ | $g^{\prime}$ | LBT/MODS | ”
15.7 | $>24.3$ | $R_{C}$ | MAO | ”
28.3 | $24.53\pm 0.21$ | $i^{\prime}$ | Gemini | [1,3]
28.3 | $>25.6$ | $r^{\prime}$ | Gemini | [1,3]
31.9 | $>25.3$ | $r^{\prime}$ | TNG | [3]
33.3 | $>25.7$ | $r^{\prime}$ | LBT/MODS | ”
33.3 | $>25.8$ | $g^{\prime}$ | LBT/MODS | ”
37.1 | $24.06\pm 0.20$ | $H$ | LBT/LUCI | ”
46.1 | $25.36\pm 0.26$ | $i^{\prime}$ | Gemini | [1,3]
46.1 | $>25.5$ | $r^{\prime}$ | Gemini | [1,3]
50.88 | $>25.6$ | $r^{\prime}$ | LBT/MODS | [3]
50.88 | $>26.2$ | $g^{\prime}$ | LBT/MODS | ”
97.0 | $>24.7$ | $H$ | LBT/LUCI | ”
74.8 | $22.85\pm 0.11$ | $r^{\prime}$ | TNG | ”
78.9 | $22.83\pm 0.04$ | $r^{\prime}$ | LBT/MODS | ”
78.9 | $23.12\pm 0.04$ | $g^{\prime}$ | LBT/MODS | ”
158.5 | $22.84\pm 0.20$ | $H$ | LBT/LUCI | ”
287 | $23.36\pm 0.10$ | Ue | LBT/LBC | ”
287 | $22.92\pm 0.08$ | $r^{\prime}$ | LBT/LBC | ”
287 | $22.84\pm 0.07$ | $R_{C}$ | LBT/LBC | ”
287 | $22.58\pm 0.05$ | $i^{\prime}$ | LBT/LBC | ”
287 | $22.25\pm 0.11$ | $z^{\prime}$ | LBT/LBC | ”
340 | $22.85\pm 0.07$ | $R_{C}$ | MAO | ”
382 | $23.29\pm 0.08$ | $B$ | MAO | ”
391 | $22.65\pm 0.14$ | $J$ | LBT/LUCI | ”

  * a

Mid-time after the _Fermi_ /GBM trigger in the observer frame.

  * b

The photometry is not corrected for Galactic extinction. The first part (above
the double line) is the result of image subtraction and represents the pure
transient. The second part has been used to study the host and as references
for the subtraction.

  * c

[1] Ahumada et al. (2021); [2] GCN 28306 (Belkin et al., 2020a); [3] this
work; [4] Zhang et al. (2021).

  * d

These are LBT/MODS acquisition images obtained using a $\sim 2\arcmin\times
2\arcmin$ FOV instead of the full $\sim 6\arcmin\times 6\arcmin$. MODS1 was
equipped with the $g^{\prime}$ filter and MODS2 with the $r^{\prime}$ filter.

  * e

We have used the $Uspec$ for its better sensitivity compared to the
$U_{Bessel}$ filter.

###  2.3 Image subtraction and photometry of the transient

To remove the contribution of the host to the afterglow/SN photometry, a
reference frame free of any transient light is required. To better investigate
any possible contamination from SN light in these earlier observations, the
GRB 200826A data sets were compared with GRB 980425/SN 1998bw (Galama et al.,
1998), which is the standard template for GRB-SNe. Following Zeh et al. (2004)
and Klose et al. (2019), the observed SN 1998bw light curves were first
corrected for Galactic extinction, moved to rest-frame, interpolated with a
polynomial curve at steps of 0.5 d and finally shifted to the GRB 200826A
observed bands, $r^{\prime}$, $i^{\prime}$, and $H$, accounting for filter
band differences and cosmological k-corrections.

At the time of the last MODS $r^{\prime}$ observation (78.9 d after the
trigger) any SN 1998bw-like GRB-SN would have had $r^{\prime}\sim 27$ mag,
more than 2 mag fainter than its peak magnitude ($r^{\prime}\sim 24.7$ mag) at
$20-40$ d, when the first observations had been obtained. Therefore, it is
acceptable to consider the late $r^{\prime}$ MODS images free from any
contamination by SN light and they can be used as templates for image
subtraction. They can also be used to measure the flux of the host galaxy
($\sim 4$ mag brighter in $r^{\prime}$ band) instead of the later LBC images,
which have a lower signal-to-noise ratio. These LBC images were instead used
as reference for the image subtraction of the $r^{\prime}$ imaging at $\sim
50$ d. Similarly, in the $H$ band666To derive the $H$-band flux of SN 1998bw
at the redshift of GRB 200826A we had to extrapolate the rest-frame $I_{C}$
band data of SN 1998bw (e.g., Zeh et al., 2004; Klose et al., 2019). any
SN1998bw-like GRB-SN contribution at 160 d ($H\sim 26$ mag at the time of our
last LBT/LUCI observation) would have been $\sim 2$ mag fainter than its peak
magnitude ($H\sim 24.3$ mag). Differences of $\sim 2$ mag translate to a
contribution from the SN to the late-time image of $\sim 0.2$ mag. This
contribution does not impact the analysis after the image-subtraction, but is
included in the photometric errors. On the contrary, any SN1998bw-like GRB-SN
would fade less than 1 mag between 97 and 160 d, thus the last $H-$band
observation (97 d) may also be affected by over-subtraction, and hence a
photometric value for the transient that is too faint at 97 d, though the SN
was likely too faint to contribute substantially at this point. For
completeness we report the resulting upper limit.

For the $i^{\prime}$ band we note that at the time of the final Gemini
observation (at 75 d, see Ahumada et al. 2020b) any SN1998bw-like GRB-SN would
have had $i^{\prime}\sim 25.5$ mag, just $\sim 1.5-2$ mag fainter than the
peak magnitude at $\sim 30$ d ($\sim 24$ mag) which could be acceptable.
Instead, this difference is certainly less in the case of the Gemini
observation at 46 d (see Table 1 and Fig. 7). Therefore, we caution that using
the value at 75 d as pure host can produce an over-subtraction, in particular
at 46 d. Therefore, in the image subtraction of the $i^{\prime}$band we use
the LBC imaging obtained at 287 d.

Before applying image subtraction, input and reference images were aligned
using the WCSREMAP package777http://tdc-www.harvard.edu/wcstools. Image
subtraction was then performed using a routine based on
HOTPANTS888https://github.com/acbecker/hotpants (Becker, 2015). This algorithm
matches the PSF and count flux of both input images. The PSF is modeled via
Gaussian functions in sub-regions of the original image. The software outputs
a noise map of the resulting difference image, which is used to derive the
uncertainties in the measured fluxes. The routine creates a grid of input
Gaussian widths and sub-region sizes and searches for the solution with the
lowest noise.

In the case of the $H$-band imaging, the average FWHM during the first epoch
was 0$\farcs$13 as measured from the AO reference star in the LUCI-1 FOV999The
PSF is best modeled with a Moffat profile. and was constant for nearly the
entire observation. The small amount of data with larger FWHMs were not used
for analysis. A total of 1180 s of exposure time with FWHM $\sim$ 0$\farcs$13
was used for analysis. For the other epochs the FWHMs ranged from 0$\farcs$08
to $<0\farcs 15$. Therefore, only the exposures with a FWHM of the AO
reference star $<0\farcs 13$ (to match the first epoch) were selected. This
yielded a combined image with a total integration time of 2400 s and 2700 s
for the second and last epochs, respectively. In particular, the AO reference
star in the last epoch has a FWHM $\sim 0\farcs 10$, and this was used as the
template for image subtraction. In contrast to the optical images, only two
stars (the AO reference star and another star close to it) were useful to map
the PSF and flux. Unfortunately, this impacts the optimal use of HOTPANTS to
scale the template image to the flux of the science image. Instead, a better
result was obtained using the PSF-MATCH task under IRAF and scaling the images
to have the same flux for the two stars. The image subtraction of the two
$H$-band images shows a transient located at RA (J2000) = 00h27m 08$\fs$55,
Dec. (J2000) = +34∘01′38$\farcs$2 with an uncertainty of 0$\farcs$15 and
calibrated against the MODS images. This is consistent with the position
reported by Ahumada et al. (2020a).

All image-subtracted data have been analyzed using aperture photometry as
detailed in §2.2. Table 1 provides a summary of all the photometry of the
transient and the host galaxy including values collected from the literature.

Apparent magnitudes were corrected for Galactic extinction using the Cardelli
et al. (1989) interstellar extinction curve, a total-to-selective extinction
of $R_{\rm V}$ = 3.1, and a reddening along the line of sight of $E(B-V)$ =
0.058 mag (Schlafly & Finkbeiner, 2011).

Figure 2: Light curves of the afterglow and SN component of GRB 200826A in the
$g^{\prime}r^{\prime}i^{\prime}H$ bands, after subtraction of the host-galaxy
contribution. The data have been modeled with a smoothly broken power-law for
the afterglow, and with a SN 1998bw template redshifted to $z=0.7486$ for the
SN phase. In the $g^{\prime}$ and $r^{\prime}$ bands, we forced the individual
SN light curve components to go through the most significant deep upper limit
in each band to obtain upper limits on the potential SN luminosity. Note the
$g^{\prime}$ band is offset by 1 mag for reasons of clarity. See Tab. 1, §2.4
and §3.3 for more information.

###  2.4 Modelling of the light curve and SED

Although the $g^{\prime}\,r^{\prime}$ light curves are quite sparse, they can
be modeled with a single power-law with $\alpha=0.94\pm 0.05$. However, this
model implies that the late afterglow is brighter than the deep $r^{\prime}$
upper limits obtained at $\sim 30$ d after subtraction of the host-galaxy
contribution. Therefore, the data were modeled with a smoothly broken power-
law (Beuermann et al., 1999) (Fig. 2). The last detections in the $g^{\prime}$
and $r^{\prime}$ bands are at $\approx 2.2$ and $\approx 4$ d (observer-
frame). Using SN 1998bw as a SN template (see below for more details), the SN
itself would have been $g^{\prime}=29.8$ mag and $r^{\prime}=26.9$ mag at
$2.2$ d and $4$ d, respectively. Therefore, it can safely be assumed to not
contribute significantly to the optical transient and can be ignored in the
afterglow fitting. This yielded decay slopes $\alpha_{1}=0.43\pm 0.55$,
$\alpha_{2}=1.59\pm 0.20$, with a break time $t_{b}=0.47\pm 0.24$ d, break
smoothness $n=10$ fixed. The post-break decay slope easily accommodates the
magnitude upper limits at later times, with values beyond $r^{\prime}\sim
27.8$ mag and $g^{\prime}\sim 28.3$ mag at $\sim 30$ d. Therefore, any late
emission detected via subtraction is not from the afterglow.

To investigate whether the optical data are affected by local dust extinction
along the line of sight, a spectral energy distribution (SED) was modeled
spanning the optical to the X-ray bands. All Swift XRT data available were
used, which have a mean arrival time of 65840 seconds (0.762 d), along with
the simultaneous $g^{\prime}$ and $r^{\prime}$ band obtained from the broken
power-law fit (see above) which is free from host contamination. The redshift
was fixed to match that of the host galaxy and the Galactic hydrogen column
density was set to $N_{H}=6.02\times 10^{20}\,\textnormal{cm}^{-2}$
(Willingale et al., 2013). The optical-to-X-ray SED is well-fit
($\chi^{2}/d.o.f.=33/47$) by a power-law with spectral index $\beta=0.79\pm
0.03$ without need for additional dust extinction and gas absorption to
improve the fit. The negligible dust extinction is well-supported by the
optical-to-X-ray spectral index $\beta_{OX}>0.5$ (Jakobsson et al., 2004;
Rossi et al., 2012). The optical-to-X-ray spectral slope was then used to
extrapolate the late-time brightness in the $i^{\prime}$ and $H$ bands. For
the first $i^{\prime}$ detection at 28 d, the brightness of the projected
afterglow was 27.6 mag, 3.2 mag fainter than the detection. The $H$-band
afterglow is $H\sim 27.4$ mag at 37 d, 3.4 mag fainter than the detection.

To consider also the contribution of an emerging SN component, we have
followed the work of Zeh et al. (2004) and Klose et al. (2019), and modeled
the afterglow and SN component in a joint $g^{\prime}r^{\prime}i^{\prime}H$
fit (rest-frame far-$UV$ and $UBz^{\prime}$ bands). The analytical light curve
of SN 1998bw and the $k,s$ parametrization were used (see §2.4). The parameter
$k$ is the luminosity factor and describes the observed luminosity ratio
between the GRB-SN at peak time and the SN template in the considered band.
The parameter $s$ is a stretch factor with respect to the used
template101010As in §2.3, the cosmological effects such as k-correction were
considered when moving the SN template to the redshift of our GRB. For further
details on the method see Zeh et al. (2004), Klose et al. (2019), and
references therein.. The observer-frame $g^{\prime}$ band (rest-frame far-UV)
is not covered by observations in the case of SN 1998bw (in contrast to the
observer-frame $r^{\prime}$ band, which is the rest-frame $U$ band), so we
assume that the flux density of the SN falls as $\nu^{-3}$ to extrapolate and
derive the corresponding far-UV SN 1998bw template (e.g., Klose et al., 2019).
Note that the $g^{\prime}$ and $r^{\prime}$ data points in Figure 2 after
$2.2$ and $4$ d (observer-frame) are upper limits only. In order to constrain
the flux density of a possible SN contribution in these bands, we considered
these limits as proxy detections in the modelling. We also remind the reader
that the $i^{\prime}$\- and $H$-band afterglow light curves have been
spectrally extrapolated (see above) because there are no observations in these
bands during the afterglow phase. The sparse data in $i^{\prime}H$ preclude
determining the precise temporal evolution of the late emission, but do not
preclude determining more information on the luminosity. The stretch factor
was fixed at $s=1$ for all bands and the luminosity factor $k$ was allowed to
vary freely and individually in each band. The results of this joint fit are
presented and discussed in §3.3.

##  3 Results

A summary of the photometry of the transient resulting from the host-
subtraction analyses is presented in Table 1. NIR emission (rest-frame $\sim
0.93\,\mu$m) is clearly detected 37 d (21.22 d rest frame) after the burst
(see also Fig. 1). Thanks to our late reference images obtained with the LBCs,
which are free from SN light, we also detect the bump in the $i^{\prime}$-band
at 28.3 and 46.1 d (14.9 and 26.3 d rest frame). Ahumada et al. (2021) report
a bump that is $\sim 1$ magnitude fainter and they do not find the transient
in the second epoch. This last detection allows us to better constrain the
late evolution of the transient. In the $r^{\prime}$-band, the presence of the
bump could only be constrained beyond the $3\sigma$ magnitude limits of
$r^{\prime}>25.5$ mag, $r^{\prime}>25.3$ mag, and $r^{\prime}>25.7$ mag in the
first Gemini, TNG and LBT epochs, respectively (the results presented here
supersede the preliminary results of Rossi et al. 2020a).

Figure 3: GRB 200826A (red) in the $E_{\rm p,i}-E_{\rm iso}$ plane. GRBs with
an associated SN are highlighted in green, outliers in blue (see §3.1). GRB
data is from Amati et al. (2019).  Figure 4:  The $T_{\rm 90,i}$ – $EH$
diagram for SGRBs (blue squares) and LGRBs (red circles) with corresponding
cluster analysis results. 68% and 95% confidence regions are shown by bold
solid and thin dashed curves. Data from Minaev & Pozanenko (2020a, b).

###  3.1 GRB 200826A

The duration of GRB 200826A, as reported by the different detectors and in
different energy bands, is $1-2$ s, placing it right at the divide between
SGRBs and LGRBs in the duration distribution commonly used to distinguish
between these two classes (but see de Ugarte Postigo et al., 2011; Bromberg et
al., 2012).

There are other events that lie in between the two populations, but none has
an observed $T_{90}$ shorter than 2 s and an associated SN which clearly
points to a collapsar origin. For example, GRB 090426 ($z=2.609$) has a
duration shorter than 2 s but also has characteristics typical of LGRBs
including softer spectra, a bright afterglow and a blue and low-mass host
(Antonelli et al. 2009; Thöne et al. 2011; Nicuesa Guelbenzu et al. 2011,
2012, Kann et al. 2022, in prep.). It could be argued that one should consider
the intrinsic duration in the rest frame ($T_{\rm 90,i}$). Doing so, the
duration of GRB 200826A would be between 0.39 (Konus-Wind) and 0.57 (GBM) s,
i.e., well below 2 s. The only other GRB with an associated SN that could be
classified as short because of its intrinsic duration ($T_{\rm 90,i}=2.4$ s,
$z=0.86$) is GRB 040924 (Wiersema et al., 2008; Soderberg et al., 2006; Huang
et al., 2005). Many other cases exist at high redshift like GRB 080913
(Greiner et al., 2009; Zhang et al., 2009), but the redshift is too high to
search for the associated SN (at least with the current facilities).

Bromberg et al. (2012) showed that the 2 s duration commonly used to separate
collapsars and non-collapsars is inconsistent with the duration distributions
of _Swift_ and _Fermi_ GRBs and only holds for old _CGRO_ /BATSE GRBs.
However, the analysis of the Konus-_Wind_ data (Svinkin et al., 2020) showed
that GRB 200826A has a duration typical of SGRBs. Thus, the short duration of
GRB 200826A is instrument-independent. In this case T90 alone is insufficient
to determine which population GRB 200826A is best associated with. Another
feature typical of LGRBs is a non-negligible spectral lag (Norris et al.,
1996). This parameter has been calculated and the details are provided in
Appendix A. We obtain a spectral lag of $96\pm 38$ ms, which lies in between
the values found by Ahumada et al. (2021) and Zhang et al. (2021). In
agreement with their analysis, we conclude that the measured spectral lag is
more typical of LGRBs.

It is only when both the spectral properties of GRB 200826A and its location
in the hardness-duration plane are considered that it appears to be more
similar to “long” GRBs. However, if this is indeed the shortest “long” GRB
associated with a SN, then additional evidence is needed to demonstrate that
it does not belong to the SGRB class. Such a result would challenge the
standard paradigm for SGRB and LGRB progenitors.

In this respect, a very useful tool is the location of a GRB in the $E_{\rm
p,i}-E_{\rm iso}$ plane111111$E_{\rm p,i}=E_{\rm p,obs}(1+z)$ is the rest-
frame photon energy at which the $\nu$Fν spectrum peaks, and $E_{\rm iso}$ is
the isotropic-equivalent radiated energy as measured in a “bolometric” band,
usually 1 keV – 10 MeV in the rest frame., where LGRBs follow a strong
correlation known as the “Amati Relation” (Amati et al., 2002; Amati, 2006).
In comparison, SGRBs populate a different region in this plane (e.g., D’Avanzo
et al., 2014; Minaev & Pozanenko, 2020a). Therefore, the fluence and spectral
parameters reported by the Konus-_Wind_ and _Fermi_ /GBM teams were used
(Ridnaia et al., 2020; Svinkin et al., 2020; Mangan et al., 2020) to compute
the values of $E_{\rm p,i}$ and $E_{\rm iso}$, and their uncertainties, for
GRB 200826A. As can be seen in Fig. 3, this event is fully consistent with the
$E_{\rm p,i}-E_{\rm iso}$ relation followed by LGRBs. This further supports
the hypothesis that it is actually a “long” GRB with a duration in the short
tail of the distribution.

Recently, the energy-hardness ($EH$) parameter – a combination of Ep,i and
Eiso ($EH$ = $E_{\rm p,i}E_{\rm iso}^{-0.4}$) – was introduced in Minaev &
Pozanenko (2020a). Although GRB 200826A is placed inside the 95% cluster
region of long bursts in the $T_{\rm 90,i}$ – $EH$ diagram (Fig. 4), it is
evident that this does not permit an unambiguous classification of a burst
being close to the cluster region intersection (see also Zhang et al. 2021 for
a similar analysis and conclusion). Also the position in the $E_{\rm
p,i}-E_{\rm iso}$ plane may not be sufficient for classification. Indeed,
interesting examples such as GRB 201221D121212 With a rest-frame Fermi/GBM
$\rm T_{90}=0.068$ s (Hamburg et al., 2020), and Swift/BAT $\rm
T_{90}=0.078\pm 0.0196$ s (Krimm et al., 2020). (Agüí Fernández et al., 2021)
exist which follow the $E_{\rm p,i}-E_{\rm iso}$ relation for LGRBs but are in
the SGRB region in the $T_{\rm 90,i}$ – $EH$ diagram.

Figure 5: The optical afterglow of GRB 200826A (red line) compared with the
sample of extinction-corrected afterglows shifted to $z=1$ from Kann et al.
(2010, 2011, 2022, in prep.). Hereby, time and magnitudes are given in the
observer frame, but assuming all GRBs are at $z=1$ in a perfectly transparent
universe. Light gray are LGRBs, thicker black lines SGRBs with secure
redshifts (solid lines connect detections, dashed lines connect upper limits).
All magnitudes are Vega magnitudes. The afterglow of GRB 200826A lies
intermediately between those of secure LGRBs and secure SGRBs.  Figure 6:  The
X-ray afterglow of GRB 200826A (red line) in the context of the X-ray
afterglows of 449 Swift GRBs with known redshifts. This event could be
followed-up by Swift/XRT only after 10ks, but the few data points obtained
show that the luminosity of GRB 200826A is in between the long and short
populations. The grayscale on the right is used to convert a given luminosity
and time into a fraction of bursts.

###  3.2 The afterglow of GRB 200826A

A well known-result is that most SGRB afterglows are much fainter than LGRB
afterglows (Gehrels et al., 2008; Nysewander et al., 2009; Kann et al., 2010,
2011). Following the method of Kann et al. (2006), using a spectral slope of
$\beta=0.79$ and no line-of-sight extinction, in Fig. 5 the optical afterglow
of GRB 200826A was compared with a large sample of SGRB and LGRB optical
afterglows (taken from Kann et al. 2006, 2010, 2011; Agüí Fernández et al.
2021, Kann et al. 2022, in prep.). Similarly, in Fig. 6 the X-ray emission of
GRB 200826A was compared with that of $\sim 500$ GRB afterglows (of which 38
are SGRBs) detected in at least two epochs and with known redshift. The X-ray
light curves where obtained from the Swift Burst analyzer131313
https://www.swift.ac.uk/burst_analyzer/ (Evans et al., 2010) and put in the
same frame using the method described in Schulze et al. (2014). The afterglow
of GRB 200826A is among the faintest afterglows of LGRBs but also among the
brightest ones of SGRBs , both in the X-ray and optical bands. Thus, the
afterglow luminosity is not a good method for discriminating between, nor
understanding the nature of this burst.

Figure 7: Light curve in $i^{\prime}$ and $H$ bands after removing the host
component via image subtraction (see Table 1). Only data after 10 d (observer
frame) are shown. The data are corrected for Galactic extinction (see § 2.3).
The SN light curve templates obtained from SN 1998bw, 2013dx, and SN 2016jca
are shown for comparison and to stress the large range of variability and
color of GRB-SNe (See §3.3). Downward-pointing triangles are upper limits.

###  3.3 The late bump as supernova emission

Although the sparse data precludes determining the evolution of the late bump
seen in the transient light curve, a comparison can be made with other GRB-SNe
to look for similarities. This comparison includes: GRB 980425/SN 1998bw
(Galama et al., 1998) GRB 060218/SN2006aj (Ferrero et al., 2006); GRB
100316D/SN1010bh (Olivares E. et al., 2012); GRB 130702A/SN 2013dx (D’Elia et
al., 2015; Toy et al., 2016; Volnova et al., 2017; Mazzali et al., 2021); and
GRB 161219B/SN 2016jca (Cano et al., 2017b; Ashall et al., 2019b). In Fig. 7
we show only those GRB-SNe with comparable peak luminosities and colors,
including SN 1998bw which has been used to also fit extreme events such as SN
2011kl (Greiner et al., 2015; Kann et al., 2019) and the SN bump of GRB
140506A (Kann et al., 2021). Due to the non-negligible redshift of GRB
200826A, the observed $r^{\prime}$-, $i^{\prime}$\- and $H$-band data sets
correspond approximately to the rest-frame $U$, $B$, and $z^{\prime}$-bands,
respectively. In the following comparison, we will refer to these rest-frame
bands.

The SN associated with GRB 200826A appears fainter than SN 1998bw in the rest-
frame $B$-band than SN 1998bw, but is of comparable luminosity or slightly
brighter ($\lesssim 0.5$ mag) than SN 1998bw in rest-frame $z$-band. The most
striking feature is the suppression in the rest-frame $U$-band, at least $1$
mag compared to SN 1998bw at 28 d. This prompted a further investigation into
GRB-SNe with redder colors, and produced a possible agreement with GRB
130702A/SN 2013dx. This GRB-SN (like GRB 161219B/SN 2016jca and possibly GRB
050525A/SN 2005nc, Della Valle et al. 2006) is characterized by a rise-to-
maximum time $\Delta t<\sim 15$ d in the respective rest frame (e.g., Belkin
et al., 2020b), which is a parameter related to properties of the progenitor
stars (e.g., González-Gaitán et al., 2015).

In section 2.4 we have modelled the late light curve considering the
analytical light curve of SN 1998bw and the $k,s$ parametrization following
the work of Zeh et al. (2004) and Klose et al. (2019), which allows us to
place quantitative constraints on the above analysis. We remind the reader
that there are no detections in $g^{\prime}r^{\prime}$ after $2.2$ and $4$ d
(observer-frame), thus with our modelling we can only place deep upper limits
on the flux density of the SN contribution in these bands (see Fig. 2). In
terms of luminosity, a potential SN contribution in the rest frame far-UV
(observed $g^{\prime}$ band) is found as $k_{g^{\prime}}<1.5$, an unremarkable
limit to its luminosity. Therefore, although the spectral slope of the
extrapolation mentioned above is insecure, this does not have any significant
impact on our modeling. However, there is clear UV suppression in the rest
frame $U$-band, we find $k_{r^{\prime}}<0.43$, implying that the SN associated
with GRB 200826A is less than half as luminous as SN 1998bw in the same rest-
frame band. In the rest frame $B$-band the suppression is also strong compared
to SN 1998bw with $k_{i^{\prime}}=0.56\pm 0.10$. The rest-frame
$z^{\prime}$-band detection (observed $H$ band) is, however, marginally
brighter than SN 1998bw ($k_{H}=1.18\pm 0.22$). Moreover, it lies close to the
SN peak for $s=1$, and thus a significantly faster or slower SN would be even
brighter. When compared with the list of $k,s$ values of Klose et al. (2019)
and Cano et al. (2017a) the $k$ factor ranges between 0.5 and 2. This provides
plausible support for a SN.

Figure 8: Light curves of GRB 200826A after host subtraction compared with the
light curves of AT2017gfo (solid lines) from Rossi et al. (2020b) and with
theoretical KN light curves boosted by a magnetar from Perego et al. (2017)
with three different magnetic field strengths (dotted, dashed, dot-dashed
lines; §3.4). Downward-pointing triangles are upper limits.

###  3.4 Possible Kilonova emission

In Fig. 8, the late-time photometry of the transient is compared with the
light curve of AT2017gfo, the KN associated with the binary NS merger GW
170817 and the SGRB 170817A (Abbott et al., 2017c). The KN light curves are
obtained from observed spectra shifted and scaled to the same redshift as GRB
200826A, following the method described in Rossi et al. (2020b). The
comparison shows that the luminosity of the transient was at all times at
least 3 mag brighter than the peak luminosity of AT2017gfo. This is not
extraordinary, because KNe $\gtrsim 10$ times more luminous in the optical
have been claimed (e.g., Gao et al., 2017; Fong et al., 2021). However, what
makes this event very different from all KNe observed so far is its slower
temporal evolution: assuming that the rest-frame $B$-band detection
($i^{\prime}$ band in observer-frame) detection is close to maximum light,
i.e. $\sim 16$ d in the rest frame, then the peak would be more than $\sim 15$
d later than that of AT2017gfo. The analysis below investigates whether such
behavior is theoretically possible.

Modeling of KNe powered by radioactive decay of $r$-process nuclei showed that
KNe produced by nearly equal-mass binary NS mergers are expected to have peak
times and magnitudes similar (within a few d and one or two magnitudes,
respectively) to the ones observed in AT2017gfo, especially in the case of
face-on mergers characterized by lanthanide-free high-latitude ejecta (e.g.,
Radice et al., 2018b; Kawaguchi et al., 2020). Viewing angle and composition
effects possibly decrease the KN luminosity compared with face-on
configurations (Korobkin et al., 2021). In the case of very unequal-mass
binary NS or black-hole NS mergers, the peak evolution can be slower,
especially in the rest-frame NIR bands, but with similar peak magnitudes
(e.g., Barbieri et al., 2019; Bernuzzi et al., 2020; Kawaguchi et al., 2020;
Zhu et al., 2020). These theoretical results seem to also disfavour the
interpretation of the observed transient as a KN powered by radioactive decay.

However, it is known from several studies (e.g., Gompertz et al., 2018;
Ascenzi et al., 2019; Rossi et al., 2020b; Rastinejad et al., 2021), that the
distribution of luminosities covers a large range, and some KNe can be ten
times more luminous than AT2017gfo, such as in the cases of those associated
with GRBs 060614 and 050724 (Gao et al., 2017). Even more extreme cases that
are $\sim 100$ times more luminous have been claimed in association with GRB
070714B (Gao et al., 2017) and more recently GRB 200522A (Fong et al., 2021;
O’Connor et al., 2021), although the evidence is not very strong. To achieve
this large blue luminosity, the KN can be boosted by energy deposition from a
magnetar remnant. Indeed, long-lived merger remnants could have a significant
impact on KN light curves. While larger amounts of ejecta, expelled due to
angular momentum excess, can increase the peak magnitudes, times, and widths
only marginally (e.g., Radice et al., 2018a), the presence of a fast-rotating
magnetar (in addition to being a possible GRB central engine) can boost the KN
luminosity via spin-down luminosity (Yu et al., 2013; Metzger & Piro, 2014;
Siegel & Ciolfi, 2016).

To explore this scenario, the KN model presented in Perego et al. (2017) was
used and extended to consider spin-down energy injection, as well as sources
at cosmological distances in which the fluxes, the (thermal) spectra, and the
observer time are corrected for the cosmological redshift. The computed KN
light curves are shown in Fig. 8. For simplicity, a spherically symmetric
ejecta model is considered for which $0.02\,M_{\odot}$ of matter expands
homologously at $0.2c$. Given that the adopted model foresees the presence of
a long-lived magnetar, an effective gray opacity $\kappa=1$ cm2 g-1, typical
of lanthanide-poor ejecta, was assumed. $P_{0}=0.7$ ms was fixed as a typical
initial rotation period (Radice et al., 2018a), while the strength of the
magnetic field $B$ and the energy deposition efficiency for the spin-down
luminosity $\epsilon_{\rm th}$ were varied to obtain a plausible agreement
with the observations. A reasonable match for $B\sim 10^{14}$ G and
$\epsilon_{\rm th}=0.03$ are shown in Fig. 8. For the considered bands, larger
magnetic field strengths ($B=10^{15}$ G) result in lower, more rapidly
declining peaks, and a plausible match with the data would require
$\epsilon_{\rm th}\gtrsim 1$. Weaker field strengths ($B=10^{13}$ G), on the
other hand, produce more luminous, slower evolving peaks, which plausibly
match with the data for $\epsilon\lesssim 0.001$. The ejecta properties also
influence the light curves, but less significantly.

The calculations suggest that the observed transient could be compatible with
the late emission of a spin-down powered KN for plausible values of the
magnetic field and thermalization efficiency. Unfortunately, all of the
magnetically-boosted KN models fail to explain the red color of the transient,
and in particular the strong UV suppression observed in the observer-frame
$r^{\prime}$ band, although modeling greatly simplifies the ejecta, the
emission properties, and in particular its opacity. But most importantly,
during the first 10 d the theoretical KN is comparable or brighter than the
observed data without accounting for the afterglow. Therefore, the
magnetically-boosted KN models are excluded.

Figure 9: Le PHARE modeling discussed in §3.5 of the SED obtained from the
final LBT/LBC $UR_{C}i^{\prime}z^{\prime}$, MAO $B$, LBT/MODS
$g^{\prime}r^{\prime}$, LBT/LUCI $J$, and LBT/LUCI+SOUL $H$ band imaging (see
Table 1). The blue points indicate where the photometry would be placed
according to the best-fit model and without contribution from emission lines.
Figure 10: LBT/MODS observed spectrum of the host galaxy of GRB 200826A binned
by 2.5 Å for presentation purposes. The detected emission lines are marked.

###  3.5 The host galaxy

Table 2: Emission lines and their measured fluxes corrected for Galactic
extinction.

Lines | flux
---|---
| [10-17 erg/cm2/s]
$[$OII] $\lambda$3727 | $12.6\pm 0.4$
$[$NeIII] $\lambda$3869 | $2.1\pm 0.4$
HeI $\lambda$3889 | $1.2\pm 0.4$
$[$NeIII] $\lambda$3968 | $1.2\pm 0.4$
H$\delta$ $\lambda$4102 | $1.8\pm 0.4$
H$\gamma$ $\lambda$4340 | $2.8\pm 0.4$
H$\beta$ $\lambda$4861 | $6.4\pm 0.6$
$[$OIII] $\lambda$4959 | $8.0\pm 0.3$
$[$OIII] $\lambda$5007 | $26.5\pm 0.9$

  * •

The FWHM of the lines is $\sim 6.1$ Å. The mean redshift of the emission lines
is $z=0.748577\pm 0.000065$.

As first reported in Rothberg et al. (2020a, b), the continuum of the host
galaxy was clearly detected between $0.38\,\mu\textnormal{m}-0.98\,\mu$m. A
redshift of $z=0.748577\pm 0.000065$ was determined from the simultaneous
detection of the following emission lines: [O II], [O III] and [Ne III]
doublets, He I $\lambda$3889, and Balmer H$\delta$ $\lambda$4101, H$\gamma$
$\lambda$4340, and H$\beta$ $\lambda$4861 (Fig. 10). Fluxes of the lines were
measured using the slinefit code (Schreiber et al., 2018) which also allows
correction of the Balmer-line fluxes for the underlying stellar absorption.
All the measured fluxes are reported in Table 2. The absorption lines of the
Mg II$\lambda\lambda$2796,2803 doublet were also detected at a lower redshift
($z=0.7462\pm 0.0002$) which may possibly imply that they are due to an
intervening Mg II absorber along the line of sight (Vergani et al., 2009;
Christensen et al., 2017). The rest-frame equivalent width for both lines in
the doublet is $W_{rest}=2.4\pm 0.6$ Å.

Using the derived redshift as a fixed input, the optical/NIR SED of the host
galaxy was modeled (Table 1) with the code Le PHARE (Arnouts et al., 1999;
Ilbert et al., 2006). The best fit ($\chi^{2}/d.o.f.=2.2/9$) points to a
galaxy dominated by a young population ($0.04_{-0.02}^{+0.08}$ Gyr) with
global dust reddening E(B-V) $\sim 0.2$ mag using the Small Magellanic Cloud
(SMC) curves from Pei (1992) and low stellar mass $\log
M_{\ast}/M_{\odot}=8.6\pm 0.2$ (Fig. 9). The $B$-band dust-corrected absolute
magnitude is M${}_{B}=-20.01$ mag and the star-formation rate is
$\textnormal{SFR}=13.0_{-6.0}^{+10.9}\,M_{\odot}/$yr. With this large
uncertainty, this SFR is consistent with what is measured from the emission
lines (see below). The dust extinction is in agreement with the broad range of
values found for LGRB hosts, also in comparison with the SFR (Hunt et al.,
2014; Japelj et al., 2016). It is different from the afterglow-derived
negligible extinction, indicating that the GRB sight-line might be crossing a
relatively dust-free region (e.g., by being placed at the front side of the
host galaxy). Respective to Ahumada et al. (2021), we find a mass that is a
factor ten lower. The computed lower mass is most likely because the NIR
observations were obtained sufficiently late to be free of any contributions
from the transient.

Using the Balmer decrement, and assuming the theoretical values for the
H$\gamma$/H$\beta$ and H$\delta$/H$\beta$ ratios, in the absence of dust, for
case B recombination at a gas temperature of 104 K (Osterbrock, 1989), and a
Milky Way (MW) extinction law141414Note that the difference between the MW and
the SMC or LMC extinction laws is small in the wavelength range of H$\delta$
to H$\beta$. (Pei, 1992) with $R_{\rm V}=3.1$, we derive an E(B-V) of $\sim
0.16$ mag and $A_{V}\sim 0.5$ mag. Using extinction corrected H$\beta$ and [O
II] fluxes and the prescriptions provided by Kennicutt (1998) and Savaglio et
al. (2009), the resulting star-formation rate (SFR) of the host galaxy is SFR
$\sim 4.0\,M_{\odot}$/yr. The SFR as determined from the line fluxes is within
$2\sigma$ of that derived from SED fitting. The high SFR obtained from two
separate methods implies a specific star-formation rate (sSFR, SFR per unit
stellar mass) of 1–3$\times 10^{-8}$ yr-1, among the highest measured so far
in the LGRB host population (e.g., Savaglio et al., 2009; Hunt et al., 2014;
Perley et al., 2013; Vergani et al., 2015; Japelj et al., 2016; Schulze et
al., 2018; Modjaz et al., 2020). For comparison, this sSFR is about two orders
of magnitude higher than for the Large Magellanic Cloud. Moreover, if the
derived SFR were constant, this would imply that the time required for the
host to build the measured stellar mass would be about 0.03–0.1 Gyr, which is
consistent with the upper limit obtained from the SED best-fit. Using several
diagnostic tools in Lamareille (2010), Trouille et al. (2011), and Marocco et
al. (2011) the presence of an AGN, which may mimic a high SFR, can be
confidently excluded.

The diagnostic ratios of [O II], [O III], and H$\beta$ emission lines were
used to derive the gas metallicity in the host galaxy. Many calibrators have
been proposed in the past (for a review, see Maiolino & Mannucci, 2019); the
method proposed by Curti et al. (2017) was adopted which computes the best-fit
metallicity by minimizing $\chi^{2}$ in the space defined by the different
possible diagnostics given the available emission lines. This yielded
$12+\log(\textnormal{O/H})=8.31\pm 0.02$. This is in agreement with the value
of $12+\log(\textnormal{O/H})\simeq 8.3$ obtained from using the [Ne
III]$\lambda$3869/[O II] line ratio (e.g., Bian et al., 2018), a method which
has more uncertainties. The resulting sub-solar metallicity
($Z/Z_{\odot}\simeq 0.4$) is consistent with the value derived for the LGRB
hosts at similar redshift (Japelj et al., 2016). However, we note that the
redshift evolution of the mass-metallicity relation in normal star-forming
galaxies derived by Bellstedt et al. (2021) shows that galaxies at $z=0.62$ or
0.8 and stellar mass similar to the GRB 200826A host have a typical
metallicity of about $12+\log(\textnormal{O/H})=7.85$ or 7.80, respectively,
significantly below our measured value. Taken together, these results indicate
that the host galaxy of GRB 200826A is characterized by a typical metallicity
but larger than usual SFR and sSFR for a LGRB host.

For the adopted cosmological parameters and using the last deep $H$-band
observation, the half-light radius of the host galaxy is $R_{h}=0\farcs 16$ or
1.2 kpc at the redshift of the GRB. This size is consistent with LGRB hosts of
similar masses (Kelly et al., 2014). The high angular resolution from the
LUCI-AO observations also makes it possible to measure the GRB-SN position
within the host. The transient has an offset of $R=0\farcs 1$ from the center
of the host, which corresponds to 0.75 kpc. This corresponds to a normalized
offset $R/R_{h}=0.62$ which is also consistent with the vast majority of LGRBs
(e.g., Bloom et al., 2002; Blanchard et al., 2016).

##  4 Discussion

Additional support for the collapsar scenario was recently reported by Rhodes
et al. (2021). By analyzing the radio and X-ray light curves, they found
evidence of a sharp rise peaking at $4-5$ d after the trigger in the radio
bands. Within the LGRB/collapsar scenario, they propose that the peak is
produced by the synchrotron self-absorption frequency moving through the radio
band, resulting from the forward shock propagating into a wind medium. Is our
modeling of the afterglow and optical-to-Xray SED in agreement with their
claim? The spectral slope of $\beta=0.79$ we have found in §2.4 favors the
emission in both optical and X-rays to be below the cooling frequency, i.e.,
$\beta=(p-1)/2$, with $p=2.58\pm 0.06$ following Sari et al. (1998), a typical
value for synchrotron emission in GRB afterglows. If the afterglow is in the
post-break phase when we measure the SED, the spectral and decay slopes are
difficult to justify within the standard afterglow theory. Therefore, assuming
that the afterglow is still in the pre-break phase (spherical expansion) the
temporal decay index for emission below the cooling break is $\alpha=3(p-1)/4$
and $\alpha=(3p-1)/4$ for an ISM and wind environment, respectively. Using
$\alpha=1.59\pm 0.20$, we obtain $p=3.12\pm 0.27$ and $p=2.45\pm 0.27$,
respectively (Granot & Sari, 2002), and thus we find that propagation into a
wind environment could well explain both spectral index and light-curve decay,
in support of the analysis of Rhodes et al. (2021). While steep, a pre-break
decay of $\alpha=1.59$ is not unheard of, the sample of Zeh et al. (2006)
contains two out of 16 well-defined light curves with $\alpha_{1}\approx 1.75$
followed by clear breaks and much steeper post-break decay slopes
$\alpha_{2}\approx 3$. In such a case, the early shallower decay of the
afterglow of GRB 200826A could represent an optical plateau (e.g., Dainotti et
al., 2020, Ronchini et al., in prep.). In this scenario the late shallow decay
observed in the X-rays can be explained as energy injection from a new-born
magnetar (see also Zhang et al., 2021), but also by the receding cooling
frequency after the passage of the wind termination-shock radius (e.g.,
Schulze et al., 2011).

All arguments presented in this work point to a massive-star origin consistent
with a collapsar event despite the very short duration. Several theoretical
routes have been presented to explain this. In one of the scenarios discussed
by Zhang et al. (2021) and by Ahumada et al. (2021) to explain the short
duration of the burst, if the progenitor was a massive star it is possible
that the total duration of the engine was longer than the rest-frame duration
of 1 s, but somehow the jet could not emit gamma-rays for a longer time. For
example the jet could spend a longer time penetrating the envelope of the
star. Alternatively, the jet might not be highly relativistic for longer than
1 s, so that no bright $\gamma$-rays could be produced after this time like,
e.g., in the case of a newborn magnetar that initially injects a baryon-
loaded, neutrino-driven wind (see also Ghisellini et al., 2020). Zhang et al.
(2021) also note that the energy injection from the newborn magnetar could
explain the late shallow decay observed in the X-rays. Other alternatives
exist like the mechanism known as the inhomogeneous jet model, proposed by
Yamazaki et al. (2004), in which the jet consists of multiple sub-jets which
we observe as short GRBs. Therefore, a fraction of SGRBs may come from
collapsars. Peng et al. (2021) have recently proposed that the burst could
have originated from the collapse of a Thorne-Żytkow-like Object (TŻlO), which
consists of a central NS and envelope formed after a coalescence with a white
dwarf. They found the collapse of such a TŻlO can naturally explain the short
duration of GRB 200826A and the interaction between the disk wind and the
ejected material can explain the “supernova bump”. However, this model needs
to be proven with the updated photometry presented here, and in particular
with our result that the SN is similar to other GRB-SNe. We have also
demonstrated the importance of Adaptive Optics (AO) to studying GRBs. The NIR
follow-up observations presented here are the first to detect and pinpoint the
location of a SN associated with a GRB, track the SN evolution, as well as
determine the properties of the host galaxy. The last published attempts were
more than 11 years ago and served only to provide information on the host
galaxy of GRB 060418 (Pollack et al., 2009), and in case of GRB 070610 to
determine that a NIR transient was actually the counterpart of a galactic
source (Castro-Tirado et al., 2008), making that GRB association uncertain
(Kasliwal et al., 2008). The only other approach similar to that outlined in
this paper was the case of GRB 071003 (Perley et al., 2008). In that case, AO
observations made possible to detect the afterglow which was localized between
two bright stars, but those observations were too early and the redshift too
high to detect the associated SN ($z=1.60435$, and $\sim$16 d, respectively).
The results presented here demonstrate clearly that AO can provide a powerful
tool for studying GRBs.

##  5 Summary and conclusions

GRB 200826A is a temporally short GRB at $z=0.748577\pm 0.000065$ with a rest-
frame duration of $\sim 0.5$ s, below the threshold of 2 s commonly used to
separate SGRBs and LGRBs. To better understand the nature of this event, we
initiated a follow-up campaign spanning a period of 1 year which involved the
LBT telescope in Arizona (USA), the TNG telescope on La Palma (Canary Islands,
Spain) and the Maidanak Astronomical Observatory (Uzbekistan). Taking
advantage of the adaptive optics capabilities of LBT, we were able to obtain
deep $H$-band observations between 37 and 159 d (observer frame),
corresponding to the rest-frame $z^{\prime}$ band at 21 to 91 d after the
burst trigger. Image subtraction shows a faint transient within its host
galaxy. Moreover, image subtraction of archival Gemini $i^{\prime}$-band
images with late reference observations obtained with the LBT revealed an
optical transient which is less affected by over-subtraction than had been
when reference images obtained at an earlier time after the GRB had been used.
Finally, we were able to put strong upper limits on the UV rest-frame
luminosity thanks to our LBT and TNG $r^{\prime}$-band observations. Our
results show that:

  * •

Despite its short duration, this event is consistent with the $E_{\rm
p,i}-E_{\rm iso}$ “Amati” relation followed by LGRBs. The spectral lag is also
more typical of LGRBs.

  * •

It was followed by a relatively faint optical and X-ray afterglow with a
luminosity that lies in between those of LGRB and SGRB afterglows.

  * •

The evolution and color of the late bump is in good agreement with other GRB-
SNe, and especially with the fast rising GRB 130702A/SN 2013dx. GRB 200826A is
one of the cosmologically most remote GRB-SNe detected to date, close to the
sensitivity limit of the present generation of 8 to 10 m class optical
telescopes.

  * •

The possible alternative scenario of a genuine SGRB followed by a KN like
AT2017gfo is not supported by the different evolution and luminosity of the
light curve of the observed transient.

  * •

The host galaxy of GRB 200826A is remarkable because it is typical of an LGRB
host galaxy, but with higher SFR and sSFR rates than expected.

  * •

The GRB lies at a projected distance of 0.75 kpc from the center of its host
galaxy, which is consistent with the majority of LGRBs.

In summary, with the obtained results we are faced with a GRB of short
duration which exploded in a star-forming galaxy, with a moderately faint
afterglow, emitted by a jet most likely propagating into a wind environment,
and followed by a bump in the light curve whose color and luminosity are
typical for a GRB-SN. Thus we firmly classify this burst as a collapsar event.
This evidence, together with the analysis of the energetics of this burst,
further weakens the effectiveness of simple duration as an indicator of the
source of a GRB. In addition, strong support is provided to theoretical
predictions that collapsar-produced events may have an observable duration
well short of the classical short/long divide (about 2 s), and down to 0.5 s
or less (e.g., Bromberg et al., 2013).

In the next years future missions, like the Space Variable Objects Monitor
(SVOM; Paul et al., 2011) and the Gamow Explorer (White et al., 2021) will
offer a combination of extended sensitivity and energy bands that will
increase the number of known GRBs. This, when coupled with the improved
capabilities of the new generation of extremely large telescopes will allow us
to observe both the GRB and SN components resulting from collapsar explosions
in increasing numbers and at higher redshifts (e.g., Maiorano et al., 2018;
Rossi et al., 2018). In this scenario, the first detection of a SN with AO
observations represents what ground-based telescopes can achieve: they will
not just offer a sharper view of the GRB-SN location within its host, but have
the necessary depth to discover GRB-SNe at larger redshift than what has been
possible up to now from the ground, and yet at similar wavelengths in rest-
frame. Eventually, these future facilities will assess whether peculiar events
like GRB 200826A are actually the result of the rich variety of the collapsar
phenomenon (Amati, 2021).

We thank the anonymous referee for providing thoughtful comments. We thank E.
Pinna, D. Miller, J. Power and G. Taylor for their support during AO
observations. We thank M. Curti for providing us with his code. A. Rossi
acknowledges support from the INAF project Premiale Supporto Arizona & Italia.
B. Rothberg would like to acknowledge the assistance and support of R. T.
Gatto. D.A.K. acknowledges support from Spanish National Research Project
RTI2018-098104-J-I00 (GRBPhot). P.D.A. acknowledges funding from the Italian
Space Agency, contract ASI/INAF n. I/004/11/4. L.I. was supported by two
grants from VILLUM FONDEN (project number 16599 and 25501). A.N.G. and S.K.
acknowledge financial support by grants DFG Kl 766/16-3, DFG Kl 766/18-1, and
DFG RA 2484/1-3. A.N.G. acknowledges support by the Thüringer Landessternwarte
Tautenburg. A.S.P., P.Y.M. and A.A.V. acknowledge a support of the RSF grant
18-12-00378. S.S. acknowledges support from the G.R.E.A.T research
environment, funded by Vetenskapsrådet, the Swedish Research Council, project
number 2016-06012. A.R., E.Pal., P.D.A., L.A., A.P., E.Pi., S.S., G.S., S.C.,
V.D.E., M.D.V., and A.M. acknowledge support from PRIN-MIUR 2017 (grant
20179ZF5KS). The LBT is an international collaboration among institutions in
the United States, Italy and Germany. LBT Corporation partners are: The
University of Arizona on behalf of the Arizona Board of Regents; Istituto
Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft, Germany,
representing the Max-Planck Society, The Leibniz Institute for Astrophysics
Potsdam, and Heidelberg University; The Ohio State University, representing
OSU, University of Notre Dame, University of Minnesota and University of
Virginia. This work made use of data supplied by the UK Swift Science Data
center at the University of Leicester.

##  Appendix A Spectral lag

We first extracted the Fermi/GBM light curves with 1 ms resolution for the
best exposed NaI detectors 6, 7, 8, 9, and 11 and calculated the corresponding
total light curve in the same energy bands as Zhang et al. (2021): 10-20 keV,
and 250-300 keV, respectively. We linearly interpolated the background counts
of the 16-ms binned curves by fitting the time windows $[-10:-2]\cup[7:10]$ s.

For the spectral lag calculation, we then restricted the following analysis to
the time interval $[-0.5:4]$ s and calculated the cross-correlation function
(CCF) between the background-subtracted profiles of the two energy bands, both
using the original binning of 1 ms as well as that of 16 ms. A positive lag
corresponds to the softer band lagging behind the harder one. The peak of the
CCF was found to be about 100 ms. To provide a more accurate estimate, we
fitted the CCF around the peak with a third-degree polynomial between $-0.4$
and $0.6$ s and it gave 95 ms. To estimate the uncertainty, we carried out the
following simulations: starting from the 16-ms profiles, we obtained smooth
versions of these curves by adopting the L1 trend filtering by Politsch et al.
(2020) properly adapted to model GRB light curves (e.g., see Ghirlanda et al.
2021). We then obtained 1000 random realisations of both profiles by assuming
uncorrelated Poisson noise, assuming the total expected counts for each
temporal bin (i.e., interpolated background plus smoothed GRB signal). For
each pair of simulated profiles the corresponding CCF was fitted around the
peak following the same procedure as for the real CCF. We finally collected
the resulting distribution of 1000 lags shown in Figure 11: this is
approximately normal with mean and standard deviation $(96\pm 38)$ ms, which
therefore represents our estimate with uncertainty for the lag between the
chosen energy bands. Our value looks slightly shorter than the analogous
result by Zhang et al. (2021), who obtained $(157\pm 51)$ ms, even though
statistically compatible and well in accord with values obtained by those
authors for adjacent energy bands (see their Extended Data Figure 4).

We finally repeated the same simulations using the 1-ms light curves, still
adopting the same smoothed versions properly calibrated to 1-ms bins, and
obtained a very similar result.

Figure 11: Distribution of the spectral lag analysis.

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