# Unveiling the Multifaceted GRB 200613A: Prompt Emission Dynamics, Afterglow
Evolution, and the Host Galaxy’s Properties

Shao-Yu Fu Key Laboratory of Space Astronomy and Technology, National
Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100101,
China  School of Astronomy and Space Science, University of Chinese Academy of
Sciences, Chinese Academy of Sciences, Beijing 100049, China  Dong Xu Key
Laboratory of Space Astronomy and Technology, National Astronomical
Observatories, Chinese Academy of Sciences, Beijing, 100101, China  Wei-Hua
Lei Department of Astronomy, School of Physics, Huazhong University of Science
and Technology, Wuhan, 430074, China  Antonio de Ugarte Postigo Université de
la Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Artemis, 06304 Nice,
France  Aix Marseille Univ, CNRS, LAM Marseille, France  D. Alexander Kann
Hessian Research Cluster ELEMENTS, Giersch Science Center, Max-von-Laue-Straße
12, Goethe University Frankfurt, Campus Riedberg, D-60438 Frankfurt am Main,
Germany  Christina C. Thöne Astronomical Institute, Czech Academy of Sciences,
Fričova 298, Ondřejov, Czech Republic  José Feliciano Agüí Fernández Centro
Astronómico Hispano en Andalucía, Observatorio de Calar Alto, Sierra de los
Filabres, 04550 Gérgal, Almería, Spain  Yi Shuang-Xi  School of Physics and
Physical Engineering, Qufu Normal University, Qufu 273165, China  Wei Xie
Department of Astronomy, School of Physics and Electronic Science, Guizhou
Normal University, Guiyang 550001, China  Guizhou Provincial Key Laboratory of
Radio Astronomy Data Processing, Guizhou Normal University, Guiyang 550001,
China  Yuan-Chuan Zou Department of Astronomy, School of Physics, Huazhong
University of Science and Technology, Wuhan, 430074, China  Xing Liu  Shuai-
Qing Jiang  Tian-Hua Lu  Jie An  Key Laboratory of Space Astronomy and
Technology, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing, 100101, China  School of Astronomy and Space Science, University of
Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049,
China  Zi-Pei Zhu Key Laboratory of Space Astronomy and Technology, National
Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100101,
China  Jie Zheng CAS Key Laboratory of Optical Astronomy, National
Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China
Qing-Wen Tang  Peng-Wei Zhao  Department of Physics, School of Science,
Nanchang University, Nanchang 330031, China  Li-Ping Xin Key Laboratory of
Space Astronomy and Technology, National Astronomical Observatories, Chinese
Academy of Sciences, Beijing, 100101, China  Jian-Yan Wei  Key Laboratory of
Space Astronomy and Technology, National Astronomical Observatories, Chinese
Academy of Sciences, Beijing, 100101, China  School of Astronomy and Space
Science, University of Chinese Academy of Sciences, Chinese Academy of
Sciences, Beijing 100049, China

###### Abstract

We present our optical observations and multi-wavelength analysis of the GRB
200613A detected by Fermi satellite. Time-resolved spectral analysis of the
prompt $\gamma$-ray emission was conducted utilizing the Bayesian block method
to determine statistically optimal time bins. Based on the Bayesian
Information Criterion (BIC), the data generally favor the Band+Blackbody
(short as BB) model. We speculate that the main Band component comes from the
Blandford-Znajek mechanism, while the additional BB component comes from the
neutrino annihilation process. The BB component becomes significant for a low-
spin, high-accretion rate black hole central engine, as evidenced by our model
comparison with the data. The afterglow light curve exhibits typical power-law
decay, and its behavior can be explained by the collision between the ejecta
and constant interstellar medium (ISM). Model fitting yields the following
parameters: $E_{K,iso}=(2.04^{+11.8}_{-1.50})\times 10^{53}$ erg,
$\Gamma_{0}=354^{+578}_{-217}$, $p=2.09^{+0.02}_{-0.03}$,
$n_{18}=(2.04^{+9.71}_{-1.87})\times 10^{2}$ cm-3,
$\theta_{j}=24.0^{+6.50}_{-5.54}$ degree,
$\epsilon_{e}=1.66^{+4.09}_{-1.39})\times 10^{-1}$ and
$\epsilon_{B}=(7.76^{+48.5}_{-5.9})\times 10^{-6}$. In addition, we employed
the public Python package Prospector perform a spectral energy distribution
(SED) modeling of the host galaxy. The results suggest that the host galaxy is
a massive galaxy ($\log(M_{\ast}/M_{\odot})=11.75^{+0.10}_{-0.09}$) with
moderate star formation rate
($\mbox{SFR}=22.58^{+13.63}_{-7.22}M_{\odot}$/yr). This SFR is consistent with
the SFR of $\sim 34.2M_{\odot}$ yr-1 derived from the [OII] emission line in
the observed spectrum.

Gamma-ray bursts (629)

††facilities: XingLong 2.16m(BFOSC), 10.4m GTC (OSIRIS), 2.2m CAHA(CAFOS),
JAST80 (T80Cam), NOT(ALFOSC), Swift(XRT and UVOT), Fermi(LAT and
GBM)††software: Astropy (Astropy Collaboration et al., 2013, 2018), Source
Extractor (Bertin & Arnouts, 1996), emcee (Foreman-Mackey et al., 2013), PyRAF
(Tody, 1986, 1993), Prospector (Johnson et al., 2021), 3ML (Vianello et al.,
2015)

##  1 Introduction

Gamma-ray bursts (GRBs) are the most energetic and luminous explosions in the
universe, which release isotropic energy $10^{48}-10^{55}$ ergs within seconds
(Kumar & Zhang, 2015). Their exceptional luminosity enables their detection
even at remarkably distant locations, reaching redshifts up to $z\sim 9$
(Cucchiara et al., 2011). The study of GRBs has provided invaluable insights
into the physics of extreme astrophysical phenomena and the evolution of the
early Universe (Bromm & Loeb, 2006).

GRBs can be categorized into two primary types based on their duration: long
and short (Kouveliotou et al., 1993). Long GRBs, which constitute about 70% of
all GRBs, typically last for a few seconds to a few minutes and exhibit a high
energy output(Kumar & Zhang, 2015). These events are hypothesized to arise
from the cataclysmic collapse of massive stars, resulting in the formation of
a black hole (Woosley & Bloom, 2006). Conversely, short GRBs, which account
for about 30% of all GRBs, exhibit durations of less than 2 seconds and lower
energy output compared to long GRBs (Gehrels et al., 2005). The prevailing
model for the origin of short GRBs involves the merger of two neutron stars
(Eichler et al., 1989), which has been substantiated by the occurrence of the
gravitational event GW 170817 (Abbott et al., 2017) accompanied by
electromagnetic counterpart GRB 170817A/AT 2017gfo (e.g., Arcavi et al., 2017;
Coulter et al., 2017; Cowperthwaite et al., 2017; Kasliwal et al., 2017;
Soares-Santos et al., 2017).

Since the discovery of GRBs over 50 years ago, the understanding of their
radiation mechanism and emission region has remained incomplete. The fireball
model, a prevailing theory, posits that the prompt emission consists of two
components: a thermal component emitted when the jet becomes optically thin
(known as the photosphere region), and a non-thermal component generated by
collisions between shells of varying velocities within the jet, in a region
distant from the progenitor star. The radiation mechanism responsible for this
emission is synchrotron radiation and synchrotron self-Compton scattering of
relativistic electrons. The fireball model predicts that the prompt emission
should be dominated by a thermal component (Goodman, 1986). However,
observations have shown that the majority of gamma-ray radiation from gamma-
ray bursts is non-thermal, often described by a smoothly joined broken power-
law known as the Band function (Band et al., 1993). With the advent of the
Fermi era, an increasing number of studies have revealed the presence of
additional components alongside the non-thermal Band components in some GRBs,
such as GRB 100507 (Ghirlanda et al., 2013), GRB 100724B (Guiriec et al.,
2011), GRB 101219B (Larsson et al., 2015), GRB 110721A (Axelsson et al., 2012)
and GRB 120323A (Guiriec et al., 2013). Some bursts even exhibit a dominance
of thermal components, as seen in the cases of GRB 090902B and GRB 220426A
(Wang et al., 2022). Wang et al. (2023) discovered a decaying thermal
component in the second brightest gamma-ray burst event, GRB 230307A, which
also displayed a broken “$\alpha$-intensity” behavior in the energy spectrum.
Li et al. (2021) conducted a comprehensive analysis of a large sample of
multi-pulse gamma-ray bursts observed by Fermi, revealing that most gamma-ray
bursts exhibited photosphere components in the early stages of radiation,
close to the trigger, while the late period was dominated by non-thermal
components.

In this paper, we present the analysis of the GRB 200613A, and find that there
is a thermal component in the prompt phase. Additionally, we conduct a
detailed investigation of the multi-band afterglow and the underlying massive
host galaxy. The structure of this paper is as follows: Section 2 provides a
description of the observation and data reduction procedures. In Section 3, we
introduce our modeling approach for both the prompt emission and afterglow
emission. The discussion and conclusion are presented in Section 4 and Section
5, respectively. Throughout this study, we adopt a conventional cosmological
model with the following parameter values: $H_{0}=69.6$ km s-1 Mpc-1,
$\Omega_{M}=0.286$, and $\Omega_{\Lambda}=0.714$ (Bennett et al., 2014).

##  2 Observations and Data Redoction

###  2.1 Space-base Observations

GRB 200613A was triggered by Gamma-ray Burst Monitor (GBM) onboard the Fermi
Gamma-ray Space Telescope (Fermi hereafter) on June 13, 2020 at 05:30:08.214UT
($T_{0}$), with duration $T_{90}\sim 470$ s (50-300keV) and fluence $(4.10\pm
0.05)\times 10^{-5}\mbox{erg/cm}^{2}$ in 10-1000keV (Bissaldi et al., 2020).
The prompt emission exhibited a double peak profile with a long, weak emission
tail that persisted until $\sim 500$s. The Large Area Telescope (LAT) of Fermi
also detected the burst after the GBM trigger, with a photon flux and photon
index higher than 100MeV of $(6.6\pm 3.6)\times 10^{-7}$ph/cm2/s and $-1.73\pm
0.36$, respectively (Ohno et al., 2020).

Subsequently, the X-ray Telescope (XRT) onboard Neil Gehrels Swift Observatory
(Swift hereafter; Gehrels et al., 2004) began to follow up on this burst at
$T_{0}+43.6$ ks after the Fermi/GBM trigger and identified seven uncatalogued
X-ray sources within the Fermi/LAT error circle. Among these sources, “Source
2” was found to be above the ROSAT ALL-SKY SURVEY (RASS) limit and is,
therefore, the most likely GRB afterglow. The position of “Source 2” was
reported as RA = 10:12:10.08, Dec = +45:45:14.7 (J2000) with an error radius
of 1.4 arcsec (90% confidence). Preliminary analysis indicates that the
spectral index of 1.89 was obtained by fitting XRT spectra with an absorbed
power-law. The best fit for the absorption column was $(2.3\pm 0.5)\times
10^{21}$ cm-2, which exceeds the Galactic value of $8.4\times 10^{19}$ cm-2
(Kennea et al., 2020).

The Ultraviolet/Optical Telescope (UVOT) slewed to the position of the burst
at $T_{0}+43.6$ks after the Fermi/GBM trigger and detected a fading source
within the XRT error region (Marshall et al., 2020). A series of images were
obtained in the U, V, UVW2, and White filters, but the optical afterglow was
only detected in the White and U bands.

###  2.2 Fermi Data Reduction

The Fermi/GBM payload carries 12 sodium iodide (NaI, 8keV-1MeV) and 2 bismuth
germanate (BGO, 200keV-40MeV) scintillation detectors (Meegan et al., 2009).
Considering the pointing direction of detectors, we employed 4 NaI detectors
(n0, n1, n3, n9) and 1 BGO detector (b0) to conduct the spectral analysis. We
obtained the Time-Tagged Event (TTE) data covering the time range of this GRB
from the Fermi/GBM public data archive
111https://heasarc.gsfc.nasa.gov/FTP/fermi/data/gbm/daily/. We employed the
Multi-Mission Maximum Likelihood Framework (3ML,Vianello et al. (2015)) as the
main tool to do analyses of Fermi/GBM data.

The Fermi/LAT extended type data for GRB 200613A is downloaded from the Fermi
Science Support Center 222https://fermi.gsfc.nasa.gov. We analyzed the
Fermi/LAT data within a $12^{\circ}\times 12^{\circ}$ region of interest (ROI)
centered on the position of GRB 200613A use Conda fermitools v2.2.0 package,
distributed by the Fermi Collaboration333https://github.com/fermi-
lat/Fermitools-conda/wiki. Data were extracted with the energy range from 100
MeV to 30 GeV, selected by the ‘TRANSIENT’ class (evclass=16,
$P8R3\\_TRANSIENT020\\_V3$), as well as limited with a maximum zenith angle of
90 degrees to reduce the contamination from the $\gamma$ ray Earth limb. The
time range of the data is from 0 to 700 s after the GBM trigger time $T_{0}$.
We used the corresponding isotropic emission template,
iso_P8R3_TRANSIENT020_V3_v1, as well as the diffuse Galactic interstellar
emission template (IEM) gll_iem_V07 for the Galactic diffuse emissions. The
parameters of isotropic emission and IEM are left free. The light curve of
prompt emission is shown in Figure 3.

###  2.3 Photometry Observation and Data Reduction

The optical afterglow of the GRB 200613A was first detected at the position of
the second XRT source within the Fermi-LAT localization, using the T80 0.8m
telescope at the Observatorio de Javalambre in Spain. The optical afterglow is
located at coordinates RA = 10:12:10.029 and Dec = +45:45:13.925 (J2000) with
uncertainty of 1.0 arcsec. Figure 1 shows a color composite image of the
optical afterglow of the GRB obtained with the T80 0.8m telescope. The image
is composed of g, r, and i band frames. The Xinglong-2.16m telescope (Xinglong
observatory, Hebei, China) equipped with the Beijing Faint Object Spectrograph
and Camera (BFOSC) conducted follow-up observation on June 14, 2020, at
12:44:18UT, approximately 1.31 days after the GBM trigger. A series of R-band
frames, each with an exposure time of 300 seconds, were acquired. The stack
image clearly reveals the presence of the GRB afterglow with a magnitude of
$19.76\pm 0.06$. Follow-up observation continued over the following days until
the telescope reached its sensitivity limit. On June 21, 2020, we employed the
2.56 m Nordic Optical Telescope (NOT; Roque de los Muchachos observatory, La
Palma, Spain) equipped with Alhambra Faint Object Spectrograph and Camera
(ALFOSC) to further observe GRB 200613A. The object remained detectable in the
image, and its brightness exhibited a power-law decay with an index of
approximately -0.8, as expected. Our follow-up observations with the NOT were
continued until July 1. Additional observaion in SDSS-g, i, and r bands was
conducted using CAFOS on the 2.2m telescope at the Calar Alto Observatory
(CAHA) in Almeria, Spain, on June 15, 27, and July 2, 2020.

Figure 1: Color composites created combining g, r and i images obtained with
OAJ T80. The bottom image, with a field of view of 1.2$\times$0.6 degrees,
shows the location of the afterglow within the LAT error box. The top panels
show the area of the images with the location of the afterglow on the first
and second nights and have a field of view of 3.0$\times$2.1 arcmin. The
optical afterglow is located at coordinates RA = 10:12:10.029 and Dec =
+45:45:13.925 (J2000).

The ground-based optical data were processed using standard procedures with
the Image Reduction and Analysis Facility (IRAF) v2.16 (Tody, 1986). This
involved bias subtraction, flat-fielding, and image combination. Aperture
photometry was performed on stacked frames, and the flux was calibrated using
nearby Pan-STARRS1 field stars (Chambers et al., 2016).

The Swift/UVOT sky images were obtained from the UK Swift Science Data
Centre444https://www.swift.ac.uk/swift_portal/. The UVOTPRODUCT tool of Xspec
was used to extract the object magnitude. The data were automatically rebinned
to ensure a signal-to-noise ratio $S/N>3$.

In addition to our own observations, we supplement our dataset with
photometric data from the GRB Coordinates Network
(GCN)555https://gcn.nasa.gov/circulars. These contributions include
observations from the Kitab-ISON RC-36 and AS-32 telescopes at the Abastumani
observatory (Pozanenko et al., 2020; Belkin et al., 2020d), the Liverpool
Telescope located in La Palma (Izzo, 2020), the MITSuME 50 cm telescope at the
Akeno Observatory (Murata et al., 2020), the AZT-33IK 1.5-m telescope at the
Sayan observatory (Belkin et al., 2020a), the Zeiss-1000 telescope at the SAO
RAS (Moskvitin, 2020), the 2-m Himalayan Chandra Telescope located at IAO,
Hanle, India (Dutta et al., 2020), and the ZTSH 2.6m telescope at the CrAO
observatory (Belkin et al., 2020c, b). All the optical photometry data are
presented in Table 1. It is important to note that the magnitudes were not
corrected for the Galactic foreground extinction of $E(B-V)=0.008$ in the
direction of the burst, which corresponds to $A_{V,MW}=0.024$ (Schlafly &
Finkbeiner, 2011).

###  2.4 Spectroscopy Observation of the Host Galaxy

To get the spectrum of the host galaxy of GRB 200613A, we perform spectroscopy
observation with OSIRIS, mounted on the 10.4m GTC telescope (Roque de los
Muchachos Observatory, La Palma, Spain) at 23:28:10 UT on 18 January 2021
(218.73 days after the burst). We got $3\times 1200$ s frame with grism
R1000R, covering wavelength range from 5100 to 10100 Å. The spectrum is
dominated by continuum. A strong emission feature is found in $\sim 8305$
Åwhich we identify as the [OII] 3727/3729 doublet with the redshift 1.228. At
the blue part of the spectrum, we also find some weak absorbtion feature of
FeII and MgII 2796/2803 at similar redshift 1.226. The reduced One- and two-
dimensional spectrum are shown in Figure 2.

The spectral analysis of the host galaxy associated with GRB 200613A employed
a one-dimensional Gaussian profile fitting procedure to model both emission
and absorption lines. This approach facilitated the precise measurement of the
redshift for both components. For the prominent [OII] doublet at 3727/3729 Å,
a redshift of $z=1.2277\pm 0.0011$ was determined. Furthermore, analysis of
the absorption lines revealed a redshift of $z=1.2262\pm 0.0009$. Taking these
results into consideration, we conclude that the host galaxy of GRB 200613A
resides at a redshift of $z=1.2277\pm 0.0011$. The observed absorption lines
are likely attributed to an intervening system located at a similar redshift
of $z=1.2262\pm 0.0009$, suggesting the presence of intervening material along
the line of sight towards the GRB.

Figure 2: One- and two-dimensional spectrum of the host galaxy of GRB,200613A.
The blue solid line shows the spectrum, while the gray dotted line shows the
error spectrum. The black vertical lines mark the positions of both emission
and absorption lines. The gray region marks the region of terrestrial
absorption lines. According to prominent emission lines [OII] 3727/3729
doublet, we get a redshift of $z=1.2277\pm 0.0011$ for GRB 200613A, and a
similar redshift of $z=1.2262\pm 0.0009$ for the intervening system by the
absorption line.

Table 1: The multi-band photometry results of GRB 200613A and publicly
available data from Gamma-ray Coordination Network (GCN).

$\Delta T$ | Band | Magnitude | Telescope | Ref.
---|---|---|---|---
(day) |  | (AB) | Inst. |
1.31 | R | $19.69\pm 0.05$ | XL216/BFOSC | this work
2.31 | R | $20.22\pm 0.09$ | XL216/BFOSC | this work
3.32 | R | $20.71\pm 0.16$ | XL216/BFOSC | this work
5.32 | R | $21.1\pm 0.16$ | XL216/BFOSC | this work
6.32 | R | $20.97\pm 0.15$ | XL216/BFOSC | this work
8.3 | R | $>21.30$ | XL216/BFOSC | this work
8.66 | r | $21.53\pm 0.08$ | NOT/ALFOSC | this work
12.67 | r | $21.84\pm 0.08$ | NOT/ALFOSC | this work
18.66 | r | $>21.67$ | NOT/ALFOSC | this work
18.68 | i | $21.73\pm 0.23$ | NOT/ALFOSC | this work
10.69 | g | $21.64\pm 0.10$ | Liverpool Telescope | this work
10.69 | r | $21.59\pm 0.10$ | Liverpool Telescope | this work
10.7 | i | $21.19\pm 0.11$ | Liverpool Telescope | this work
2.64 | g | $20.86\pm 0.19$ | CAHA/CAFOS | this work
3.68 | g | $21.37\pm 0.11$ | CAHA/CAFOS | this work
6.64 | g | $21.49\pm 0.06$ | CAHA/CAFOS | this work
2.65 | r | $20.51\pm 0.10$ | CAHA/CAFOS | this work
3.69 | r | $20.92\pm 0.08$ | CAHA/CAFOS | this work
6.67 | r | $21.17\pm 0.05$ | CAHA/CAFOS | this work
19.68 | r | $>21.54$ | CAHA/CAFOS | this work
2.66 | i | $20.53\pm 0.23$ | CAHA/CAFOS | this work
3.70 | i | $20.59\pm 0.11$ | CAHA/CAFOS | this work
6.68 | i | $20.99\pm 0.06$ | CAHA/CAFOS | this work
0.69 | g | $19.62\pm 0.02$ | OAJ-T80 | this work
1.71 | g | $20.41\pm 0.04$ | OAJ-T80 | this work
0.68 | r | $19.35\pm 0.02$ | OAJ-T80 | this work
1.70 | r | $20.16\pm 0.03$ | OAJ-T80 | this work
0.67 | i | $19.19\pm 0.02$ | OAJ-T80 | this work
1.69 | i | $19.99\pm 0.04$ | OAJ-T80 | this work
0.55 | R | $19.27\pm 0.07$ |  $\cdots$ | Pozanenko et al. (2020)
0.71 | r | $19.45\pm 0.20$ | Liverpool Telescope | Izzo (2020a)
2.53 | R | $20.47\pm 0.11$ | AS-32 Telescope | Belkin et al. (2020d)
3.58 | R | $20.58\pm 0.05$ |  $\cdots$ | Moskvitin (2020)
4.47 | R | $20.94\pm 0.14$ |  $\cdots$ | Belkin et al. (2020a)
6.41 | R | $20.59\pm 0.26$ |  $\cdots$ | Dutta et al. (2020)
6.58 | R | $21.06\pm 0.09$ |  $\cdots$ | Belkin et al. (2020c)
6.77 | r | $21.20\pm 0.30$ |  $\cdots$ | Izzo (2020b)
7.93 | R | $21.13\pm 0.10$ |  $\cdots$ | Belkin et al. (2020b)
0.62 | white | $20.18\pm 0.05$ | Swift/UVOT | this work
0.78 | white | $20.33\pm 0.13$ | Swift/UVOT | this work
3.07 | white | $21.73\pm 0.12$ | Swift/UVOT | this work
3.53 | white | $21.58\pm 0.28$ | Swift/UVOT | this work
6.03 | white | $22.01\pm 0.14$ | Swift/UVOT | this work
8.15 | white | $21.99\pm 0.16$ | Swift/UVOT | this work
10.04 | white | $22.44\pm 0.25$ | Swift/UVOT | this work
10.34 | white | $>22.04$ | Swift/UVOT | this work
14.16 | white | $22.46\pm 0.20$ | Swift/UVOT | this work
0.54 | U | $19.89\pm 0.12$ | Swift/UVOT | this work
0.68 | U | $19.87\pm 0.09$ | Swift/UVOT | this work
0.78 | U | $19.97\pm 0.13$ | Swift/UVOT | this work
0.59 | V | $>19.05$ | Swift/UVOT | this work
4.03 | UVW2 | $>23.51$ | Swift/UVOT | this work

Note. — The photometry results presented in this table have not been corrected
for Galactic extinction and have not taken into account the potential
contamination of host galaxy emission.

##  3 Results

###  3.1 Prompt Emission

####  3.1.1 Evolution of Spectral Index

The prompt emission of GRB 200613A exhibits a bright main multi-structure
pulse followed by a week-long emission tail with duration $T_{90}=478.03\pm
3.17$ s (in 50-300 keV). We select a time interval from $T_{0}-0.32$ to
$T_{0}+37.96$ s to build time-average spectra for the main pulse using
different models, namely the Band, Cutoff power-law, and Blackbody (BB). Our
analysis reveals that the Band function can well describe the spectrum, with
the best-fit results of $\alpha=-1.16_{-0.03}^{+0.03}$,
$\beta=-3.20_{-0.36}^{+0.29}$, and $E_{p}=116.0_{-4.4}^{+4.6}$ keV. Combined
with the redshift of the burst $z=1.2277$, we calculated the isotropic energy
of the main pulse of prompt emission
$E_{\gamma,iso}=1.68_{-0.06}^{+0.07}\times 10^{53}$ erg.

To further investigate the spectral evolution of the prompt emission, we
conduct time-resolved spectral analysis for the main pulse using the Bayesian
block method to determine statistically optimal time bins. Each binned
spectrum was then fitted using various models, including the Band, BB,
powerlaw+BB, and Band+BB models. The results of these fits are presented in
Table 6. In Figure 4, we plot the evolution of the spectral index derived by
Band model and overlay it with the GBM light curve. The dashed horizon line
and dotted line in the second panel represent the synchrotron “Line of Death”
index (-2/3) and the synchrotron fast-cooling spectral index (-3/2),
respectively. It’s evident that the low-energy index $\alpha$ between $T_{0}$
to $T_{0}+6$ s exceeds the “Line of Death”. However, after $T_{0}+7$ s, it
drops within the allowed region of the synchrotron and exhibits a “flux-
tracking” pattern. The peak energy also shows a similar transition pattern.

Based on the Bayesian Information Criterion (BIC; Schwarz, 1978), the data
generally favors the Band+BB model. We present the best-fit spectral energy
distribution (SED) for the time intervals $T_{0}-0.32$ to $T_{0}+6.57$ s and
$T_{0}+10.48$ to $T_{0}+13.84$ s in Figure 5. In these intervals, a
significant blackbody radiation component can be observed. However, blackbody
components are not apparent in other time periods.

Figure 3: Fermi/GBM and Fermi/LAT observational data for GRB 200613A. The
points show the arriving times and energies of Fermi/LAT photons $\geq$
100MeV, and the photons whose probabilities associated with GRB 200613A excess
90% are highlighted by red. A third-order polynomial fit to the background
level is shown as a green dot-dashed line. Figure 4: Observational data and
parameter evolution of the main pulse of GRB 200613A. The light curve (red) of
the main pulse with a time resolution of 0.128s and the Bayesian block (black)
are shown in the first panel. The background level is indicated by the green
dot-dashed line. The subsequent three panels display the evolution of the
spectral index ($\alpha$), peak energy ($E_{p}$), and energy flux (10 - 1,000
keV) in the Band model. In the second panel, the synchrotron limit (-2/3) and
fast cooling limit (-3/2) are illustrated by a dashed line and a dotted line,
respectively.  Figure 5: The best fit spectral energy distribution (SED) of
the Gamma-ray Burst Monitor (GBM) data using a combination of the Band
function and blackbody model. The purple dot-dashed line and green dot-dashed
represent the Band component and blackbody component, respectively. Solid
dashed lines represent the $\nu F_{\nu}$ spectra resulting from the
combination of these two models, and red shade show the 1-sigma error.

####  3.1.2 Spectral Lag

There is a time difference between high-energy and low-energy bands of GRB
photons, which is called spectral lag. Spectral lag is always significant for
those long duration GRBs (e.g., Norris et al., 2000; Ukwatta et al., 2012;
Bernardini et al., 2015), while it is typically negligible for short duration
GRBs (e.g., Bernardini et al., 2015; Xiao et al., 2022).

We calculated the spectral lag of GRB 200613A by using cross-correlation
function (CCF; Band, 1997; Norris et al., 2000; Ukwatta et al., 2010) method
between (100-150)/(1+z) keV and (200-250)/(1+z) keV. For the uncertainty of
lags, we used the Monte Carlo simulation (see Peterson et al., 1998; Ukwatta
et al., 2010). The lag of the main pulse is $607.6\pm 57.8$ ms. The results of
the lag in 32 ms time bins of light curves and its uncertainty are illustrated
in Fig. 6. Over the entire duration of the burst, the spectral lag measures
$614.7\pm 56.1$ ms, which is in good agreement with the observed lag in the
main pulse.

Figure 6: Left panel: cross-correlation function (CCF) vs. time delay between
the $(100-150)/(1+z)$ keV and $(200-250)/(1+z)$ keV channels for the main
pulse. The error in each bin of the CCF is determined by running the Monte
Carlo simulation 1000 times. The blue solid line shows a Gaussian fit. The
time delay corresponding to the peak of the Gaussian fit determines the
spectral lag. Right panel: histogram of 1000 simulated spectral lag values for
the main pulse between $(100-150)/(1+z)$ keV and $(200-250)/(1+z)$ keV. The
standard deviation of this simulated spectral lag distribution is considered
as its associated uncertainty. The derived spectral lag of the main pulse is
$607.6\pm 57.8$ ms.

####  3.1.3 Minimal Variable Time Scale

The variable central engine emits relativistic outflow consisting of multiple
shells with different velocities (Rees & Meszaros, 1994). The kinetic energy
converts to radiation when the faster shell hits the slower shell ahead,
resulting in the production of a complex light curve in the prompt emission
phase. The rapid variability of prompt emission within a short period of time
provides insights into the dimensions of the emission region. The minimum
variability time scales ($t_{\mbox{mv}}$) can be used to constrain the size of
the minimum emission region ($R_{c}$) and the minimal bulk Lorentz factor
($\Gamma_{min}$). We employ the Bayesian Blocks algorithm and define the 1/2
shortest significant structures of blocks as the duration of minimum time
interval (Vianello et al., 2018), and the minimum variability time scales of
GRB 200613A is $t_{\mbox{mv}}=267$ ms. Thus, we can evaluate the minimal bulk
Lorentz factor and the size of the emission region ($R_{c}$) from the
following equation (Golkhou et al., 2015):

$\Gamma_{\mbox{min}}\gtrsim 110\left(\frac{L_{\gamma,iso}}{10^{51}\mbox{ erg
s}^{-1}}\frac{1+z}{t_{\mbox{mv}}/0.1\mbox{ s}}\right)^{1/5}$ (1)

$R_{c}\simeq 7.3\times 10^{13}\left(\frac{L_{\gamma,iso}}{10^{51}\mbox{ erg
s}^{-1}}\right)^{2/5}\left(\frac{t_{\mbox{mv}}/0.1\mbox{
s}}{1+z}\right)^{3/5}\mbox{cm.}$ (2)

Here, for simplicity, the luminosity in the equation is estimated as
$L_{\gamma,iso}=E_{\gamma,iso}/T_{90}$. The derived values for
$\Gamma_{\mbox{min}}$ and $R_{c}$ are found to be $\Gamma_{\mbox{min}}\gtrsim
89$ and $R_{c}\simeq 5.7\times 10^{13}$ cm, respectively.

###  3.2 Afterglow Analysis

####  3.2.1 Temporal Analysis

The multi-band afterglow light curves of GRB 200613A were obtained from $\sim$
0.5 days to 19 days after the GBM trigger (Figure 7). Empirical functions were
employed to model the temporal profile in the optical/X-ray light curve. Given
the smooth decay in the optical bands, a single-power law (SPL) was used to
fit the optical data, which is expressed as

$F=F_{0}t^{-\alpha},$ (3)

where $F_{0}$ is the flux and $\alpha$ is the decay index.

The X-ray light curve exhibits a discernible break around 7 days after the
burst. So we use both single-power law and broken power law (BPL) models to
fit the data. The BPL function is expressed

$F=\begin{cases}F_{0}\left(t/t_{b}\right)^{-\alpha_{1}},\quad&t\leq t_{b}\\\
F_{0}\left(t/t_{b}\right)^{-\alpha_{2}},\quad&t>t_{b}\end{cases}$ (4)

where $t_{b}$ is the break time of light curve. The temporal fitting results
are presented in Table 2.

Figure 7: Multi-band afterglow light curve of GRB 200613A spanning a temporal
range of 0.5 to 16.25 days post-burst. Solid (hollow) green data points
represent R(r) band observations. The inverted triangle denotes the limiting
magnitude. For convenience, we added offsets in fluxes as shown in the legend.
Note that the data are not corrected for the Galactic extinctions and the host
galaxy contribution.  Table 2: Measurements of temporal index

Band | Model | Parameters | $\chi^{2}/d.o.f$
---|---|---|---
X-ray | SPL | $\alpha=1.09^{+0.02}_{-0.02}$ | 1.42
| BPL | $\alpha_{1}=1.04^{+0.03}_{-0.04}$ |
|  | $\alpha_{2}=1.51^{+0.49}_{-0.26}$ | 1.36
|  | $\log t_{b}=5.80^{+0.10}_{-0.31}$ |
White | SPL | $\alpha=0.74^{+0.04}_{-0.04}$ | 1.34
R/r | SPL | $\alpha=0.76^{+0.02}_{-0.02}$ | 2.05

Note. — SPL: single power-law; BPL: broken power-law. The break time $t_{b}$
is in a unit of seconds. The jet break effect at late time in optical may be
counteracted by the emission of the host galaxy.

####  3.2.2 Forward Shock Modeling

A relativistic jet moving forward collides with the circumstellar medium,
resulting in a pair of forward and reverse shocks. Electrons are accelerated
in the shocks, producing multi-wavelength synchrotron radiation, known as the
afterglow of GRB. In the standard external shock fireball model, the behavior
of an afterglow can be described by several parameters: the isotropic energy
$E_{k}$, the initial Lorentz factor $\Gamma_{0}$, the electron spectral index
$p$, the circumburst medium density $n_{18}$ (the density at $10^{18}$ cm,
defined in PyFRS666https://github.com/leiwh/PyFRS), jet half-opening angle
$\theta_{j}$, viewing angle of observer $\theta_{obs}$, the fractions of shock
energy that go to electrons $\epsilon_{e}$ and magnetic ﬁeld $\epsilon_{B}$.

We fit the multi-wavelength data of GRB 200613A using the standard afterglow
model code PyFRS, as described in Wang et al. (2014), Lei et al. (2016), Zhu
et al. (2023) and Zhou et al. (2024), assuming a constant interstellar medium
(see Discussion in 4.3). Due to limitations in the available data, we were
unable to constrain the observational angle effectively, thus setting
$\theta_{obs}=0$. For the initial Lorentz factor $\Gamma_{0}$, we obtained its
lower limit of $\sim 89$ in Section 3.1.3. In the study of $\Gamma_{0}$ by
Ghirlanda et al. (2018), there were individual events with $\Gamma_{0}$
greater than 1000, although the results given by different models will have
some differences. Thus, the prior range of $\Gamma_{0}$ was set to [90, 1500].
According to Aksulu et al. (2022), the value of the circumstellar medium
density in the ISM case has a large numerical span, from $\sim 10^{-3}$ to
$\sim 10^{3}$ cm-3. Therefore, we set its range slightly wider to [$10^{-4}$,
$10^{4}$].

The emcee Python package is used for performing Markov Chain Monte Carlo
(MCMC) sampling to get the posterior distribution of afterglow parameters. We
assume log-uniform prior distribution for $E_{\rm k}$, $\Gamma_{0}$, $n_{18}$,
$\epsilon_{\rm e}$ and $\epsilon_{\rm B}$, and uniform prior distribution for
$p$ and $\theta_{\rm j}$. We use 30 walkers to explore the parameter space
with 40000 steps and discard the first 50% of steps as burn-in. The prior
range and best-fit results are listed in Table 3, the best-fit light curves
and posterior probability distributions of the parameters are shown in Figure
8 and Figure 9, respectively.

The fitting results show that the initial Lorentz factor $\Gamma_{0}$ is not
well constrained. This is because in order to constrain $\Gamma_{0}$ well, it
is necessary to observe the peak time of the early optical/X-ray light curve,
i.e., the deceleration timescale

$t_{\rm dec}=\left(\frac{3E_{\rm K,iso}}{16\pi nm_{\rm
p}\Gamma_{0}^{8}c^{5}}\right)^{1/3},$ (5)

where $n$ is circumburst density, $m_{p}$ is the mass of proton and $c$ is
speed of light. It’s typically timescale is few hundred seconds.
Unfortunately, for this event, the data is not sufficient to constrain
$\Gamma_{0}$ due to the lack of early observation of the afterglow.

At around $10^{5}$ seconds, a break is observed in the X-ray model light
curve. Prior to this break, the X-ray and optical decay indices are
consistent, while the X-ray decay index becomes slightly larger after the
break. This chromatic break can be interpreted as the cooling frequency
$\nu_{c}$ crossing the X-ray band at this time. Additionally, there is an
achromatic break at around $10^{6}$ s in the i, r, and X-ray bands, which is
caused by the jet-break. At this time, the reciprocal of Lorentz factor is
comparable to the jet angle, i.e. $1/\Gamma\sim\theta_{j}$. Thus, the jet
half-opening angle could be well constrained to $24.0^{+6.50}_{-5.54}$
degrees.

For the circumstellar medium density $n_{18}$, although the theoretical
expectation is that it may be relatively large for LGRB, the Aksulu et al.
(2022) study shows that its distribution range is very wide for ISM. Our
results are consistent with their statistical results. Santana et al. (2014)’s
study of $\epsilon_{e}$ and $\epsilon_{B}$ found that the distribution of
$\epsilon_{e}$ is consistent with theoretical expectations, ranging from 0.02
to 0.6, with a mean of 0.24; while the distribution of $\epsilon_{B}$ has a
wide range, spanning 5 orders of magnitude, from $3.5\times 10^{-5}$ to 0.33.
Our results are also basically consistent with their statistical results.

For the uvot-u bands, the data is lower than the theoretical expectation,
which we suspect is due to additional host galaxy extinction. According to the
Prospector fitting results (see Section 3.3), the V-band extinction of the
host is $A_{V}=0.28$, which means the original flux is 1.3 times the observed
flux. This correction may be larger for the blue-end. Therefore, after adding
additional corrections, the u-band data can roughly match the theoretical
expectations.

Table 3: Parameters of afterglow modeling Parameters | Prior Type | Prior | Results
---|---|---|---
$E_{K,iso}$ | log-uniform | $[10^{51},10^{56}]$ |  $(2.04^{+11.8}_{-1.50})\times 10^{53}$ erg
$\Gamma_{0}$ | log-uniform | $[90,1500]$ | $354^{+578}_{-217}$
$p$ | uniform | $[2.01,3.0]$ | $2.09^{+0.02}_{-0.03}$
$n_{18}$ | log-uniform | $[10^{-4},10^{4}]$ |  $(2.04^{+9.71}_{-1.87})\times 10^{2}$ cm-3
$\theta_{j}$ | uniform | $[0.01,45]$ |  $24.0^{+6.50}_{-5.54}$ degrees
$\theta_{obs}$ | fixed | $0$ |  $0$ degrees
$\epsilon_{e}$ | log-uniform | $[10^{-4},1]$ | $(1.66^{+4.09}_{-1.39})\times 10^{-1}$
$\epsilon_{B}$ | log-uniform | $[10^{-6},1]$ | $(7.76^{+48.5}_{-5.90})\times 10^{-6}$
Figure 8: Best fit PyFRS afterglow model light curve of GRB 200613A (solid
lines). All optical data plot in this figure are subtracted by host galaxy
flux, with u- and i-band estimates from SDSS and g- and r-band estimates from
LS (Table 4). For convenience, we added offsets in fluxes as shown in the
legend.  Figure 9: Posterior probability distributions of the afterglow
parameters of GRB 200613A.

###  3.3 Host Galaxy

Large sky surveys offer a unique opportunity to study the underlying host
galaxies of GRBs. We searched the Sloan Digital Sky Survey (SDSS) (Almeida et
al., 2023), Legacy Survey (Dey et al., 2019), and The Wide-field Infrared
Survey Explorer (WISE) (Wright et al., 2010) sky survey databases and found a
galaxy overlapping with the burst position of GRB 200613A, which was confirmed
to be the host galaxy of GRB 200613A. The magnitude of each band of the host
galaxy is listed in Table 4.

Table 4: Host galaxy magnitude in sky surveys

Band | Magnitude (AB) | References
---|---|---
u | $21.57\pm 0.23$ | SDSS
g | $21.70\pm 0.11$ | SDSS
r | $22.37\pm 0.33$ | SDSS
i | $\sim 22.2$ | SDSS
z | $\sim 21.1$ | SDSS
g | $22.26\pm 0.06$ | Legacy Survey
r | $22.08\pm 0.09$ | Legacy Survey
z | $21.43\pm 0.09$ | Legacy Survey
W1 | $20.60\pm 0.10$ | WISE
W2 | $21.16\pm 0.31$ | WISE
W3 | $>16.5$ | WISE
W4 | $>14.6$ | WISE

Note. — SDSS: Sloan Digital Sky Survey; Legacy Survey: DESI Legacy Imaging
Surveys; WISE: The Wide-field Infrared Survey Explorer.

To investigate the stellar population properties of the host galaxy, we use
Prospector (Johnson et al., 2021) to fit the photometry results of the host.
Prospector is a software for SED fitting to constrain the host galaxies’
properties. We fit the photometric data of the host galaxy to determine key
stellar population parameters, including the formed total mass ($M_{F}$, which
refers to the cumulative mass of stars that have been formed in a galaxy over
its history), the age of the galaxy at the time of observation ($t_{age}$),
the stellar metallicities ($Z$), and the dust attenuation ($A_{V}$). During
the fitting process, these parameters are allowed to vary within a prior
distribution across the parameter space. To model the host galaxy, we adopt a
Chabrier initial mass function (IMF) (Chabrier, 2003), the Milky Way
extinction law (Cardelli et al., 1989), and include nebular emission to
account for star-forming activity. We also employ a parametric delayed-$\tau$
star formation history (SFH), which is given by the equation:

$\mbox{SFR}(t)=M_{F}\times\left[\int_{0}^{t}te^{-t/\tau}\mbox{d}t\right]^{-1}\times
te^{-t/\tau}.$ (6)

Here, $\tau$ represents the e-folding time of the delayed-$\tau$ SFH. To
determine the mass-weighted age of the galaxy ($t_{m}$), we use the observed
age ($t_{age}$) and $\tau$ to calculate mass-weighted age $t_{m}$ using the
formula (Nugent et al., 2020):

$t_{m}=t_{age}-\frac{\int_{0}^{t_{age}}t\times\mbox{SFR}(t)\mbox{d}t}{\int_{0}^{t_{age}}\mbox{SFR}(t)\mbox{d}t}.$
(7)

In practical observation, the stellar mass $M_{*}$ is easier to obtain because
it measures the mass retained by the stellar population, which is estimated by
$t_{m}$ and $M_{F}$ with the following approximation (Nugent et al., 2020):

$M_{\ast}\approx M_{F}\times 10^{1.06-0.24\log(t_{m})+0.01\log(t_{m})^{2}}.$
(8)

And we derive the total dust attenuation $A_{V}$ from the optical depth of
young stellar light $\tau_{V,1}$ (assumed to be 0 here, see Nugent et al.,
2022) and optical depth of old stellar light $\tau_{V,2}$:

$A_{V}=1.086\times(\tau_{V,1}+\tau_{V,2}).$ (9)

During the fitting process, we adopt the the g, r, and z bands magnitudes from
the LS rather than SDSS. This is because the object in the LS have a higher
signal-to-noise ratio compared to those in the SDSS. Since the host galaxy is
not detected in the W3 and W4 bands, we adopt the magnitudes of W3 and W4 as
the typical limiting magnitudes of WISE. We derive the following parameters of
host galaxy: $\log(M_{\ast}/M_{\odot})=11.75^{+0.10}_{-0.09}$,
$\log(Z/Z_{\odot})=-0.37^{+0.43}_{-0.60}$, $t_{m}=1.26^{+0.53}_{-0.62}$ Gyr,
$A_{V}=0.28^{+0.22}_{-0.17}$ mag, $\log(\tau)=0.51^{+0.40}_{-0.41}$ ($\tau$ is
in unit of Gyr) and $\mbox{SFR}=22.58^{+13.63}_{-7.22}M_{\odot}$/yr. The best-
fit model SED is shown in Figure 10, and the posterior probability
distributions of parameters are shown in Figure 11. The galaxy spectrum
observed with GTC is also plotted in Figure 10, where 2.5 is the slit-correct
factor obtained by correcting the spectral flux using the photometric data in
the r, i, and z bands.

Table 5: Parameters and Prior Distributions of Prospector Parameters | Definition | Prior Type | Prior
---|---|---|---
$M_{F}(M_{\odot})$ | formed total mass | log-uniform | $[10^{10},10^{12}]$
$log(Z/Z_{\odot})$ | stellar metallicity | uniform | $[-1,1]$
$\tau_{V,2}$ | optical depth of old stellar light | uniform | $[0,0.5]$
$\tau$ (Gyr) | e-folding time of delayed-$\tau$ SFH | log-uniform | $[10^{-3},13.6]$
$t_{age}$ (Gyr) | age of the galaxy at the time of observation | uniform | $[0,5.081]$
Figure 10: The figure shows the SED of the host galaxy of GRB 200613A. The
best-fit model SED is shown in red line, and the slit-corrected observed GTC
spectrum is shown in blue line. The model photometry results are marked as
squares, and the sky survey results are represented by black data points. The
g, r, and z bands magnitudes were adopted from the LS rather than SDSS due to
higher S/N. All the data are corrected for the Galactic extinctions. Figure
11: Posterior probability distributions of the host galaxy parameters of GRB
200613A.

The hydrogen Balmer line $H_{\alpha}$ is a direct indicator of the star
formation rate (SFR) of galaxies and is commonly used to calculate the SFR of
nearby galaxies. However, for galaxies at higher redshifts ($z>0.4$),
$H_{\alpha}$ falls outside the visible band. In the redshift range of
$z=0.4–1.5$, the most common emission lines are the [OII] 3737 and 3729
doublet. Although [OII] is not a direct indicator of SFR, it can also be used
to indicate the SFR of galaxies after calibration (e.g. Gallagher et al.,
1989; Kennicutt, 1998; Rosa-González et al., 2002; Kewley et al., 2004). We
estimated the SFR using the method described by Kewley et al. (2004):

$SFR(M_{\odot}yr^{-1})=(9.53\pm 0.91)\times 10^{-42}L([OII])\mbox{ erg
s}^{-1}$ (10)

where L([OII]) is the observed, extinction-corrected luminosity. For the GTC
spectra corrected for Galactic extinction, we fit its [OII] line with a
Gaussian profile, and obtain the observed [OII] luminosity of $2.47\times
10^{42}$ erg/s. Following Savaglio et al. (2009), we adopt a mean visual
extinction $\langle A_{V}\rangle=0.53$, and assume the MW extinction law, to
obtain a SFR correction factor of 2.1, resulting in a host extinction-
corrected SFR of 46.4 $M_{\odot}$yr-1. If we use the extinction value
$A_{V}=0.28$ derived from Prospector, we obtain a correction factor of 1.5,
resulting in a SFR of 34.2 $M_{\odot}$ yr-1. Both of these results are in
basically agreement with the SFRs derived from Prospector.

##  4 Discussion

###  4.1 Classification of GRB 200613A

The burst duration, denoted by $T_{90}$, has often been employed as a primary
criterion for classifying GRBs into Short GRBs (SGRBs) and Long GRBs (LGRBs),
with distinct underlying physical origins generally associated with these
temporal divisions. However, a growing number of observations requires a more
refined perspective on this issue. Some discoveries, such as GRB 060614 (Zhang
et al., 2007), GRB 160410A (Agüí Fernández et al., 2023), and GRB 211211A
(Rastinejad et al., 2022; Yang et al., 2022), demonstrate that GRBs with
$T_{90}>2$ s can also originate from mergers, defying the traditional SGRB
classification. Conversely, GRB 200826A (Rossi et al., 2022) exemplifies a GRB
with $T_{90}<2$ s arising from the collapse of a massive star, challenging the
presumed exclusivity of LGRBs with this temporal characteristic. These
observations collectively highlight the limitations of relying solely on
$T_{90}$ as a definitive indicator of a GRB’s physical origin. To achieve a
more accurate representation of the origin for the two types of GRBs, Zhang et
al. (2007) proposed a classification scheme for GRBs that is analogous to the
supernova classification scheme. In this scheme, GRBs are divided into two
types: Type I (typically short and associated with old populations) and Type
II (typically long and associated with young populations). Effectively
disentangling the different mechanisms driving GRB generation necessitates the
development and application of more comprehensive and multifaceted
methodologies.

In the field of GRB classification, the Amati relation, which links the
equivalent isotropic energy $E_{\gamma,iso}$ and the intrinsic peak energy
$E_{p,i}$, offers a valuable tool for differentiating between Type I and Type
II bursts (Amati et al., 2002; Amati, 2006). In this context, we construct
time-averaged spectra for the entirety of GRB 200613A utilizing the Band
model. With the measured redshift z = 1.2277, we derive the equivalent
isotropic energy and peak energy to be
$E_{\gamma,iso}=2.34_{-0.20}^{+0.23}\times 10^{53}$ erg and
$E_{p}=79.0_{-11.1}^{+15.3}$ keV, respectively. Consequently, the intrinsic
peak energy is $E_{p,i}=(1+z)E_{p,obs}=176.0_{-24.7}^{+34.1}$ keV. To
construct the Amati relation sample, we compiled data from three primary
sources: Fermi GBM Burst Catalog (von Kienlin et al., 2020), Konus-Wind Burst
Catalog (Tsvetkova et al., 2017), and some literature (Amati et al., 2008;
Zhang et al., 2009; Nava et al., 2012; Pozanenko et al., 2018; Zou et al.,
2018; Minaev & Pozanenko, 2020). The positions of these collected samples and
GRB 200613A are visualized within $E_{p,i}-E_{iso}$ plane in the left panel of
Figure 12. Furthermore, the right panel of Figure 12 presents the peak energy
($E_{p}$) and burst duration ($T_{90}$) data for 1647 Fermi GBM GRBs (von
Kienlin et al., 2020), where either the Comptonized function or the Band
function model provided the best fit for each burst. These data are fit with
two log-normal distributions, corresponding to the two distinct GRB types. The
color indicates the probability of being SGRB, with red being 100% SGRB and
blue being 100% LGRB. As evident in both plots, GRB 200613A resides on the
lower-right edge of the sample distribution, indicating its classification as
a typical LGRB.

Although GRB 200613A is located on the LGRB side in the $E_{p}-T_{90}$
diagram, it becomes an exception due to its large $T_{90}$. This is because
the prompt emission of GRB 200613A consists of two parts: the bright main
pulse radiation in the first tens of seconds, and the weak radiation that
lasts for hundreds of seconds. If GRB 200613A is located at a larger redshift,
limited by the sensitivity of the detector, we can only observe the main pulse
of this burst, and we will get a smaller $T_{90}$. This also means that the
$T_{90}$ we observe in the GRB sample has an instrumental selection effect.
For some LGRBs, the actual $T_{90}$ may be much larger than the observed
value, that is, the sample will extend to the right in the $E_{p}-T_{90}$
diagram.

In addition, in Section 3.1.2, we calculated the spectral lag of GRB 200613A.
Long GRBs (LGRBs) typically exhibit larger spectral lags compared to short
GRBs (SGRBs), which can often be negligible. Our measured spectral lag of
$614.7\pm 56.1$ ms indecates that GRB 200613A aligns more closely with the
characteristics of an LGRB.

The combined evidence of GRB 200613A’s long duration $T_{90}$, location on the
lower-right edge of the Amati relation diagram, and significant spectral lag
strongly suggests that it is a typical collapse burst (Type II burst).

Figure 12: Left panel: $E_{p,i}-E_{iso}$ diagram of GRB 200613A (yellow star).
Blue and red points represent LGRBs and SGRBs, respectively. Right panel:
$E_{p}-T_{90}$ diagram of GRB 200613A (yellow star). The color indicates the
probability of being SGRB, with red being 100% SGRB and blue being 100% LGRB.

###  4.2 Possible Origin for the Spectral Evolution of Prompt Emission

As shown in Section 3.1, the spectrum of the prompt emission of GRB 200613A
can be best described with Band+BB model. The BB components are only
significant for the time intervals $T_{0}+1.32$ to $T_{0}+3.84$ s and
$T_{0}+11.22$ to $T_{0}+11.86$ s, and not appear in other time periods (See
Figure 5). Such evolution behavior of prompt spectra could be understood with
the black hole (BH) central engine model.

In the GRB BH central engine model, two mechanisms are considered to power the
relativistic jet: the neutrino-antineutrino annihilation mechanism, which
liberates the gravitational energy from the accretion disk (Popham et al.,
1999; Di Matteo et al., 2002; Gu et al., 2006; Chen & Beloborodov, 2007;
Janiuk et al., 2007; Liu et al., 2007, 2017; Lei et al., 2009) and the
Blandford-Znajek (Blandford & Znajek, 1977, hereafter BZ) mechanism, which
extracts the spin energy from the Kerr BH (Lee et al., 2000; Li, 2000; Liu et
al., 2015; Lei et al., 2013, 2017).

The neutrino-antineutrino annihilation mechanism launches a thermal
“fireball”, leaving an imprint of the thermal component in GRB spectrum. The
neutrino annihilation luminosity can be described with smooth power law with
two breaks (Lei et al., 2017), i.e.,

$\displaystyle\dot{E}_{\nu\bar{\nu}}\simeq$
$\displaystyle\dot{E}_{\nu\bar{\nu},\rm
ign}\left[\left(\frac{\dot{m}}{\dot{m}_{\rm
ign}}\right)^{-\alpha_{\nu\bar{\nu}}}+\left(\frac{\dot{m}}{\dot{m}_{\rm
ign}}\right)^{-\beta_{\nu\bar{\nu}}}\right]^{-1}$ (11)
$\displaystyle\times\left[1+(\frac{\dot{m}}{\dot{m}_{\rm
trap}})^{\beta_{\nu\bar{\nu}}-\gamma_{\nu\bar{\nu}}}\right]^{-1},$

where,

$\displaystyle\left\\{\begin{tabular}[]{l}$\dot{E}_{\nu\bar{\nu},\rm
ign}=10^{(48.0+0.15a_{\bullet})}\left(\frac{m_{\bullet}}{3}\right)^{\log(\dot{m}/\dot{m}_{\rm
ign})-3.3}{\rm erg\ s^{-1}},$\\\ $\alpha_{\nu\bar{\nu}}=4.7,\
\beta_{\nu\bar{\nu}}=2.23,\ \gamma_{\nu\bar{\nu}}=0.3,$\end{tabular}\right.$
(14) $\displaystyle\dot{m}_{\rm ign}=0.07-0.063a_{\bullet},\ \dot{m}_{\rm
trap}=6.0-4.0a_{\bullet}^{3},$ (15)

where $\dot{m}_{\rm ign}$ and $\dot{m}_{\rm trap}$ are the igniting and
trapping accretion rates, respectively.

However, the jet powered by the BZ mechanism is Poynting-flux-dominated. The
BZ jet power from a BH with mass $M_{\bullet}$ and angular momentum
$J_{\bullet}$ is (Lee et al., 2000; Li, 2000; Wang et al., 2002; McKinney,
2005; Lei et al., 2005; Lei & Zhang, 2011; Lei et al., 2013, 2017),

$\displaystyle\dot{E}_{\rm B}$ $\displaystyle=$ $\displaystyle 9\times
10^{53}a_{\bullet}^{2}\dot{m}X(a_{\bullet})\ {\rm erg\ s^{-1}}$ (16)

where $X(a_{\bullet})=F(a_{\bullet})/(1+\sqrt{1-a_{\bullet}^{2}})^{2}$, and
$F(a_{\bullet})=[(1+q^{2})/q^{2}][(q+1/q)\arctan q-1]$. Here
$q=a_{\bullet}/(1+\sqrt{1-a^{2}_{\bullet}})$. The comparison between these two
powers (the BZ power $\dot{E}_{\rm B}$ (blue lines) and neutrino annihilation
power $\dot{E}_{\nu\bar{\nu}}$) is presented in Figure 13. In the following
calculations, we adopt the BH mass $m_{\bullet}=3$ as a typical value.

Figure 13: The BZ power $\dot{E}_{\rm B}$ (blue lines) and neutrino
annihilation power $\dot{E}_{\nu\bar{\nu}}$ (red lines) as a function of
accretion rate $\dot{m}$ for different BH spin $a_{\bullet}=0.01$ (thick solid
lines) and $0.9$ (dashed lines). We adopt the BH mass $m_{\bullet}=3$. Same
results can also be found in Lei et al. (2017).

One can see from Equations (14) - (16) and Figure 13, both the neutrino-
annihilation power and the BZ power depend on accretion rate $\dot{m}$ and BH
spin $a_{\bullet}$ . However, the dependence on accretion rate is more serious
for neutrino-annihilation power. Comparing these two mechanisms, we find that:
(1) the magnetic power is much greater than the neutrino annihilation power
for a moderate to high spin BH (see the dashed lines in Figure 13); (2) The
neutrino annihilation power dominates over the BZ power for BHs with a very
small spin at high accretion rates (see the thick solid lines in Figure 13);
(3) compared with the magnetic power, $\dot{E}_{\nu\bar{\nu}}$ is much more
sensitive to the mass accretion rate $\dot{m}$, especially at low accretion
rates.

As a result, for low-spin BH, the jet can evolve from thermal significant via
neutrino-annihilation mechanism to Poynting-flux dominated via BZ process if
accretion rate drops, and from Poynting-flux dominated to thermal significant
if reverse (Lei et al., 2017).

Inspecting Figure 5, GRB 200613A indeed shows significant spectral evolution
in prompt emission. For convenience, we define the six time slides as T1
(-0.32 - 1.32 s), T2 (1.32 - 3.84), T3 (3.84 - 6.57 s), T4 (10.48 - 11.22 s),
T5 (11.22 - 11.86 s) and T6 (11.86 - 13.84 s). Only in episodes T2 and T5, one
can find significant thermal component, with BB component $L_{\gamma,\rm
iso}^{\rm BB}=3.17_{-0.65}^{+0.57}\times 10^{51}\ \rm erg\ s^{-1}$
($7.41_{-3.46}^{+2.41}\times 10^{51}\ \rm erg\ s^{-1}$) and Band component
$L_{\gamma,\rm iso}^{\rm Band}=1.07_{-0.13}^{+0.17}\times 10^{52}\ \rm erg\
s^{-1}$ ($2.68_{-0.36}^{+0.41}\times 10^{52}\ \rm erg\ s^{-1}$) for T2 (T5).
The central engine parameters can be constrained by relating the BB component
to the neutrino annihilation power and the Band component to the BZ power,
respectively, i.e.,

$\dot{E}_{\nu\bar{\nu}}\eta_{\gamma}=L_{\gamma,\rm iso}^{\rm BB}f_{\rm b},\ \
\dot{E}_{\rm B}\eta_{\gamma}=L_{\gamma,\rm iso}^{\rm Band}f_{\rm b},$ (17)

where $\eta_{\gamma}\equiv\frac{E_{\gamma,\rm iso}}{E_{\gamma,\rm iso}+E_{\rm
K,iso}}$ is the efficiency of converting jet power to gamma-ray radiation and
$f_{\rm b}\equiv 1-\cos\theta_{\rm j}\simeq\theta_{\rm j}^{2}/2$ is the
beaming factor of the jet. We have $\eta_{\gamma}\simeq 0.45$ by substituting
the observed gamma-ray isotropic energy $E_{\gamma,\rm
iso}=1.68_{-0.06}^{+0.07}\times 10^{53}$ erg and model fit isotropic jet
kinetic energy $E_{\rm K,iso}=2.04_{-1.50}^{+11.8}\times 10^{53}$ erg, and
$f_{\rm b}=0.09$ by adopting the model fit opening angle $\theta_{\rm j}\simeq
24$ degrees (see Table 3). For episodes T1, T3, T4 and T6, the BB component
can not be resolved from prompt spectra. We thus assume $L_{\gamma,\rm
iso}^{\rm BB}\leq L_{\gamma,\rm iso}^{\rm Band}/100$ as an upper limit to get
a limit for the central engine parameters by using Equation (17) for these
time episodes. Since both BZ power and neutrino annihilation power are
functions of the accretion rate and BH spin, one can constrain $\dot{m}$ and
$a_{\bullet}$ based on the above assumptions, the results are presented in
Figure 14.

Figure 14: The constraint on central engine parameters, i.e., the accretion
rate $\dot{m}$ and BH spin $a_{\bullet}$, for GRB 200613A. The shaded region
is obtained by equating $\dot{E}_{\rm B}\eta_{\gamma}/f_{\rm b}=3.5\times
10^{52}\ {\rm erg\ s^{-1}}$ (the upper boundary, the solid black line) and
$\dot{E}_{\rm B}\eta_{\gamma}/f_{\rm b}=1\times 10^{52}\ {\rm erg\ s^{-1}}$
(lower boundary, the dashed black line). The blue triangles are the ones
obtained by assuming the upper limit of BB component as $L_{\gamma,\rm
iso}^{\rm BB}\leq L_{\gamma,\rm iso}^{\rm Band}/100$. The true value might be
left the blue triangles in the shaded region. The BH mass $m_{\bullet}=3$,
efficiency $\eta_{\gamma}\simeq 0.45$ and beaming factore $f_{\rm b}=0.09$ are
adopted when producing this figure.

From Figure 14, we can see that the BB component become significant (see
episodes T2 and T5) for a BH central engine with low spin and high accretion
rate. Therefore, the temporal behavior of GRB spectra in the prompt emission
phase might provide meaningful clues to the central engine models. The
evolution of BB component in prompt spectra may reflect the combination of
these two mechanisms, and the evolution of central engine parameters (mainly
the accretion rate) during the prompt emission in GRB 200613A.

We would also like to check the BH central engine model with other
observations. The baryonic jet driven by neutrino annihilation model will
produce a GRB via internal shock at $R_{\rm IS}$. The BZ mechanism launch a
less baryonic jet, and convert the magnetic energy to gamma-rays by magnetic
reconnection, e.g., ICMART (the Internal-Collision induced Magnetic
Reconnection and Turbulence, Zhang & Yan (2011)). In such case, many
collisions are needed to trigger an ICMART event, so that one would have the
gamma-ray emission radius $R_{\rm ICMART}\geq R_{\rm IS}$. The estimated size
of emission region $R_{\rm c}\simeq 5.7\times 10^{13}$ cm is a typical value
for GRBs, we can not rule out any of the two models.

Lei et al. (2013) addressed the fundamental problem of baryon loading in GRB
jets. For neutrino annihilation driven jet, the maximum available Lorentz
factor $\Gamma_{\rm max}=\eta$ with (Lei et al., 2013)

$\displaystyle\eta$ $\displaystyle\simeq$ $\displaystyle
50A^{-0.85}B^{1.35}C^{-0.22}\theta_{j,-1}^{-2}\alpha_{-1}^{-0.57}\epsilon_{-1}^{-1.7}\left(\frac{\xi}{2}\right)^{-0.32}$
(18) $\displaystyle\times$
$\displaystyle\left(\frac{R_{ms}}{2}\right)^{-5.12}\left(\frac{m}{3}\right)^{-0.6}\dot{m}^{0.55},$

where $A,B,C$ are relativistic correction factors for a thin accretion disk
around a Kerr BH, $\xi\equiv r/r_{\rm ms}$ is the disk radius in terms of the
radius of the marginally stable orbit $r_{\rm ms}$, and $\alpha$ is the
viscous parameter. Here $\epsilon\simeq(1-E_{\rm ms})$ is the neutrino
emission efficiency, and $E_{\rm ms}$ is the specific energy corresponding to
$r_{\rm ms}$. The expressions for these parameters can be found in Lei et al.
(2013).

For the BZ powered jet, one can define a parameter denoting the maximum
available energy per baryon (Lei et al., 2013)

$\displaystyle\mu_{0}$ $\displaystyle\simeq$ $\displaystyle 1.5\times
10^{5}A^{-0.58}B^{0.83}F_{\rm p,-1}^{0.5}\theta_{\rm j,-1}^{-1}\theta_{\rm
B,-2}\alpha_{-1}^{-0.38}\epsilon_{-1}^{-0.83}$ (19) $\displaystyle
a_{\bullet}^{2}X(a_{\bullet})\left(\frac{m}{3}\right)^{-0.55}\dot{m}_{-1}^{0.17}r_{z,11}^{-0.5},$

where $F_{\rm p}$ is the fraction of protons, $r_{\rm z}$ is the distance from
the BH in the jet direction. Protons with an ejected direction larger than
$\theta_{\rm B}$ with respect to the field lines would be blocked because of
the existence of a strong magnetic field. The BZ jet will reach a terminating
Lorentz factor $\Gamma$ that satisfies $\Gamma_{\rm min}<\Gamma<\Gamma_{\rm
max}$ with the explicit value depending on the detailed dissipation process.
We take $\Gamma_{\rm min}=\mu_{0}^{1/3}$ and $\Gamma_{\rm max}=\mu_{0}$ for
efficient magnetic acceleration.

It is found that a magnetically dominated jet can be much cleaner and is more
consistent with the requirement of large Lorentz factors in GRBs. For GRB
200316A, we only obtain a minimum Lorentz factor $\Gamma_{\rm min}\leq 89$,
and the neutrino annihilation model is still possible jet launching model
although it is typically “dirtier” (Lei et al., 2013). To show this, in Figure
15 we reproduce the $\Gamma$ \- $\dot{E}$ relation (including observational
data and model predictions) in Yi et al. (2017, Figure 3 therein), and the
observational result of GRB 200613A with green triangle. The beaming corrected
total jet luminosity is detemined by $L_{\rm j}=(E_{\gamma,\rm iso}+E_{\rm
K,iso})f_{\rm b}/T_{90}$, which is $\sim 8.4\times 10^{50}\ {\rm erg\ s^{-1}}$
for GRB 200613A. From Figure 15, one finds that both neutrino annihilation
model and BZ mechanism can work for GRB 200613A.

Figure 15: A comparison between the observations and the predictions from the
neutrino annihilation mechanism (red dashed lines) and the BZ mechanism (blue
dashed lines), reproduced from Yi et al. (2017). The blue dots indicate GRBs
with the beaming corrected luminosity, whereas magenta triangles are the ones
with only lower limit. The red dashed lines show
$\eta(\dot{m})-\dot{E}_{\nu\bar{\nu}}(\dot{m})$ relation for $\theta_{\rm j}$
= 0.022 (top), 0.04(middle) and 0.12 (bottom), respectively. The blue dashed
line shows the $\Gamma_{\rm max}(\dot{m})$ \- $\dot{E}_{\rm B}(\dot{m})$
relation. The $\Gamma_{\rm min}(\dot{m})$ \- $\dot{E}_{\rm B}(\dot{m})$ is
plotted with the blue dotted line. The best-fit to the data $\Gamma_{0}\propto
L_{\rm tot}^{0.14}$ are shown with a sold line (Yi et al., 2017). The green
triangles indicate the GRB 200613A with lower limit.

###  4.3 Closure Relations

The multi-band light curve of GRB 200613A from 0.5 days to 19 days is
presented in Figure 7. The optical flux displays a smooth decay
($\alpha_{opt}\sim 0.75$) with no discernible break, while the X-ray flux
follows a relatively steep decay index ($\alpha_{X_{1}}\sim 1.04$) within a
week. This chromatic evolution between X-ray and optical may indicate that the
X-ray energy band and optical band are in different spectral regimes. A
natural explanation is that the cooling break ($\nu_{c}$) is located between
the optical ($\nu_{opt}$) and X-ray bands ($\nu_{X}$). According to closure
relation (e.g. Zhang & Mészáros, 2004; Gao et al., 2013), different
circumburst density proﬁle predict different temporal and spectral indices.
The expected decline rate of X-ray is $\alpha_{X}=(3p-2)/4$ for both the ISM
case and the wind case, and one can derive the electron energy distribution
index $p=(4\alpha_{X}+2)/3=2.05$. However, the expected r-band decline rate is
$\alpha_{r,ISM}=3(p-1)/4=0.78$ for ISM case and
$\alpha_{r,wind}=(3p-1)/4=1.29$ for wind case. Therefore, the ISM-like
circumburst medium is more consistent with observational results. Time-
averaged spectrum of X-ray gives the photon
index777https://www.swift.ac.uk/xrt_spectra/00021003/ of
$\Gamma=1.91_{-0.14}^{+0.15}$, i.e. $\beta_{X}=0.91_{-0.14}^{+0.15}$ (Evans et
al., 2009). The expected spectral index $\beta_{X,exp}=p/2=1.03$
$\sim\beta_{X,obs}=0.91\pm 0.15$, which is consistent with the fitting results
of the X-ray SED.

The X-ray flux begins to decay more steeply than before ($\alpha_{X_{2}}\sim
1.5$) after a week. However, this effect is not observed in the optical band.
We speculate that the emission of the host galaxy may counteract the break
effect in the optical, thus rendering the break effect in the optical is
undetectable at late times. The most possible explanation for the X-ray break
is the jet-break effect. According to the theoretical prediction, the change
of temporal index is $\Delta\alpha_{jb}=0.75$ (e.g. Panaitescu et al., 1998;
Mészáros & Rees, 1999; Gao et al., 2013), which is consistent with the
temporal fitting result when considering the large uncertainty.

###  4.4 Comparison with GRB host galaxy samples

LGRBs are believed to originate from massive stellar explosions, which have
relatively short lifetimes. Consequently, such events tend to occur in star-
forming galaxies or star-forming regions of the galaxy. In a recent study by
Schneider et al. (2022), a sample of 44 long GRB host galaxies observed with
the HST/WFC3 in the IR band at redshift range from 1 to 3.1 was examined. The
study revealed no systematic offset in physical properties between LGRBs host
galaxies and star-forming galaxies. However, when the samples were grouped by
redshift, it was found that the host galaxies in the redshift range of $1<z<2$
exhibited higher stellar mass and star formation density than expected, while
host galaxies in the range of $2<z<3.1$ were more consistent with star-forming
galaxies in the field.

On the other hand, short-duration gamma-ray bursts (SGRBs) are thought to
originate from the coalescence of compact binary systems, which have a long
delay time between binary formation and merger. Studies of some pulsars have
shown that such ultra-compact objects receive a significant kick velocity at
birth (Lai et al., 1995; Lai, 1996; Kaspi et al., 1996). Recent numerical
modeling studies, however, suggest that different natal-kick mechanisms can
result in different mean natal-kick values for NS binaries. For instance, the
collapse-asymmetry mechanism may result in lower kicks for NS binaries
compared to other mechanisms, potentially biasing the overall mean natal-kick
value for this population (e.g. Belczynski et al., 2018; Banerjee et al.,
2020). Consequently, SGRBs can occur in various locations within the host
galaxy and are not limited to star-forming regions. Fong et al. (2022)
demonstrated that the host-normalized offset for SGRBs is 2.5 times larger
than that observed for LGRBs. Furthermore, due to their long formation
timescales, SGRBs can also occur in different types of galaxies. Recent
research has indicated that the majority of SGRBs are associated with star-
forming galaxies (Leibler & Berger, 2010; Fong et al., 2013; Berger, 2014),
and their hosts exhibit higher stellar mass and lower specific star formation
rates (Nugent et al., 2022).

To conduct a comparative analysis of the host galaxy of GRB200613A with a
representative sample of GRB hosts, we assembled a collection of LGRB and SGRB
host galaxies from Savaglio et al. (2009), Schneider et al. (2022), Nugent et
al. (2022), Gupta et al. (2022), Ahumada et al. (2021), Blanchard et al.
(2023) and Levan et al. (2023), which consists of 89 LGRB hosts and 72 SGRB
hosts. As depicted in Figure 16, the host galaxy of GRB 200613A is identified
as the second most massive galaxy within our sample, with the exception of the
host galaxy of GRB 190829A as reported by Gupta et al. (2022). The star
formation rate of GRB 200613A’s host galaxy falls within a moderate range when
compared to other LGRB samples.

Figure 16: The stellar mass of the host galaxies versus the star formation
rate (left panel) and specific star formation rate (right panel) of our
sample. Open squares represent parameters derived using Prospector, while
solid circles represent those derived in other ways (e.g., via other numerical
models or mass-to-light relations). The host galaxy of GRB 200613A is
represented by a black open square. Notably, the most massive host galaxy in
our sample is GRB 190829A.

In Figure 16, six LGRBs’ host derived from Prospector deviate from the other
LGRBs’ host, generally located in the lower right corner of the mass-SFR
diagram. These LGRBs’ host samples are from different literature sources and
employ diverse calculation methods, leading to systematic biases in the
derived stellar masses and SFRs. As emphasized in Schneider et al. (2022),
different methods can yield stellar mass that differ by nearly an order of
magnitude. Underlying assumptions within galaxy SED models, such as the dust
attenuation, IMF, and SFH, can introduce discrepancies in derived stellar
masses and SFRs. In the MAGPHYS model (da Cunha et al., 2008), for example,
using a Salpeter IMF (Salpeter, 1955) instead of the Chabrier IMF (Chabrier,
2003) would result in stellar mass estimates that are 40% larger. Our
[OII]-derived SFR are approximately 50% higher than those derived from SED
fitting, although they are still within error margins. This observation aligns
with Nugent et al. (2022), who found most emission-line SFR estimates exceed
those from SED fitting. Leja et al. (2019) demonstrated that contributions
from ”older” stellar populations and AGNs can lead to lower SFR compared to
those derived from $L_{\rm UV+IR}$. Therefore, implementing a consistent
approach for all LGRBs’ host in estimating stellar masses and SFRs would
undoubtedly enhance result comparability. However, this lies beyond the scope
of the present study. Even after considering these systematic biases, the host
galaxy masses remain comparatively large within the sample.

##  5 Summary

We present our optical photometry observation of GRB 200613A afterglow using
OAJ T80 telescope, Xinglong 2.16m telescope, NOT 2.56 m telescope and CAHA
2.2m telescope, as well as spectroscopy of host galaxy using 10.4m-GTC
telescope. We conducted a comprehensive analysis of the multi-band radiation
of GRB 200613A, which included gamma-ray emission in prompt phase, X-ray, and
optical afterglow. We also utilized the photometric data obtained from SDSS,
Legacy Survey, and WISE to analyze the properties of its host galaxy. The main
results of our study are summarized as follows:

  * 1.

We obtain the host galaxy spectrum of GRB 200613A using 10.4m-GTC telescope
218 days after the burst. According to prominent emission lines [OII]
3727/3729 doublet, we get a redshift of $z=1.2277\pm 0.0011$ for GRB 200613A,
and a similar redshift of $z=1.2262\pm 0.0009$ for the likely intervening
system by the absorption line.

  * 2.

The combined evidence of long duration $T_{90}$, location on the lower-right
edge of the Amati relation diagram, and significant spectral lag strongly
suggests that GRB 200613A is a typical collapse burst (Type II burst).

  * 3.

The time-resolved spectral analysis of the prompt gamma-ray emission reveals
that the Band component dominates the entire time period, with an additional
blackbody component appearing in the early phase and at the time of the flux
peak. We speculate that the main Band component comes from the Blandford-
Znajek mechanism, and the additional BB component comes from the neutrino
annihilation mechanism. Compared with observed data, we find that the BB
component become significant (see episodes T2 and T5) for a BH central engine
with low spin and high accretion rate. Therefore, the temporal behavior of GRB
spectra in the prompt emission phase provide meaningful trace of the central
engine.

  * 4.

The multi-band afterglow shows a power-law decay, with signs of a jet break
seen in the X-ray band seven days after the burst. This afterglow can be
explained by the model of a jet colliding with the interstellar medium (ISM),
with the physical parameters: $E_{K,iso}=(2.04^{+11.8}_{-1.50})\times 10^{53}$
erg, $\Gamma_{0}=354^{+578}_{-217}$, $p=2.09^{+0.02}_{-0.03}$,
$n_{18}=(2.04^{+9.71}_{-1.87})\times 10^{2}$ cm-3,
$\theta_{j}=24.0^{+6.50}_{-5.54}$ degree,
$\epsilon_{e}=1.66^{+4.09}_{-1.39})\times 10^{-1}$ and
$\epsilon_{B}=(7.76^{+48.5}_{-5.9})\times 10^{-6}$. Due to the lack of early
afterglow observation, the initial Lorentz factor, $\Gamma_{0}$, cannot be
constrained. We can only derive a lower bound of $\Gamma_{0,min}\sim 89$ based
on the minimum variability scales of the prompt emission.

  * 5.

We collected the magnitudes of the host galaxy from the SDSS, Legacy Survey,
and WISE sky surveys and modeled its spectral energy distribution (SED) using
the Prospector Python package. The results suggest that the host galaxy is a
massive galaxy with a stellar mass of
$\log(M_{\ast}/M_{\odot})=11.75^{+0.10}_{-0.09}$ and a moderate star formation
rate of $\mbox{SFR}=22.58^{+13.63}_{-7.22}M_{\odot}$/yr in our GRB host
galaxies sample. We additionally employed the [OII] emission line to
independently estimate SFR of the host galaxy and the results ($\sim
46.4M_{\odot}$yr-1 if $\langle A_{V}\rangle=0.53$ and $\sim 34.2M_{\odot}$
yr-1 if $A_{V}=0.28$) were basically consistent with the value derived from
Prospector.

We acknowledge the support of the staff of the Xinglong 2.16-m telescope. This
work was also partially supported by the Open Project Program of the Key
Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese
Academy of Sciences. This publication is partly based on observations made
with the Gran Telescopio Canarias (GTC), within programs GTC06-20ADDT (PI:
Antonio de Ugarte Postigo) and GTCMULTIPLE2G-20B (PI: Antonio de Ugarte
Postigo). This publication is partly based on observations made with the Calar
Alto Observatory (CAHA), within program F20-2.2-024 (PI: Antonio de Ugarte
Postigo) This publication is partly based on observations made with the
Javalambre Observatory (OAJ), within program 1900170 (PI: David Alexander
Kann). The data presented here were obtained in part with ALFOSC, which is
provided by the Instituto de Astrofisica de Andalucia (IAA) under a joint
agreement with the University of Copenhagen and NOT. This research has made
use of the Spanish Virtual Observatory (http://svo.cab.inta-csic.es) supported
by the MINECO/FEDER through grant AyA2017-84089.7. This work is supported by
the National Key R&D Program of China (Nos. 2020YFC2201400), the National
Natural Science Foundation of China under grants U2038107 and U1931203. W. H.
Lei acknowledges support by the science research grants from the China Manned
Space Project with NO.CMS-CSST-2021-B11. This work made use of data supplied
by the UK Swift Science Data Centre at the University of Leicester. This
publication makes use of data products from the Wide-field Infrared Survey
Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration.

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##  Appendix A Time-resolved spectral analysis results

Table 6: Time-resolved spectral analysis results of prompt emission

$t_{start}$ (s) |  $t_{stop}$ (s) | Model | BIC | $\alpha$ | $\beta$ | $E_{p}$ | $kT$
---|---|---|---|---|---|---|---
-0.32 | 1.32 | Band | 2693.99 | $-0.51^{+0.11}_{-0.1}$ | $-2.78^{+0.37}_{-0.43}$ | $623.87^{+93.63}_{-76.97}$ | $\cdots$
1.32 | 3.84 | Band | 3342.7 | $-0.16^{+0.12}_{-0.11}$ | $-2.39^{+0.14}_{-0.19}$ | $152.91^{+12.81}_{-11.42}$ | $\cdots$
3.84 | 6.57 | Band | 3483.79 | $-0.64^{+0.08}_{-0.07}$ | $-2.78^{+0.12}_{-0.14}$ | $75.22^{+3.24}_{-3.35}$ | $\cdots$
6.57 | 9.13 | Band | 3287.12 | $-1.09^{+0.09}_{-0.1}$ | $-2.56^{+0.1}_{-0.13}$ | $51.89^{+2.43}_{-1.32}$ | $\cdots$
9.13 | 9.80 | Band | 1407.77 | $-1.43^{+0.06}_{-0.05}$ | $-2.88^{+0.37}_{-0.42}$ | $145.52^{+22.65}_{-19.69}$ | $\cdots$
9.80 | 10.48 | Band | 1468.66 | $-1.3^{+0.06}_{-0.06}$ | $-3.04^{+0.36}_{-0.4}$ | $163.39^{+19.86}_{-16.58}$ | $\cdots$
10.48 | 11.22 | Band | 1630.04 | $-1.17^{+0.05}_{-0.04}$ | $-3.2^{+0.33}_{-0.37}$ | $238.51^{+23.69}_{-20.74}$ | $\cdots$
11.22 | 11.86 | Band | 1516.66 | $-0.85^{+0.05}_{-0.05}$ | $-3.17^{+0.29}_{-0.35}$ | $200.5^{+12.08}_{-11.27}$ | $\cdots$
11.86 | 13.84 | Band | 3186.8 | $-0.7^{+0.03}_{-0.03}$ | $-3.48^{+0.28}_{-0.31}$ | $180.69^{+5.09}_{-5.16}$ | $\cdots$
13.84 | 14.82 | Band | 1997.08 | $-0.83^{+0.05}_{-0.05}$ | $-3.42^{+0.3}_{-0.34}$ | $123.18^{+5.6}_{-5.4}$ | $\cdots$
14.82 | 15.64 | Band | 1685.13 | $-0.8^{+0.07}_{-0.07}$ | $-3.34^{+0.27}_{-0.31}$ | $96.85^{+4.66}_{-4.23}$ | $\cdots$
15.64 | 16.13 | Band | 1062.99 | $-0.87^{+0.13}_{-0.11}$ | $-3.12^{+0.31}_{-0.36}$ | $86.07^{+7}_{-6.57}$ | $\cdots$
16.13 | 18.81 | Band | 3275.07 | $-1.08^{+0.05}_{-0.05}$ | $-3.26^{+0.26}_{-0.32}$ | $96.35^{+4.45}_{-4.11}$ | $\cdots$
18.81 | 21.15 | Band | 3096.59 | $-1.06^{+0.06}_{-0.06}$ | $-3.2^{+0.27}_{-0.32}$ | $99.53^{+5.54}_{-4.95}$ | $\cdots$
21.15 | 22.38 | Band | 2050.54 | $-0.94^{+0.14}_{-0.13}$ | $-2.89^{+0.28}_{-0.34}$ | $76.6^{+7.29}_{-6.66}$ | $\cdots$
22.38 | 27.77 | Band | 4313.25 | $-0.97^{+0.1}_{-0.1}$ | $-2.93^{+0.17}_{-0.22}$ | $52.44^{+2.24}_{-1.61}$ | $\cdots$
27.77 | 30.91 | Band | 3361.75 | $-1.3^{+0.11}_{-0.1}$ | $-3.35^{+0.29}_{-0.34}$ | $51^{+1.27}_{-0.72}$ | $\cdots$
30.91 | 33.62 | Band | 3098.74 | $-1.39^{+0.11}_{-0.08}$ | $-3.21^{+0.3}_{-0.35}$ | $51.34^{+1.74}_{-0.96}$ | $\cdots$
33.62 | 37.96 | Band | 3791.64 | $-1.45^{+0.06}_{-0.04}$ | $-2.84^{+0.31}_{-0.39}$ | $51.75^{+2.38}_{-1.27}$ | $\cdots$
37.96 | 47.74 | Band | 4953.63 | $-1.44^{+0.07}_{-0.04}$ | $-3.16^{+0.33}_{-0.37}$ | $51.57^{+2.14}_{-1.13}$ | $\cdots$
47.74 | 58.90 | Band | 5084.68 | $-1.39^{+0.13}_{-0.08}$ | $-2.88^{+0.38}_{-0.43}$ | $54.18^{+5.67}_{-3.02}$ | $\cdots$
-0.32 | 1.32 | BB | 2690 | $\cdots$ | $\cdots$ | $\cdots$ | $82.12^{+4.51}_{-4.19}$
1.32 | 3.84 | BB | 3461.25 | $\cdots$ | $\cdots$ | $\cdots$ | $33.06^{+0.81}_{-0.79}$
3.84 | 6.57 | BB | 4144.9 | $\cdots$ | $\cdots$ | $\cdots$ | $16.85^{+0.07}_{-0.07}$
6.57 | 9.13 | BB | 4293.82 | $\cdots$ | $\cdots$ | $\cdots$ | $15.44^{+0.08}_{-0.08}$
9.13 | 9.80 | BB | 1819.97 | $\cdots$ | $\cdots$ | $\cdots$ | $17^{+0.17}_{-0.16}$
9.80 | 10.48 | BB | 1997.6 | $\cdots$ | $\cdots$ | $\cdots$ | $18.46^{+0.39}_{-0.28}$
10.48 | 11.22 | BB | 2498.91 | $\cdots$ | $\cdots$ | $\cdots$ | $24.14^{+0.63}_{-0.61}$
11.22 | 11.86 | BB | 2185.88 | $\cdots$ | $\cdots$ | $\cdots$ | $29.53^{+0.65}_{-0.62}$
11.86 | 13.84 | BB | 5330.19 | $\cdots$ | $\cdots$ | $\cdots$ | $29.02^{+0.31}_{-0.31}$
13.84 | 14.82 | BB | 2753.49 | $\cdots$ | $\cdots$ | $\cdots$ | $20.46^{+0.26}_{-0.19}$
14.82 | 15.64 | BB | 2118.04 | $\cdots$ | $\cdots$ | $\cdots$ | $19.22^{+0.12}_{-0.11}$
15.64 | 16.13 | BB | 1259.99 | $\cdots$ | $\cdots$ | $\cdots$ | $18.06^{+0.16}_{-0.16}$
16.13 | 18.81 | BB | 4293.41 | $\cdots$ | $\cdots$ | $\cdots$ | $16.74^{+0.08}_{-0.08}$
18.81 | 21.15 | BB | 3745.19 | $\cdots$ | $\cdots$ | $\cdots$ | $16.3^{+0.26}_{-0.2}$
21.15 | 22.38 | BB | 2191.87 | $\cdots$ | $\cdots$ | $\cdots$ | $15.04^{+0.18}_{-0.15}$
22.38 | 27.77 | BB | 4771.6 | $\cdots$ | $\cdots$ | $\cdots$ | $13.4^{+0.07}_{-0.07}$
27.77 | 30.91 | BB | 3574.2 | $\cdots$ | $\cdots$ | $\cdots$ | $12.52^{+0.1}_{-0.11}$
30.91 | 33.62 | BB | 3155.48 | $\cdots$ | $\cdots$ | $\cdots$ | $11.22^{+0.16}_{-0.15}$
33.62 | 37.96 | BB | 3845.04 | $\cdots$ | $\cdots$ | $\cdots$ | $10.33^{+0.16}_{-0.15}$
37.96 | 47.74 | BB | 4969.07 | $\cdots$ | $\cdots$ | $\cdots$ | $8.67^{+0.21}_{-0.18}$
47.74 | 58.90 | BB | 5074.36 | $\cdots$ | $\cdots$ | $\cdots$ | $7.85^{+0.64}_{-0.44}$
-0.32 | 1.32 | BB+PL | 2587.96 | $-1.43^{+0.05}_{-0.06}$ | $\cdots$ | $\cdots$ | $92.61^{+7.48}_{-6.89}$
1.32 | 3.84 | BB+PL | 3245.16 | $-1.48^{+0.03}_{-0.03}$ | $\cdots$ | $\cdots$ | $33.07^{+1.22}_{-1.18}$
3.84 | 6.57 | BB+PL | 3434.79 | $-1.83^{+0.03}_{-0.03}$ | $\cdots$ | $\cdots$ | $17.55^{+0.57}_{-0.56}$
6.57 | 9.13 | BB+PL | 3247.3 | $-1.94^{+0.03}_{-0.03}$ | $\cdots$ | $\cdots$ | $12.03^{+0.4}_{-0.33}$
9.13 | 9.80 | BB+PL | 1331.82 | $-1.85^{+0.04}_{-0.05}$ | $\cdots$ | $\cdots$ | $27.74^{+4.64}_{-4.28}$
9.80 | 10.48 | BB+PL | 1389.46 | $-1.84^{+0.04}_{-0.05}$ | $\cdots$ | $\cdots$ | $30.82^{+2.64}_{-2.49}$
10.48 | 11.22 | BB+PL | 1577.85 | $-1.78^{+0.03}_{-0.03}$ | $\cdots$ | $\cdots$ | $40.07^{+2.37}_{-2.26}$
11.22 | 11.86 | BB+PL | 1435.15 | $-1.74^{+0.03}_{-0.04}$ | $\cdots$ | $\cdots$ | $38.45^{+1.49}_{-1.46}$
11.86 | 13.84 | BB+PL | 3206.63 | $-1.69^{+0.02}_{-0.02}$ | $\cdots$ | $\cdots$ | $35.03^{+0.7}_{-0.67}$
13.84 | 14.82 | BB+PL | 1952.73 | $-1.81^{+0.03}_{-0.03}$ | $\cdots$ | $\cdots$ | $25.96^{+0.97}_{-0.94}$
14.82 | 15.64 | BB+PL | 1614.66 | $-1.93^{+0.05}_{-0.05}$ | $\cdots$ | $\cdots$ | $22.99^{+0.91}_{-0.87}$
15.64 | 16.13 | BB+PL | 999.76 | $-1.89^{+0.06}_{-0.06}$ | $\cdots$ | $\cdots$ | $19.48^{+1.45}_{-1.37}$
16.13 | 18.81 | BB+PL | 3247.84 | $-1.94^{+0.03}_{-0.03}$ | $\cdots$ | $\cdots$ | $22.81^{+0.94}_{-0.92}$
18.81 | 21.15 | BB+PL | 3028.63 | $-1.93^{+0.04}_{-0.04}$ | $\cdots$ | $\cdots$ | $23.48^{+1.11}_{-1.06}$
21.15 | 22.38 | BB+PL | 1977.08 | $-1.9^{+0.06}_{-0.07}$ | $\cdots$ | $\cdots$ | $17.3^{+1.44}_{-1.31}$
22.38 | 27.77 | BB+PL | 4255.62 | $-1.97^{+0.04}_{-0.04}$ | $\cdots$ | $\cdots$ | $12.37^{+0.65}_{-0.6}$
27.77 | 30.91 | BB+PL | 3297.07 | $-2.12^{+0.06}_{-0.07}$ | $\cdots$ | $\cdots$ | $11.4^{+1.2}_{-0.92}$
30.91 | 33.62 | BB+PL | 2873.76 | $-2.18^{+0.08}_{-0.1}$ | $\cdots$ | $\cdots$ | $10.8^{+1.93}_{-1.31}$
33.62 | 37.96 | BB+PL | 3376.19 | $-2.11^{+0.06}_{-0.06}$ | $\cdots$ | $\cdots$ | $85.19^{+76.57}_{-66.98}$
37.96 | 47.74 | BB+PL | 4479.78 | $-2.25^{+0.07}_{-0.08}$ | $\cdots$ | $\cdots$ | $80.51^{+77.14}_{-61.83}$
47.74 | 58.90 | BB+PL | 4663.33 | $-2.18^{+0.11}_{-0.13}$ | $\cdots$ | $\cdots$ | $90.65^{+72.12}_{-68.01}$
-0.32 | 1.32 | Band+BB | 2401.55 | $-0.72^{+0.04}_{-0.1}$ | $-2.69^{+0.35}_{-0.43}$ | $815.04^{+182.82}_{-132.32}$ | $96.99^{+52.29}_{-33.18}$
1.32 | 3.84 | Band+BB | 3242.65 | $-1.01^{+0.19}_{-0.17}$ | $-2.65^{+0.43}_{-0.49}$ | $445.66^{+228.51}_{-132.61}$ | $29.22^{+1.97}_{-2.0}$
3.84 | 6.57 | Band+BB | 3167.61 | $-0.71^{+0.03}_{-0.05}$ | $-2.86^{+0.15}_{-0.14}$ | $77.73^{+2.87}_{-2.38}$ | $83.12^{+66.27}_{-67.28}$
6.57 | 9.13 | Band+BB | 2953.73 | $-1.1^{+0.1}_{-0.1}$ | $-2.56^{+0.11}_{-0.14}$ | $51.77^{+2.33}_{-1.21}$ | $69.41^{+79.75}_{-58.8}$
9.13 | 9.80 | Band+BB | 1087.4 | $-1.42^{+0.07}_{-0.05}$ | $-2.92^{+0.38}_{-0.43}$ | $142.98^{+20.85}_{-19.56}$ | $76.52^{+71.54}_{-55.09}$
9.80 | 10.48 | Band+BB | 1145.82 | $-1.3^{+0.06}_{-0.06}$ | $-3.06^{+0.37}_{-0.39}$ | $163.42^{+20.56}_{-17.93}$ | $85.24^{+71.91}_{-56.07}$
10.48 | 11.22 | Band+BB | 1220.39 | $-1.17^{+0.05}_{-0.05}$ | $-3.18^{+0.31}_{-0.37}$ | $237.03^{+22.45}_{-22.42}$ | $92.94^{+67.45}_{-59.67}$
11.22 | 11.86 | Band+BB | 1300.36 | $-1.13^{+0.2}_{-0.17}$ | $-2.91^{+0.39}_{-0.48}$ | $205.08^{+46.98}_{-44.85}$ | $42.65^{+7.12}_{-4.66}$
11.86 | 13.84 | Band+BB | 2861.4 | $-0.71^{+0.03}_{-0.03}$ | $-3.51^{+0.33}_{-0.31}$ | $182.16^{+5.86}_{-5.65}$ | $53.39^{+73.36}_{-22.62}$
13.84 | 14.82 | Band+BB | 1611.61 | $-0.82^{+0.06}_{-0.05}$ | $-3.4^{+0.31}_{-0.35}$ | $122.57^{+5.45}_{-5.12}$ | $79.84^{+75.9}_{-51.58}$
14.82 | 15.64 | Band+BB | 1390.04 | $-0.82^{+0.08}_{-0.09}$ | $-3.3^{+0.29}_{-0.34}$ | $97.14^{+5.27}_{-5.32}$ | $35.37^{+104.73}_{-15.27}$
15.64 | 16.13 | Band+BB | 688.36 | $-0.88^{+0.12}_{-0.11}$ | $-3.16^{+0.31}_{-0.31}$ | $86.41^{+7.11}_{-6.34}$ | $79.09^{+79.24}_{-59.24}$
16.13 | 18.81 | Band+BB | 2890.32 | $-1.08^{+0.05}_{-0.05}$ | $-3.24^{+0.25}_{-0.31}$ | $95.55^{+4.89}_{-4.32}$ | $68.28^{+75.52}_{-47.58}$
18.81 | 21.15 | Band+BB | 2710.11 | $-1.06^{+0.06}_{-0.07}$ | $-3.17^{+0.3}_{-0.34}$ | $98.89^{+5.99}_{-5.68}$ | $59.83^{+89.53}_{-38.74}$
21.15 | 22.38 | Band+BB | 1701.06 | $-0.94^{+0.13}_{-0.13}$ | $-2.92^{+0.27}_{-0.35}$ | $76.13^{+6.94}_{-5.78}$ | $79.11^{+72.9}_{-57.9}$
22.38 | 27.77 | Band+BB | 3957.98 | $-0.98^{+0.1}_{-0.09}$ | $-2.95^{+0.18}_{-0.25}$ | $52.58^{+2.38}_{-1.67}$ | $79.37^{+75.2}_{-60.53}$
27.77 | 30.91 | Band+BB | 3032.73 | $-1.3^{+0.11}_{-0.1}$ | $-3.35^{+0.29}_{-0.31}$ | $50.91^{+1.18}_{-0.67}$ | $74.96^{+80.0}_{-64.08}$
30.91 | 33.62 | Band+BB | 2714.41 | $-1.39^{+0.1}_{-0.07}$ | $-3.22^{+0.31}_{-0.35}$ | $51.38^{+1.7}_{-0.97}$ | $72.15^{+76.71}_{-56.63}$
33.62 | 37.96 | Band+BB | 3425.53 | $-1.45^{+0.07}_{-0.04}$ | $-2.87^{+0.34}_{-0.36}$ | $51.64^{+2.19}_{-1.2}$ | $81.73^{+73.91}_{-69.65}$
37.96 | 47.74 | Band+BB | 4643.79 | $-1.43^{+0.09}_{-0.05}$ | $-3.14^{+0.33}_{-0.36}$ | $51.77^{+2.63}_{-1.27}$ | $45.3^{+98.24}_{-38.87}$
47.74 | 58.90 | Band+BB | 4774.79 | $-1.36^{+0.17}_{-0.1}$ | $-2.9^{+0.41}_{-0.42}$ | $54.75^{+8.02}_{-3.57}$ | $43.25^{+93.44}_{-36.18}$

Note. — Band: Band model; BB: blackbody; PL: power-law