<figure><img src="image_1.png" /></figure>

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

Shao-Yu Fu¹,², Dong Xu¹, Wei-Hua Lei³, Antonio de Ugarte Postigo⁴,⁵, D. Alexander Kann⁶, Christina C. Thöne⁷, José Feliciano Agúi Fernández⁸, Yi Shuang-Xi⁹, Wei Xie¹⁰,¹¹, Yuan-Chuan Zou³, Xing Liu¹,², Shuai-Qing Jiang¹,², Tian-Hua Lu¹,², Jie An¹,², Zi-Pei Zhu¹, Jie Zheng¹², Qing-Wen Tang¹³, Peng-Wei Zhao¹³, Li-Ping Xin¹, and Jian-Yan Wei¹,²

¹ Key Laboratory of Space Astronomy and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100101, People's Republic of China; dnx@nao.cas.cn

² School of Astronomy and Space Science, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, People's Republic of China

³ Department of Astronomy, School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, People's Republic of China; leiwh@hust.edu.cn

⁴ Université de la Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Artemis, 06304 Nice, France

⁵ Aix Marseille Univ, CNRS, LAM Marseille, France

⁶ Hessian Research Cluster ELEMENTS, Giersch Science Center, Max-von-Laue-Straße 12, Goethe University Frankfurt, Campus Riedberg, D-60438 Frankfurt am Main, Germany

⁷ Astronomical Institute, Czech Academy of Sciences, Fričova 298, Ondřejov, Czech Republic

⁸ Centro Astronómico Hispano en Andalucía, Observatorio de Calar Alto, Sierra de los Filabres, 04550 Gérgal, Almería, Spain

⁹ School of Physics and Physical Engineering, Qufu Normal University, Qufu 273165, People's Republic of China

¹⁰ Department of Astronomy, School of Physics and Electronic Science, Guizhou Normal University, Guiyang 550001, People's Republic of China

¹¹ Guizhou Provincial Key Laboratory of Radio Astronomy Data Processing, Guizhou Normal University, Guiyang 550001, People's Republic of China

¹² CAS Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, People's Republic of China
¹³ Department of Physics, School of Science, Nanchang University, Nanchang 330031, People's Republic of China

Received 2024 February 3; revised 2024 July 4; accepted 2024 July 10; published 2024 October 14

## Abstract

We present our optical observations and multiwavelength analysis of the GRB 200613A detected by the 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, the data generally favor the Band+blackbody (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 the constant interstellar medium. 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 to perform a spectral energy distribution modeling of the host galaxy. The results suggest that the host galaxy is a massive galaxy ($\log(M_*/M_\odot) = 11.75^{+0.10}_{-0.09}$) with a moderate star formation rate (SFR = $22.58^{+13.63}_{-7.22} M_\odot$ yr$^{-1}$). This SFR is consistent with the SFR of $\sim 34.2 M_\odot$ yr$^{-1}$ derived from the [O II] emission line in the observed spectrum.

*Unified Astronomy Thesaurus concepts: Gamma-ray bursts* (629); *High energy astrophysics* (739); *Transient sources* (1851)

## 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 (LGRBs), 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 (SGRBs), which account for about 30% of all GRBs, exhibit durations of less than 2 s and lower energy output compared to LGRBs (Gehrels et al. 2005). The prevailing model for the origin of SGRBs involves the merger of two neutron stars (Eichler et al. 1989), which has been substantiated by the occurrence of the gravitational event GW170817 (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 yr ago, the understanding of their radiation mechanism and emission region has remained incomplete. The fireball model, a prevailing theory,

<figure><img src="image_2.png" /></figure>

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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 nonthermal 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 nonthermal, 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 nonthermal 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 multipulse 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 nonthermal components.

In this paper, we present the analysis of GRB 200613A and find that there is a thermal component in the prompt phase. Additionally, we conduct a detailed investigation of the multiband 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 Sections 4 and 5, respectively. Throughout this study, we adopt a conventional cosmological model with the following parameter values: $H_0=69.6 \text{ km s}^{-1} \text{ Mpc}^{-1}$, $\Omega_M = 0.286$, and $\Omega_\Lambda = 0.714$ (Bennett et al. 2014).

# 2. Observations and Data Reduction

## 2.1. Space-based Observations

GRB 200613A was triggered by the Gamma-Ray Burst Monitor (GBM) on board the Fermi Gamma-Ray Space Telescope (Fermi, hereafter) on 2020 June 13, at 05:30:08.214 UT ($T_0$), with duration $T_{90} \sim 470 \text{ s (50–300 keV)}$ and fluence ($4.10 \pm 0.05) \times 10^{-5} \text{ erg cm}^{-2}$ in 10–1000 keV (Bissaldi et al. 2020). The prompt emission exhibited a double peak profile with a long, weak emission tail that persisted until ~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 100 MeV of ($6.6 \pm 3.6) \times 10^{-7} \text{ ph cm}^{-2} \text{ s}^{-1}$ and $-1.73 \pm 0.36$, respectively (Ohno et al. 2020).

Subsequently, the X-ray Telescope (XRT) on board the 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 limit and is, therefore, the most likely GRB afterglow. The position of “Source 2” was reported as R. A. = 10:12:10.08, decl. = +45:45:14.7 (J2000) with an error radius of $1''/4$ (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 $(2.3 \pm 0.5) \times 10^{21} \text{ cm}^{-2}$, which exceeds the Galactic value of $8.4 \times 10^{19} \text{ cm}^{-2}$ (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; 8 keV–1 MeV) and 2 bismuth germanate (BGO; 200 keV–40 MeV) scintillation detectors (Meegan et al. 2009). Considering the pointing direction of detectors, we employed four NaI detectors (n0, n1, n3, n9) and one BGO detector (b0) to conduct the spectral analysis. We obtained the time-tagged event data covering the time range of this GRB from the Fermi/GBM public data archive.<fnref n="14" /> 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 are downloaded from the Fermi Science Support Center.<fnref n="15" /> We analyzed the Fermi/LAT data within a $12^\circ \times 12^\circ$ region of interest centered on the position of GRB 200613A using Conda fermitools v2.2.0 package, distributed by the Fermi Collaboration.<fnref n="16" /> 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° 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 1.

## 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 0.8 m telescope at the Observatorio de Javalambre in Spain. The optical afterglow is located at coordinates R.A. = 10:12:10.029 and decl. = +45:45:13.925 (J2000) with uncertainty of $1''/0$. Figure 2 shows a color composite image of the optical afterglow of the GRB obtained with the T80 0.8 m telescope. The image is composed of g-, r-, and i-band frames. The Xinglong 2.16 m telescope (Xinglong

<footnote n="14">¹⁴ https://heasarc.gsfc.nasa.gov/FTP/fermi/data/gbm/daily/</footnote>

<footnote n="15">¹⁵ https://fermi.gsfc.nasa.gov</footnote>

<footnote n="16">¹⁶ https://github.com/fermi-lat/Fermitools-conda/wiki</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Fermi/GBM and Fermi/LAT observational data for GRB 200613A. The points show the arriving times and energies of Fermi/LAT photons $\ge$100 MeV, and the photons whose probabilities associated with GRB 200613A excess 90% are highlighted in red. A third-order polynomial fit to the background level is shown as a green dotted-dashed line.</figcaption></figure>

observatory, Hebei, China) equipped with the Beijing Faint Object Spectrograph and Camera (BFOSC) conducted follow-up observation on 2020 June 14, at 12:44:18 UT, approximately 1.31 days after the GBM trigger. A series of R-band frames, each with an exposure time of 300 s, 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 2020 June 21, we employed the 2.56 m Nordic Optical Telescope (NOT; Roque de los Muchachos observatory, La Palma, Spain) equipped with the 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 observations in the Sloan Digital Sky Survey (SDSS) g, i, and r bands were conducted using CAFOS on the 2.2 m telescope at the Calar Alto Observatory (CAHA) in Almeria, Spain, on 2020 June 15, 27, and July 2.

The ground-based optical data were processed using standard procedures with 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 Centre.<fnref n="17" /> 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) of S/N > 3.

In addition to our own observations, we supplement our data set with photometric data from the GRB Coordinates Network (GCN).<fnref n="18" /> These contributions include observations from the

Kitab-ISON RC-36 and AS-32 telescopes at the Abastumani observatory (Belkin et al. 2020d; Pozanenko et al. 2020), the Liverpool Telescope located in La Palma (Izzo 2020a), 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 2.6 m telescope at the CrAO observatory (Belkin et al. 2020b, 2020c). 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 10.4 m Gran Telescopio Canarias (GTC; Roque de los Muchachos Observatory, La Palma, Spain) at 23:28:10 UT on 2021 January 18 (218.73 days after the burst). We got a 3 × 1200 s frame with grism R1000R, covering the wavelength range from 5100 to 10100 Å. The spectrum is dominated by the continuum. A strong emission feature is found in ~8305 Å which we identify as the [O II] 3727/3729 doublet with the redshift 1.228. At the blue part of the spectrum, we also find some weak absorption features of Fe II and Mg II 2796/2803 at similar redshift 1.226. The reduced one- and two-dimensional spectra are shown in Figure 3.

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 [O II] 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

<footnote n="17">¹⁷ https://www.swift.ac.uk/swift_portal/</footnote>

<footnote n="18">¹⁸ https://gcn.nasa.gov/circulars</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Color composites created by combining *g*, *r*, and *i* images obtained with OAJ T80. The bottom image, with a field of view of 1.°2 × 0.6, 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′0 × 2.1′1. The optical afterglow is located at coordinates R.A. = 10:12:10.029 and decl. = +45:45:13.925 (J2000).</figcaption></figure>

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 toward the GRB.

## 3. Results

### 3.1. Prompt Emission

#### 3.1.1. Evolution of Spectral Index

The prompt emission of GRB 200613A exhibits a bright main multistructure 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 A1. In Figure 4, we plot the evolution of the spectral index derived by the 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
<table><caption>**Table 1**
Multiband Photometry Results of GRB 200613A and Publicly Available Data from the GCN</caption><thead><tr><th>ΔT (day)</th><th>Band</th><th>Magnitude (AB)</th><th>Telescope Inst.</th><th>References</th></tr></thead><tbody><tr><td>1.31</td><td><i>R</i></td><td>19.69 ± 0.05</td><td>XL216/BFOSC</td><td>this work</td></tr><tr><td>2.31</td><td><i>R</i></td><td>20.22 ± 0.09</td><td>XL216/BFOSC</td><td>this work</td></tr><tr><td>3.32</td><td><i>R</i></td><td>20.71 ± 0.16</td><td>XL216/BFOSC</td><td>this work</td></tr><tr><td>5.32</td><td><i>R</i></td><td>21.1 ± 0.16</td><td>XL216/BFOSC</td><td>this work</td></tr><tr><td>6.32</td><td><i>R</i></td><td>20.97 ± 0.15</td><td>XL216/BFOSC</td><td>this work</td></tr><tr><td>8.3</td><td><i>R</i></td><td>>21.30</td><td>XL216/BFOSC</td><td>this work</td></tr><tr><td>8.66</td><td><i>r</i></td><td>21.53 ± 0.08</td><td>NOT/ALFOSC</td><td>this work</td></tr><tr><td>12.67</td><td><i>r</i></td><td>21.84 ± 0.08</td><td>NOT/ALFOSC</td><td>this work</td></tr><tr><td>18.66</td><td><i>r</i></td><td>>21.67</td><td>NOT/ALFOSC</td><td>this work</td></tr><tr><td>18.68</td><td><i>i</i></td><td>21.73 ± 0.23</td><td>NOT/ALFOSC</td><td>this work</td></tr><tr><td>10.69</td><td><i>g</i></td><td>21.64 ± 0.10</td><td>Liverpool<br>Telescope</td><td>this work</td></tr><tr><td>10.69</td><td><i>r</i></td><td>21.59 ± 0.10</td><td>Liverpool<br>Telescope</td><td>this work</td></tr><tr><td>10.7</td><td><i>i</i></td><td>21.19 ± 0.11</td><td>Liverpool<br>Telescope</td><td>this work</td></tr><tr><td>2.64</td><td><i>g</i></td><td>20.86 ± 0.19</td><td>CAHA/CAFOS</td><td>this work</td></tr><tr><td>3.68</td><td><i>g</i></td><td>21.37 ± 0.11</td><td>CAHA/CAFOS</td><td>this work</td></tr><tr><td>6.64</td><td><i>g</i></td><td>21.49 ± 0.06</td><td>CAHA/CAFOS</td><td>this work</td></tr><tr><td>2.65</td><td><i>r</i></td><td>20.51 ± 0.10</td><td>CAHA/CAFOS</td><td>this work</td></tr><tr><td>3.69</td><td><i>r</i></td><td>20.92 ± 0.08</td><td>CAHA/CAFOS</td><td>this work</td></tr><tr><td>6.67</td><td><i>r</i></td><td>21.17 ± 0.05</td><td>CAHA/CAFOS</td><td>this work</td></tr><tr><td>19.68</td><td><i>r</i></td><td>>21.54</td><td>CAHA/CAFOS</td><td>this work</td></tr><tr><td>2.66</td><td><i>i</i></td><td>20.53 ± 0.23</td><td>CAHA/CAFOS</td><td>this work</td></tr><tr><td>3.70</td><td><i>i</i></td><td>20.59 ± 0.11</td><td>CAHA/CAFOS</td><td>this work</td></tr><tr><td>6.68</td><td><i>i</i></td><td>20.99 ± 0.06</td><td>CAHA/CAFOS</td><td>this work</td></tr><tr><td>0.69</td><td><i>g</i></td><td>19.62 ± 0.02</td><td>OAJ T80</td><td>this work</td></tr><tr><td>1.71</td><td><i>g</i></td><td>20.41 ± 0.04</td><td>OAJ T80</td><td>this work</td></tr><tr><td>0.68</td><td><i>r</i></td><td>19.35 ± 0.02</td><td>OAJ T80</td><td>this work</td></tr><tr><td>1.70</td><td><i>r</i></td><td>20.16 ± 0.03</td><td>OAJ T80</td><td>this work</td></tr><tr><td>0.67</td><td><i>i</i></td><td>19.19 ± 0.02</td><td>OAJ T80</td><td>this work</td></tr><tr><td>1.69</td><td><i>i</i></td><td>19.99 ± 0.04</td><td>OAJ T80</td><td>this work</td></tr><tr><td>0.55</td><td><i>R</i></td><td>19.27 ± 0.07</td><td>...</td><td>Pozanenko et al.<br>(2020)</td></tr><tr><td>0.71</td><td><i>r</i></td><td>19.45 ± 0.20</td><td>Liverpool<br>Telescope</td><td>Izzo (2020a)</td></tr><tr><td>2.53</td><td><i>R</i></td><td>20.47 ± 0.11</td><td>AS-32 Telescope</td><td>Belkin et al. (2020d)</td></tr><tr><td>3.58</td><td><i>R</i></td><td>20.58 ± 0.05</td><td>...</td><td>Moskvitin (2020)</td></tr><tr><td>4.47</td><td><i>R</i></td><td>20.94 ± 0.14</td><td>...</td><td>Belkin et al. (2020a)</td></tr><tr><td>6.41</td><td><i>R</i></td><td>20.59 ± 0.26</td><td>...</td><td>Dutta et al. (2020)</td></tr><tr><td>6.58</td><td><i>R</i></td><td>21.06 ± 0.09</td><td>...</td><td>Belkin et al. (2020c)</td></tr><tr><td>6.77</td><td><i>r</i></td><td>21.20 ± 0.30</td><td>...</td><td>Izzo (2020b)</td></tr><tr><td>7.93</td><td><i>R</i></td><td>21.13 ± 0.10</td><td>...</td><td>Belkin et al. (2020b)</td></tr><tr><td>0.62</td><td>white</td><td>20.18 ± 0.05</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>0.78</td><td>white</td><td>20.33 ± 0.13</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>3.07</td><td>white</td><td>21.73 ± 0.12</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>3.53</td><td>white</td><td>21.58 ± 0.28</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>6.03</td><td>white</td><td>22.01 ± 0.14</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>8.15</td><td>white</td><td>21.99 ± 0.16</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>10.04</td><td>white</td><td>22.44 ± 0.25</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>10.34</td><td>white</td><td>>22.04</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>14.16</td><td>white</td><td>22.46 ± 0.20</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>0.54</td><td><i>U</i></td><td>19.89 ± 0.12</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>0.68</td><td><i>U</i></td><td>19.87 ± 0.09</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>0.78</td><td><i>U</i></td><td>19.97 ± 0.13</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>0.59</td><td><i>V</i></td><td>>19.05</td><td>Swift/UVOT</td><td>this work</td></tr><tr><td>4.03</td><td><i>UVW2</i></td><td>>23.51</td><td>Swift/UVOT</td><td>this work</td></tr></tbody></table>

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

($-3/2$), respectively. It is 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 favor 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.

### 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 the 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 Figure 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.

### 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 timescales ($t_{mv}$) 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 timescales of GRB 200613A is $t_{mv} = 267$ 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):

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

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

Here, for simplicity, the luminosity in the equation is estimated as $L_{\gamma, \text{iso}} = E_{\gamma, \text{iso}}/T_{90}$. The derived values for $\Gamma_{\min}$ and $R_c$ are found to be $\Gamma_{\min} \gtrsim 89$ and $R_c \approx 5.7 \times 10^{13}$ cm, respectively.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** One- and two-dimensional spectra 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 [O II] 3727/3729 doublet, we get a redshift of z = 1.2277 ± 0.0011 for GRB 200613A, and a similar redshift of z = 1.2262 ± 0.0009 for the intervening system by the absorption line.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**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 0.128 s and the Bayesian block (black) are shown in the first panel. The background level is indicated by the green dotted-dashed line. The subsequent three panels display the evolution of the spectral index (α), peak energy (E<sub>p</sub>), and energy flux (10–1000 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.</figcaption></figure>

## 3.2. Afterglow Analysis

### 3.2.1. Temporal Analysis

The multiband afterglow light curves of GRB 200613A were obtained from ~0.5 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

$$F = F_0 t^{-\alpha}, \quad (3)$$

where F<sub>0</sub> is the flux and α is the decay index.

The X-ray light curve exhibits a discernible break around seven days after the burst. So we use both single-power-law
<figure><img src="image_7.png" /><figcaption>Figure 5. Best-fit SED of GBM data using a combination of the Band function and BB model. The purple dotted-dashed line and green dotted-dashed represent the Band component and BB component, respectively. Solid dashed lines represent the $\nu F_\nu$ spectra resulting from the combination of these two models, and the red shade shows the $1\sigma$ error.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 6. Left panel: 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 ± 57.8 ms.</figcaption></figure>

and broken-power-law (BPL) models to fit the data. The BPL function is expressed

$$F = \begin{cases} F_0(t/t_b)^{-\alpha_1}, & t \le t_b \\ F_0(t/t_b)^{-\alpha_2}, & t > t_b \end{cases} \quad (4)$$

where $t_b$ is the break time of the light curve. The temporal fitting results are presented in Table 2.

### 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 multiwavelength 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
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Multiband afterglow light curve of GRB 200613A spanning a temporal range of 0.5–16.25 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.</figcaption></figure>

<table><caption>**Table 2**
Measurements of the Temporal Index</caption><thead><tr><th>Band</th><th>Model</th><th>Parameters</th><th>χ<sup>2</sup>/d. o.f</th></tr></thead><tbody><tr><td rowspan="3">X-ray</td><td>SPL</td><td>α = 1.09<sup>+0.02</sup><sub>-0.02</sub></td><td>1.42</td></tr><tr><td rowspan="3">BPL</td><td>α<sub>1</sub> = 1.04<sup>+0.03</sup><sub>-0.04</sub></td><td rowspan="3">1.36</td></tr><tr><td>α<sub>2</sub> = 1.51<sup>+0.49</sup><sub>-0.26</sub></td></tr><tr><td>log t<sub>b</sub> = 5.80<sup>+0.10</sup><sub>-0.31</sub></td></tr><tr><td>White</td><td>SPL</td><td>α = 0.74<sup>+0.04</sup><sub>-0.04</sub></td><td>1.34</td></tr><tr><td>R/r</td><td>SPL</td><td>α = 0.76<sup>+0.02</sup><sub>-0.02</sub></td><td>2.05</td></tr></tbody></table>

**Note.** SPL: single power law; BPL: broken power law. The break time $t_b$ is in units of seconds. The jet-break effect at late time in optical may be counteracted by the emission of the host galaxy.

$\Gamma_0$, the electron spectral index $p$, the circumburst medium density $n_{18}$ (the density at $10^{18}$ cm, defined in PyFRS<fnref n="19" />), jet half-opening angle $\theta_j$, the viewing angle of the observer $\theta_{obs}$, and the fractions of the shock energy that go to electrons $\epsilon_e$ and magnetic field $\epsilon_B$.

We fit the multiwavelength 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 ~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 $\Gamma_0$

<table><caption>**Table 3**
Parameters of Afterglow Modeling</caption><thead><tr><th>Parameters</th><th>Prior Type</th><th>Prior</th><th>Results</th></tr></thead><tbody><tr><td>E<sub>K,iso</sub></td><td>log-uniform</td><td>[10<sup>51</sup>, 10<sup>56</sup>]</td><td>(2.04<sup>+11.8</sup><sub>-1.50</sub>) × 10<sup>53</sup> erg</td></tr><tr><td>Γ<sub>0</sub></td><td>log-uniform</td><td>[90, 1500]</td><td>354<sup>+578</sup><sub>-217</sub></td></tr><tr><td>p</td><td>uniform</td><td>[2.01, 3.0]</td><td>2.09<sup>+0.02</sup><sub>-0.03</sub></td></tr><tr><td>n<sub>18</sub></td><td>log-uniform</td><td>[10<sup>-4</sup>, 10<sup>4</sup>]</td><td>(2.04<sup>+9.71</sup><sub>-1.87</sub>) × 10<sup>2</sup> cm<sup>-3</sup></td></tr><tr><td>θ<sub>j</sub></td><td>uniform</td><td>[0.01, 45]</td><td>24.0<sup>+6.50</sup><sub>-5.54</sub> degrees</td></tr><tr><td>θ<sub>obs</sub></td><td>fixed</td><td>0</td><td>0°</td></tr><tr><td>ε<sub>e</sub></td><td>log-uniform</td><td>[10<sup>-4</sup>, 1]</td><td>(1.66<sup>+4.09</sup><sub>-1.39</sub>) × 10<sup>-1</sup></td></tr><tr><td>ε<sub>B</sub></td><td>log-uniform</td><td>[10<sup>-6</sup>, 1]</td><td>(7.76<sup>+48.5</sup><sub>-5.90</sub>) × 10<sup>-6</sup></td></tr></tbody></table>

was set to [90, 1500]. According to Aksulu et al. (2022), the value of the circumstellar medium density in the interstellar medium (ISM) case has a large numerical span, from ~$10^{-3}$ to ~$10^3$ 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 sampling to get the posterior distribution of afterglow parameters. We assume log-uniform prior distribution for $E_k$, $\Gamma_0$, $n_{18}$, $\epsilon_e$, and $\epsilon_B$, and uniform prior distribution for $p$ and $\theta_j$. We use 30 walkers to explore the parameter space with 40,000 steps and discard the first 50% of steps as burn-in. The prior range and best-fit results are listed in Table 3, and the best-fit light curves and posterior probability distributions of the parameters are shown in Figures 8 and 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

$$t_{\text{dec}} = \left( \frac{3E_{K,\text{iso}}}{16\pi\text{nm}_p\Gamma_0^8c^5} \right)^{1/3}, \qquad (5)$$

<footnote n="19">¹⁹ https://github.com/leiwh/PyFRS</footnote>
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Best-fit PyFRS afterglow model light curve of GRB 200613A (solid lines). All optical data plots in this figure are subtracted by the 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.</figcaption></figure>

where n is circumburst density, $m_p$ is the mass of the proton and c is the speed of light. Its typical timescale is a few hundred seconds. Unfortunately, for this event, the data are not sufficient to constrain $\Gamma_0$ due to the lack of early observation of the afterglow.

At around $10^5$ s, 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 the 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 LGRBs, the Aksulu et al. (2022) study shows that its distribution range is very wide for the 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 are 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.

### 3.3. Host Galaxy

Large sky surveys offer a unique opportunity to study the underlying host galaxies of GRBs. We searched the SDSS (Almeida et al. 2023), Legacy Survey (LS; 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.

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. The a priori types and ranges of these parameters are listed in Table 5. To model the host galaxy, we adopt a Chabrier initial mass function (IMF; Chabrier 2003) and 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:

$$SFR(t) = M_F \times \left[ \int_{0}^{t} te^{-t/\tau} dt \right]^{-1} \times te^{-t/\tau}. \quad (6)$$

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 $t_m$.
<figure><img src="image_11.png" /><figcaption>Figure 9. Posterior probability distributions of the afterglow parameters of GRB 200613A.</figcaption></figure>

using the formula (Nugent et al. 2020):

$$t_m = t_{\text{age}} - \frac{\int_{0}^{t_{\text{age}}} t \times \text{SFR}(t) dt}{\int_{0}^{t_{\text{age}}} \text{SFR}(t) dt} \quad (7)$$

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):

$$M_* \approx M_F \times 10^{1.06-0.24 \log(t_m)+0.01 \log(t_m)^2} \quad (8)$$

We derive the total dust attenuation $A_V$ from the optical depth of young stellar light $\tau_{V,1}$ (assumed to be zero here; see Nugent

et al. 2022) and optical depth of old stellar light $\tau_{V,2}$:

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

During the fitting process, we adopt the g-, r-, and z-band magnitudes from the LS rather than the SDSS. This is because the objects 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: $\log(M_*/M_\odot) = 11.75_{-0.09}^{+0.10}$, $\log(Z/Z_\odot) = -0.37_{-0.60}^{+0.43}$, $t_m = 1.26_{-0.62}^{+0.53}$ Gyr, $A_V = 0.28_{-0.17}^{+0.22}$ mag, $\log(\tau) = 0.51_{-0.41}^{+0.40}$ ($\tau$ is in units of Gyr) and SFR = $22.58_{-7.22}^{+13.63} M_\odot$ yr$^{-1}$. The best-fit model SED is shown in Figure 10, and the posterior probability distributions of parameters are shown in Figure 11.
<figure><img src="image_12.png" /><figcaption>**Figure 10.** SED of the host galaxy of GRB 200613A. The best-fit model SED is shown in the red line, and the slit-corrected observed GTC spectrum is shown in the 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-band magnitudes were adopted from the LS rather than SDSS due to higher S/N. All the data are corrected for the Galactic extinctions.</figcaption></figure>

<table><caption>**Table 4**
Host Galaxy Magnitude in Sky Surveys</caption><thead><tr><th>Band</th><th>Magnitude (AB)</th><th>References</th></tr></thead><tbody><tr><td>u</td><td>21.57 ± 0.23</td><td>SDSS</td></tr><tr><td>g</td><td>21.70 ± 0.11</td><td>SDSS</td></tr><tr><td>r</td><td>22.37 ± 0.33</td><td>SDSS</td></tr><tr><td>i</td><td>~22.2</td><td>SDSS</td></tr><tr><td>z</td><td>~21.1</td><td>SDSS</td></tr><tr><td>g</td><td>22.26 ± 0.06</td><td>LS</td></tr><tr><td>r</td><td>22.08 ± 0.09</td><td>LS</td></tr><tr><td>z</td><td>21.43 ± 0.09</td><td>LS</td></tr><tr><td>W1</td><td>20.60 ± 0.10</td><td>WISE</td></tr><tr><td>W2</td><td>21.16 ± 0.31</td><td>WISE</td></tr><tr><td>W3</td><td>>16.5</td><td>WISE</td></tr><tr><td>W4</td><td>>14.6</td><td>WISE</td></tr></tbody></table>

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

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.

The hydrogen Balmer line $H_\alpha$ is a direct indicator of the 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 [O II] 3737 and 3729 doublet. Although [O II] 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; Rosal-González et al. 2002; Kewley et al. 2004). We estimated the SFR using the method described by Kewley et al. (2004):

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

where $L([\text{O II}])$ is the observed, extinction-corrected luminosity. For the GTC spectra corrected for Galactic extinction, we

<table><caption>**Table 5**
Parameters and Prior Distributions of Prospector</caption><thead><tr><th>Parameters</th><th>Definition</th><th>Prior Type</th><th>Prior</th></tr></thead><tbody><tr><td>$M_R(M_\odot)$</td><td>formed total mass</td><td>log-uniform</td><td>[10<sup>10</sup>, 10<sup>12</sup>]</td></tr><tr><td>$\log(Z/Z_\odot)$</td><td>stellar metallicity</td><td>uniform</td><td>[-1, 1]</td></tr><tr><td>$\tau_{V,2}$</td><td>optical depth of old stellar light</td><td>uniform</td><td>[0, 0.5]</td></tr><tr><td>$\tau$ (Gyr)</td><td>e-folding time of delayed-$\tau$ SFH</td><td>log-uniform</td><td>[10<sup>-3</sup>, 13.6]</td></tr><tr><td>$t_{\text{age}}$ (Gyr)</td><td>age of the galaxy at the time of observation</td><td>uniform</td><td>[0, 5.081]</td></tr></tbody></table>

fit its [O II] line with a Gaussian profile and obtain the observed [O II] luminosity of $2.47 \times 10^{42} \text{ erg s}^{-1}$. 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 an SFR correction factor of 2.1, resulting in a host extinction-corrected SFR of $46.4 M_\odot \text{ yr}^{-1}$. If we use the extinction value $A_V = 0.28$ derived from Prospector, we obtain a correction factor of 1.5, resulting in an SFR of $34.2 M_\odot \text{ yr}^{-1}$. 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 SGRBs and 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 (Aguí 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
<figure><img src="image_13.png" /><figcaption>Figure 11. Posterior probability distributions of the host galaxy parameters of GRB 200613A.</figcaption></figure>

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 of 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
<figure><img src="image_14.png" /><figcaption>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.</figcaption></figure>

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 the $E_{p,i}-E_{iso}$ 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. LGRBs typically exhibit larger spectral lags compared to SGRBs, which can often be negligible. Our measured spectral lag of $614.7 \pm 56.1$ ms indicates 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).

## 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 the 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 do 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; Lei et al. 2009; Liu et al. 2017) 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; Lei et al. 2013; Liu et al. 2015; Lei et al. 2017).

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

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

where

$$ \begin{cases} \dot{E}_{\nu\bar{\nu},\text{ign}} = 10^{(48.0+0.15a_{\nu})} \left(\frac{m}{3}\right)^{\log(\dot{m}/\dot{m}_{\text{ign}})-3.3} \text{ erg s}^{-1}, \\ \alpha_{\nu\bar{\nu}} = 4.7, \quad \beta_{\nu\bar{\nu}} = 2.23, \quad \gamma_{\nu\bar{\nu}} = 0.3, \\ \dot{m}_{\text{ign}} = 0.07 - 0.063a_{\nu}, \quad \dot{m}_{\text{trap}} = 6.0 - 4.0a_{\nu}^3 \end{cases} \quad (12) $$

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

However, a jet that is 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; Lei et al. 2005; McKinney 2005; Lei & Zhang 2011; Lei et al. 2013, 2017),

$$ \dot{E}_{\text{B}} = 9 \times 10^{53} a_{\nu}^{2} \dot{m} X(a_{\nu}) \text{ erg s}^{-1}, \quad (13) $$

where $X(a_{\nu}) = F(a_{\nu})/(1 + \sqrt{1 - a_{\nu}^2})^2$, and $F(a_{\nu}) = [(1 + q^2)/q^2][(q + 1/q)\arctan q - 1]$. Here $q = a_{\nu}/$
<figure><img src="image_15.png" /><figcaption>**Figure 13.** BZ power $\dot{E}_B$ (blue lines) and neutrino annihilation power $\dot{E}_{\nu\bar{\nu}}$ (red lines) as a function of the accretion rate $\dot{m}$ for different BH spins $a_* = 0.01$ (thick solid lines) and 0.9 (dashed lines). We adopt a BH mass of $m_* = 3$. The same results can also be found in Lei et al. (2017).</figcaption></figure>

($1 + \sqrt{1 - a_*^2}$). The comparison between these two powers (the BZ power $\dot{E}_B$ (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 $m_* = 3$ as a typical value.

One can see from Equations (12) and (13) and Figure 13 that both the neutrino annihilation power and the BZ power depend on the accretion rate $\dot{m}$ and BH spin $a_*$. However, the dependence on the accretion rate is more serious for the 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 the neutrino annihilation mechanism to Poynting-flux-dominated via the BZ process if the accretion rate drops, and from Poynting-flux-dominated to thermal-significant if the 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 a significant thermal component, with a BB component of $L_{\gamma,iso}^{BB} = 3.17_{-0.65}^{+0.57} \times 10^{51}$ erg s$^{-1}$ ($7.41_{-3.46}^{+2.41} \times 10^{51}$ erg s$^{-1}$) and a Band component of $L_{\gamma,iso}^{Band} = 1.07_{-0.13}^{+0.17} \times 10^{52}$ erg s$^{-1}$ ($2.68_{-0.36}^{+0.41} \times 10^{52}$ 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.,

$$ \dot{E}_{\nu\bar{\nu}}\eta_{\gamma} = L_{\gamma,iso}^{BB} f_{b}, \quad \dot{E}_{B}\eta_{\gamma} = L_{\gamma,iso}^{Band} f_{b}, \qquad (14) $$

where $\eta_{\gamma} \equiv \frac{E_{\gamma,iso}}{E_{\gamma,iso} + \dot{E}_{K,iso}}$ is the efficiency of converting jet power to gamma-ray radiation and $f_b \equiv 1 - \cos\theta_j \approx \theta_j^2/2$ is the beaming factor of the jet. We have $\eta_{\gamma} \approx 0.45$ by substituting the observed gamma-ray isotropic energy $E_{\gamma,iso} = 1.68_{-0.06}^{+0.07} \times 10^{53}$ erg and model fit isotropic jet kinetic energy $E_{K,iso} = 2.04_{-1.50}^{+11.8} \times 10^{53}$ erg, and $f_b = 0.09$ by adopting the model fit opening angle $\theta_j \approx 24^{\circ}$ (see Table 3). For episodes T1, T3, T4, and T6, the BB component cannot be resolved from prompt spectra. We thus assume $L_{\gamma,iso}^{BB} \le L_{\gamma,iso}^{Band}/100$ as an upper limit to get a limit for the central engine parameters by using Equation (14) 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 $a_*$ based on the above assumptions; the results are presented in Figure 14.

From Figure 14, we can see that the BB component becomes 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 the 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 the neutrino annihilation model will produce a GRB via internal shock at $R_{IS}$. The BZ mechanism launches a less baryonic jet and converts 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 cases, many collisions are needed to trigger an ICMART event, so that one would have the gamma-ray emission radius $R_{ICMART} \ge R_{IS}$. The estimated size of emission region $R_c \approx 5.7 \times 10^{13}$ cm is a typical value for GRBs, we cannot rule out any of the two models.
<figure><img src="image_16.png" /><figcaption>**Figure 14.** Constraint on the central engine parameters, i.e., the accretion rate $\dot{m}$ and BH spin $a_*$, for GRB 200613A. The shaded region is obtained by equating $\dot{E}_B\eta_\gamma/f_b = 3.5 \times 10^{52}$ erg s$^{-1}$ (the upper boundary, the solid black line) and $\dot{E}_B\eta_\gamma/f_b = 1 \times 10^{52}$ 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 $L_{\gamma,\text{iso}}^{\text{BB}} \le L_{\gamma,\text{iso}}^{\text{Band}}/100$. The true value is shown with blue triangles in the shaded region. The BH mass $m_* = 3$, efficiency $\eta_\gamma \approx 0.45$, and beaming factor $f_b = 0.09$ are adopted when producing this figure.</figcaption></figure>

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

$$ \eta \approx 50A^{-0.85}B^{1.35}C^{-0.22}\theta_{j,-1}^{-2}\alpha_{-1}^{-0.57}\epsilon_{-1}^{-1.7}\left(\frac{\xi}{2}\right)^{-0.32} \times \left(\frac{R_{\text{ms}}}{2}\right)^{-5.12}\left(\frac{m}{3}\right)^{-0.6} \dot{m}^{0.55}, \quad (15) $$

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

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

$$ \mu_0 \approx 1.5 \times 10^5 A^{-0.58} B^{0.83} F_{p,-1}^{0.5} \theta_{j,-1}^{-1} \theta_{B,-2} \alpha_{-1}^{-0.38} \epsilon_{-1}^{-0.83} a_*^2 X(a_*) \left(\frac{m}{3}\right)^{-0.55} \dot{m}_{-1}^{0.17} r_{z,11}^{-0.5}, \quad (16) $$

where $F_p$ is the fraction of protons, $r_z$ is the distance from the BH in the jet direction. Protons with an ejected direction larger than $\theta_B$ 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 $\Gamma_{\text{min}} < \Gamma < \Gamma_{\text{max}}$ with the explicit value depending on the detailed dissipation process. We take $\Gamma_{\text{min}} = \mu_0^{1/3}$ and $\Gamma_{\text{max}} = \mu_0$ 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 $\Gamma_{\text{min}} \le 89$, and the neutrino

annihilation model is still a 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 is shown with a green triangle. The beaming corrected total jet luminosity is determined by $L_j = (E_{\gamma,\text{iso}} + E_{\text{K,iso}})f_b/T_{90}$, which is $\sim 8.4 \times 10^{50}$ erg s$^{-1}$ for GRB 200613A. From Figure 15, one finds that both the neutrino annihilation model and the BZ mechanism can work for GRB 200613A.

### 4.3. Closure Relations

The multiband light curve of GRB 200613A from 0.5 to 19 days is presented in Figure 7. The optical flux displays a smooth decay ($\alpha_{\text{opt}} \sim 0.75$) with no discernible break, while the X-ray flux follows a relatively steep decay index ($\alpha_{\chi} \sim 1.04$) within a week. This chromatic evolution between X-ray and optical may indicate that the X-ray energy band and the optical band are in different spectral regimes. A natural explanation is that the cooling break ($\nu_c$) is located between the optical ($\nu_{\text{opt}}$) and X-ray bands ($\nu_X$). According to closure relation (e.g., Zhang & Mészáros 2004; Gao et al. 2013), different circumburst density profiles 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 $\alpha_{\text{r,ISM}} = 3(p-1)/4 = 0.78$ for the ISM case and $\alpha_{\text{r,wind}} = (3p-1)/4 = 1.29$ for the wind case. Therefore, the ISM-like circumburst medium is more consistent with observational results. The time-averaged spectrum of X-ray gives the photon index$^{20}$ 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

<footnote>$^{20}$ https://www.swift.ac.uk/xrt_spectra/00021003/</footnote>
<figure><img src="image_17.png" /><figcaption>**Figure 15.** Comparison between the observations and the predictions from the neutrino annihilation mechanism (red dashed lines) and the BZ mechanism (blue dashed lines), reproduced by Yi et al. (2017). The blue dots indicate GRBs with the beaming corrected luminosity, whereas magenta triangles are the ones with only a lower limit. The red dashed lines show $\eta(\dot{m}) - \dot{E}_{\nu\bar{\nu}}(\dot{m})$ relation for $\theta_j = 0.022$ (top), 0.04 (middle) and 0.12 (bottom), respectively. The blue dashed line shows the $\Gamma_{\text{max}}(\dot{m}) - \dot{E}_{\text{B}}(\dot{m})$ relation. The $\Gamma_{\text{min}}(\dot{m}) - \dot{E}_{\text{B}}(\dot{m})$ is plotted with the blue dotted line. The best fits to the data $\Gamma_0 \propto L_{\text{tot}}^{0.14}$ are shown with a solid line (Yi et al. 2017). The green triangles indicate the GRB 200613A with a lower limit.</figcaption></figure>

$\beta_{X,\text{exp}} = p/2 = 1.03 \sim \beta_{X,\text{obs}} = 0.91 \pm 0.15$, 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 in the 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 LGRB host galaxies observed with the Hubble Space Telescope Wide Field Camera 3 in the IR band at a 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, 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 ultracompact objects receive a significant kick velocity at birth (Lai et al. 1995;

Kaspi et al. 1996; Lai 1996). Recent numerical modeling studies, however, suggest that different natal-kick mechanisms can result in different mean natal-kick values for neutron star (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 GRB 200613A with a representative sample of GRB hosts, we assembled a collection of LGRB and SGRB host galaxies from Savaglio et al. (2009), Ahumada et al. (2021), Gupta et al. (2022), Nugent et al. (2022), Schneider et al. (2022), 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.

In Figure 16, six LGRB hosts derived from Prospector deviate from the other LGRB hosts, generally located in the lower-right corner of the mass–SFR diagram. These LGRB
<figure><img src="image_18.png" /><figcaption>**Figure 16.** Stellar mass of the host galaxies vs. SFR (left panel) and specific SFR (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.</figcaption></figure>

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 masses that differ by nearly an order of magnitude. Underlying assumptions within galaxy SED models, such as 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 [O II]-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 active galactic nuclei can lead to lower SFRs compared to those derived from $L_{UV+IR}$. Therefore, implementing a consistent approach for all LGRB hosts 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 the GRB 200613A afterglow using the Observatorio Astrofísico de Javalambre (OAJ) T80 telescope, Xinglong 2.16 m telescope, NOT 2.56 m telescope, and CAHA 2.2 m telescope, as well as spectroscopy of the host galaxy using the 10.4 m GTC telescope. We conducted a comprehensive analysis of the multiband radiation of GRB 200613A, which included gamma-ray emission in the prompt phase, X-ray afterglow, and optical afterglow. We also utilized the photometric data obtained from SDSS, LS, 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 the 10.4 m GTC telescope 218 days after the burst.

According to prominent emission lines [O II] 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 BB component appearing in the early phase and at the time of the flux peak. We speculate that the main Band component comes from the BZ mechanism, and the additional BB component comes from the neutrino annihilation mechanism. Compared with observed data, we find that the BB component becomes 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 provides a meaningful trace of the central engine.

4. The multiband 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 ISM, with the physical parameters: $E_{K,iso} = (2.04_{-1.50}^{+11.8}) \times 10^{53}$ erg, $\Gamma_0 = 354_{-217}^{+578}$, $p = 2.09_{-0.03}^{+0.02}$, $n_{18} = (2.04_{-1.87}^{+9.71}) \times 10^2$ cm$^{-3}$, $\theta_j = 24.0_{-5.54}^{+6.50}$ degree, $\epsilon_e = 1.66_{-1.39}^{+4.09}) \times 10^{-1}$ and $\epsilon_B = (7.76_{-5.9}^{+48.5}) \times 10^{-6}$. 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, LS, and WISE sky surveys and modeled its SED using the Prospector Python package. The results suggest that the host galaxy is a massive galaxy with a stellar mass of $\log(M_*/M_\odot) = 11.75_{-0.09}^{+0.10}$ and a moderate star formation rate of SFR = $22.58_{-7.22}^{+13.63} M_\odot \text{ yr}^{-1}$ in our
GRB host galaxies sample. We additionally employed the [O II] emission line to independently estimate the SFR of the host galaxy and the results (~46.4 M$_{\odot}$ yr$^{-1}$ if $\langle A_V \rangle = 0.53$ and ~34.2 M$_{\odot}$ yr$^{-1}$ if $A_V = 0.28$) were basically consistent with the value derived from Prospector.

## Acknowledgments

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 Astrofísica de Andalucía (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 (No. 2020YFC2201400), and the National Natural Science Foundation of China under grants U2038107 and U1931203. D.X. acknowledges the science research grants from the China Manned Space Project with No. CMS-CSST-2021-A13 and No. CMS-CSST-2021-B11. W.H. L. 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.

**Facility:** Beijing: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).

## Appendix

### Time-resolved Spectral Analysis Results

The results of time-resolved spectral analysis for the main pulse using the Bayesian block method are listed in Table A1.

<table><caption>Table A1

Time-resolved Spectral Analysis Results of Prompt Emission</caption><thead><tr><th>t<sub>start</sub> (s)</th><th>t<sub>stop</sub> (s)</th><th>Model</th><th>BIC</th><th>α</th><th>β</th><th>E<sub>p</sub></th><th>kT</th></tr></thead><tbody><tr><td>-0.32</td><td>1.32</td><td>Band</td><td>2693.99</td><td>-0.51<sup>+0.11</sup><sub>-0.1</sub></td><td>-2.78<sup>+0.37</sup><sub>-0.43</sub></td><td>623.87<sup>+93.63</sup><sub>-76.97</sub></td><td>...</td></tr><tr><td>1.32</td><td>3.84</td><td>Band</td><td>3342.7</td><td>-0.16<sup>+0.12</sup><sub>-0.11</sub></td><td>-2.39<sup>+0.14</sup><sub>-0.19</sub></td><td>152.91<sup>+12.81</sup><sub>-11.42</sub></td><td>...</td></tr><tr><td>3.84</td><td>6.57</td><td>Band</td><td>3483.79</td><td>-0.64<sup>+0.08</sup><sub>-0.07</sub></td><td>-2.78<sup>+0.12</sup><sub>-0.14</sub></td><td>75.22<sup>+3.24</sup><sub>-3.35</sub></td><td>...</td></tr><tr><td>6.57</td><td>9.13</td><td>Band</td><td>3287.12</td><td>-1.09<sup>+0.09</sup><sub>-0.1</sub></td><td>-2.56<sup>+0.1</sup><sub>-0.13</sub></td><td>51.89<sup>+2.43</sup><sub>-1.32</sub></td><td>...</td></tr><tr><td>9.13</td><td>9.80</td><td>Band</td><td>1407.77</td><td>-1.43<sup>+0.06</sup><sub>-0.05</sub></td><td>-2.88<sup>+0.37</sup><sub>-0.42</sub></td><td>145.52<sup>+22.65</sup><sub>-19.69</sub></td><td>...</td></tr><tr><td>9.80</td><td>10.48</td><td>Band</td><td>1468.66</td><td>-1.3<sup>+0.06</sup><sub>-0.06</sub></td><td>-3.04<sup>+0.36</sup><sub>-0.4</sub></td><td>163.39<sup>+19.86</sup><sub>-16.58</sub></td><td>...</td></tr><tr><td>10.48</td><td>11.22</td><td>Band</td><td>1630.04</td><td>-1.17<sup>+0.05</sup><sub>-0.04</sub></td><td>-3.2<sup>+0.33</sup><sub>-0.37</sub></td><td>238.51<sup>+23.69</sup><sub>-20.74</sub></td><td>...</td></tr><tr><td>11.22</td><td>11.86</td><td>Band</td><td>1516.66</td><td>-0.85<sup>+0.05</sup><sub>-0.05</sub></td><td>-3.17<sup>+0.29</sup><sub>-0.35</sub></td><td>200.5<sup>+12.08</sup><sub>-11.27</sub></td><td>...</td></tr><tr><td>11.86</td><td>13.84</td><td>Band</td><td>3186.8</td><td>-0.7<sup>+0.03</sup><sub>-0.03</sub></td><td>-3.48<sup>+0.28</sup><sub>-0.31</sub></td><td>180.69<sup>+5.09</sup><sub>-5.16</sub></td><td>...</td></tr><tr><td>13.84</td><td>14.82</td><td>Band</td><td>1997.08</td><td>-0.83<sup>+0.05</sup><sub>-0.05</sub></td><td>-3.42<sup>+0.3</sup><sub>-0.34</sub></td><td>123.18<sup>+5.6</sup><sub>-5.4</sub></td><td>...</td></tr><tr><td>14.82</td><td>15.64</td><td>Band</td><td>1685.13</td><td>-0.8<sup>+0.07</sup><sub>-0.07</sub></td><td>-3.34<sup>+0.27</sup><sub>-0.31</sub></td><td>96.85<sup>+4.66</sup><sub>-4.23</sub></td><td>...</td></tr><tr><td>15.64</td><td>16.13</td><td>Band</td><td>1062.99</td><td>-0.87<sup>+0.13</sup><sub>-0.11</sub></td><td>-3.12<sup>+0.31</sup><sub>-0.36</sub></td><td>86.07<sup>+7</sup><sub>-6.57</sub></td><td>...</td></tr><tr><td>16.13</td><td>18.81</td><td>Band</td><td>3275.07</td><td>-1.08<sup>+0.05</sup><sub>-0.05</sub></td><td>-3.26<sup>+0.26</sup><sub>-0.32</sub></td><td>96.35<sup>+4.45</sup><sub>-4.11</sub></td><td>...</td></tr><tr><td>18.81</td><td>21.15</td><td>Band</td><td>3096.59</td><td>-1.06<sup>+0.06</sup><sub>-0.06</sub></td><td>-3.2<sup>+0.27</sup><sub>-0.32</sub></td><td>99.53<sup>+5.54</sup><sub>-4.95</sub></td><td>...</td></tr><tr><td>21.15</td><td>22.38</td><td>Band</td><td>2050.54</td><td>-0.94<sup>+0.14</sup><sub>-0.13</sub></td><td>-2.89<sup>+0.28</sup><sub>-0.34</sub></td><td>76.6<sup>+7.29</sup><sub>-6.66</sub></td><td>...</td></tr><tr><td>22.38</td><td>27.77</td><td>Band</td><td>4313.25</td><td>-0.97<sup>+0.1</sup><sub>-0.1</sub></td><td>-2.93<sup>+0.17</sup><sub>-0.22</sub></td><td>52.44<sup>+2.24</sup><sub>-1.61</sub></td><td>...</td></tr><tr><td>27.77</td><td>30.91</td><td>Band</td><td>3361.75</td><td>-1.3<sup>+0.11</sup><sub>-0.1</sub></td><td>-3.35<sup>+0.29</sup><sub>-0.34</sub></td><td>51<sup>+1.27</sup><sub>-0.72</sub></td><td>...</td></tr><tr><td>30.91</td><td>33.62</td><td>Band</td><td>3098.74</td><td>-1.39<sup>+0.11</sup><sub>-0.08</sub></td><td>-3.21<sup>+0.3</sup><sub>-0.35</sub></td><td>51.34<sup>+1.74</sup><sub>-0.96</sub></td><td>...</td></tr><tr><td>33.62</td><td>37.96</td><td>Band</td><td>3791.64</td><td>-1.45<sup>+0.06</sup><sub>-0.04</sub></td><td>-2.84<sup>+0.31</sup><sub>-0.39</sub></td><td>51.75<sup>+2.38</sup><sub>-1.27</sub></td><td>...</td></tr><tr><td>37.96</td><td>47.74</td><td>Band</td><td>4953.63</td><td>-1.44<sup>+0.07</sup><sub>-0.04</sub></td><td>-3.16<sup>+0.33</sup><sub>-0.37</sub></td><td>51.57<sup>+2.14</sup><sub>-1.13</sub></td><td>...</td></tr><tr><td>47.74</td><td>58.90</td><td>Band</td><td>5084.68</td><td>-1.39<sup>+0.13</sup><sub>-0.08</sub></td><td>-2.88<sup>+0.38</sup><sub>-0.43</sub></td><td>54.18<sup>+5.67</sup><sub>-3.02</sub></td><td>...</td></tr><tr><td>-0.32</td><td>1.32</td><td>BB</td><td>2690</td><td>...</td><td>...</td><td>...</td><td>82.12<sup>+4.51</sup><sub>-4.19</sub></td></tr><tr><td>1.32</td><td>3.84</td><td>BB</td><td>3461.25</td><td>...</td><td>...</td><td>...</td><td>33.06<sup>+0.81</sup><sub>-0.79</sub></td></tr><tr><td>3.84</td><td>6.57</td><td>BB</td><td>4144.9</td><td>...</td><td>...</td><td>...</td><td>16.85<sup>+0.07</sup><sub>-0.07</sub></td></tr><tr><td>6.57</td><td>9.13</td><td>BB</td><td>4293.82</td><td>...</td><td>...</td><td>...</td><td>15.44<sup>+0.08</sup><sub>-0.08</sub></td></tr><tr><td>9.13</td><td>9.80</td><td>BB</td><td>1819.97</td><td>...</td><td>...</td><td>...</td><td>17<sup>+0.17</sup><sub>-0.16</sub></td></tr><tr><td>9.80</td><td>10.48</td><td>BB</td><td>1997.6</td><td>...</td><td>...</td><td>...</td><td>18.46<sup>+0.39</sup><sub>-0.28</sub></td></tr><tr><td>10.48</td><td>11.22</td><td>BB</td><td>2498.91</td><td>...</td><td>...</td><td>...</td><td>24.14<sup>+0.63</sup><sub>-0.61</sub></td></tr><tr><td>11.22</td><td>11.86</td><td>BB</td><td>2185.88</td><td>...</td><td>...</td><td>...</td><td>29.53<sup>+0.65</sup><sub>-0.62</sub></td></tr></tbody></table>
<table><caption>Table A1
(Continued)</caption><thead><tr><th>t<sub>start</sub> (s)</th><th>t<sub>stop</sub> (s)</th><th>Model</th><th>BIC</th><th>α</th><th>β</th><th>E<sub>p</sub></th><th>kT</th></tr></thead><tbody><tr><td>11.86</td><td>13.84</td><td>BB</td><td>5330.19</td><td>...</td><td>...</td><td>...</td><td>29.02<sup>+0.31</sup><sub>-0.31</sub></td></tr><tr><td>13.84</td><td>14.82</td><td>BB</td><td>2753.49</td><td>...</td><td>...</td><td>...</td><td>20.46<sup>+0.26</sup><sub>-0.19</sub></td></tr><tr><td>14.82</td><td>15.64</td><td>BB</td><td>2118.04</td><td>...</td><td>...</td><td>...</td><td>19.22<sup>+0.12</sup><sub>-0.11</sub></td></tr><tr><td>15.64</td><td>16.13</td><td>BB</td><td>1259.99</td><td>...</td><td>...</td><td>...</td><td>18.06<sup>+0.16</sup><sub>-0.16</sub></td></tr><tr><td>16.13</td><td>18.81</td><td>BB</td><td>4293.41</td><td>...</td><td>...</td><td>...</td><td>16.74<sup>+0.08</sup><sub>-0.08</sub></td></tr><tr><td>18.81</td><td>21.15</td><td>BB</td><td>3745.19</td><td>...</td><td>...</td><td>...</td><td>16.3<sup>+0.26</sup><sub>-0.2</sub></td></tr><tr><td>21.15</td><td>22.38</td><td>BB</td><td>2191.87</td><td>...</td><td>...</td><td>...</td><td>15.04<sup>+0.18</sup><sub>-0.15</sub></td></tr><tr><td>22.38</td><td>27.77</td><td>BB</td><td>4771.6</td><td>...</td><td>...</td><td>...</td><td>13.4<sup>+0.07</sup><sub>-0.07</sub></td></tr><tr><td>27.77</td><td>30.91</td><td>BB</td><td>3574.2</td><td>...</td><td>...</td><td>...</td><td>12.52<sup>+0.1</sup><sub>-0.11</sub></td></tr><tr><td>30.91</td><td>33.62</td><td>BB</td><td>3155.48</td><td>...</td><td>...</td><td>...</td><td>11.22<sup>+0.16</sup><sub>-0.15</sub></td></tr><tr><td>33.62</td><td>37.96</td><td>BB</td><td>3845.04</td><td>...</td><td>...</td><td>...</td><td>10.33<sup>+0.16</sup><sub>-0.15</sub></td></tr><tr><td>37.96</td><td>47.74</td><td>BB</td><td>4969.07</td><td>...</td><td>...</td><td>...</td><td>8.67<sup>+0.21</sup><sub>-0.18</sub></td></tr><tr><td>47.74</td><td>58.90</td><td>BB</td><td>5074.36</td><td>...</td><td>...</td><td>...</td><td>7.85<sup>+0.64</sup><sub>-0.44</sub></td></tr><tr><td>-0.32</td><td>1.32</td><td>BB+PL</td><td>2587.96</td><td>-1.43<sup>+0.05</sup><sub>-0.06</sub></td><td>...</td><td>...</td><td>92.61<sup>+7.48</sup><sub>-6.89</sub></td></tr><tr><td>1.32</td><td>3.84</td><td>BB+PL</td><td>3245.16</td><td>-1.48<sup>+0.03</sup><sub>-0.03</sub></td><td>...</td><td>...</td><td>33.07<sup>+1.22</sup><sub>-1.18</sub></td></tr><tr><td>3.84</td><td>6.57</td><td>BB+PL</td><td>3434.79</td><td>-1.83<sup>+0.03</sup><sub>-0.03</sub></td><td>...</td><td>...</td><td>17.55<sup>+0.57</sup><sub>-0.56</sub></td></tr><tr><td>6.57</td><td>9.13</td><td>BB+PL</td><td>3247.3</td><td>-1.94<sup>+0.03</sup><sub>-0.03</sub></td><td>...</td><td>...</td><td>12.03<sup>+0.4</sup><sub>-0.33</sub></td></tr><tr><td>9.13</td><td>9.80</td><td>BB+PL</td><td>1331.82</td><td>-1.85<sup>+0.04</sup><sub>-0.05</sub></td><td>...</td><td>...</td><td>27.74<sup>+4.64</sup><sub>-4.28</sub></td></tr><tr><td>9.80</td><td>10.48</td><td>BB+PL</td><td>1389.46</td><td>-1.84<sup>+0.04</sup><sub>-0.05</sub></td><td>...</td><td>...</td><td>30.82<sup>+2.64</sup><sub>-2.49</sub></td></tr><tr><td>10.48</td><td>11.22</td><td>BB+PL</td><td>1577.85</td><td>-1.78<sup>+0.03</sup><sub>-0.03</sub></td><td>...</td><td>...</td><td>40.07<sup>+3.37</sup><sub>-2.26</sub></td></tr><tr><td>11.22</td><td>11.86</td><td>BB+PL</td><td>1435.15</td><td>-1.74<sup>+0.03</sup><sub>-0.04</sub></td><td>...</td><td>...</td><td>38.45<sup>+1.49</sup><sub>-1.46</sub></td></tr><tr><td>11.86</td><td>13.84</td><td>BB+PL</td><td>3206.63</td><td>-1.69<sup>+0.02</sup><sub>-0.02</sub></td><td>...</td><td>...</td><td>35.03<sup>+0.7</sup><sub>-0.67</sub></td></tr><tr><td>13.84</td><td>14.82</td><td>BB+PL</td><td>1952.73</td><td>-1.81<sup>+0.03</sup><sub>-0.03</sub></td><td>...</td><td>...</td><td>25.96<sup>+0.97</sup><sub>-0.94</sub></td></tr><tr><td>14.82</td><td>15.64</td><td>BB+PL</td><td>1614.66</td><td>-1.93<sup>+0.05</sup><sub>-0.05</sub></td><td>...</td><td>...</td><td>22.99<sup>+0.91</sup><sub>-0.87</sub></td></tr><tr><td>15.64</td><td>16.13</td><td>BB+PL</td><td>999.76</td><td>-1.89<sup>+0.06</sup><sub>-0.06</sub></td><td>...</td><td>...</td><td>19.48<sup>+1.45</sup><sub>-1.37</sub></td></tr><tr><td>16.13</td><td>18.81</td><td>BB+PL</td><td>3247.84</td><td>-1.94<sup>+0.03</sup><sub>-0.03</sub></td><td>...</td><td>...</td><td>22.81<sup>+0.94</sup><sub>-0.92</sub></td></tr><tr><td>18.81</td><td>21.15</td><td>BB+PL</td><td>3028.63</td><td>-1.93<sup>+0.04</sup><sub>-0.04</sub></td><td>...</td><td>...</td><td>23.48<sup>+1.11</sup><sub>-1.06</sub></td></tr><tr><td>21.15</td><td>22.38</td><td>BB+PL</td><td>1977.08</td><td>-1.9<sup>+0.06</sup><sub>-0.07</sub></td><td>...</td><td>...</td><td>17.3<sup>+1.44</sup><sub>-1.31</sub></td></tr><tr><td>22.38</td><td>27.77</td><td>BB+PL</td><td>4255.62</td><td>-1.97<sup>+0.04</sup><sub>-0.04</sub></td><td>...</td><td>...</td><td>12.37<sup>+0.65</sup><sub>-0.6</sub></td></tr><tr><td>27.77</td><td>30.91</td><td>BB+PL</td><td>3297.07</td><td>-2.12<sup>+0.06</sup><sub>-0.07</sub></td><td>...</td><td>...</td><td>11.4<sup>+1.2</sup><sub>-0.92</sub></td></tr><tr><td>30.91</td><td>33.62</td><td>BB+PL</td><td>2873.76</td><td>-2.18<sup>+0.08</sup><sub>-0.1</sub></td><td>...</td><td>...</td><td>10.8<sup>+1.93</sup><sub>-1.31</sub></td></tr><tr><td>33.62</td><td>37.96</td><td>BB+PL</td><td>3376.19</td><td>-2.11<sup>+0.06</sup><sub>-0.06</sub></td><td>...</td><td>...</td><td>85.19<sup>+76.57</sup><sub>-66.98</sub></td></tr><tr><td>37.96</td><td>47.74</td><td>BB+PL</td><td>4479.78</td><td>-2.25<sup>+0.07</sup><sub>-0.08</sub></td><td>...</td><td>...</td><td>80.51<sup>+77.14</sup><sub>-61.83</sub></td></tr><tr><td>47.74</td><td>58.90</td><td>BB+PL</td><td>4663.33</td><td>-2.18<sup>+0.11</sup><sub>-0.13</sub></td><td>...</td><td>...</td><td>90.65<sup>+72.12</sup><sub>-68.01</sub></td></tr><tr><td>-0.32</td><td>1.32</td><td>Band+BB</td><td>2401.55</td><td>-0.72<sup>+0.04</sup><sub>-0.1</sub></td><td>-2.69<sup>+0.35</sup><sub>-0.43</sub></td><td>815.04<sup>+182.82</sup><sub>-132.32</sub></td><td>96.99<sup>+52.29</sup><sub>-33.18</sub></td></tr><tr><td>1.32</td><td>3.84</td><td>Band+BB</td><td>3242.65</td><td>-1.01<sup>+0.19</sup><sub>-0.17</sub></td><td>-2.65<sup>+0.43</sup><sub>-0.49</sub></td><td>445.66<sup>+228.51</sup><sub>-132.61</sub></td><td>29.22<sup>+1.97</sup><sub>-2.0</sub></td></tr><tr><td>3.84</td><td>6.57</td><td>Band+BB</td><td>3167.61</td><td>-0.71<sup>+0.03</sup><sub>-0.05</sub></td><td>-2.86<sup>+0.15</sup><sub>-0.14</sub></td><td>77.73<sup>+2.87</sup><sub>-2.38</sub></td><td>83.12<sup>+66.27</sup><sub>-67.28</sub></td></tr><tr><td>6.57</td><td>9.13</td><td>Band+BB</td><td>2953.73</td><td>-1.1<sup>+0.1</sup><sub>-0.1</sub></td><td>-2.56<sup>+0.11</sup><sub>-0.14</sub></td><td>51.77<sup>+2.33</sup><sub>-1.21</sub></td><td>69.41<sup>+79.75</sup><sub>-58.8</sub></td></tr><tr><td>9.13</td><td>9.80</td><td>Band+BB</td><td>1087.4</td><td>-1.42<sup>+0.07</sup><sub>-0.05</sub></td><td>-2.92<sup>+0.38</sup><sub>-0.43</sub></td><td>142.98<sup>+20.85</sup><sub>-19.56</sub></td><td>76.52<sup>+71.54</sup><sub>-55.09</sub></td></tr><tr><td>9.80</td><td>10.48</td><td>Band+BB</td><td>1145.82</td><td>-1.3<sup>+0.06</sup><sub>-0.06</sub></td><td>-3.06<sup>+0.37</sup><sub>-0.39</sub></td><td>163.42<sup>+20.56</sup><sub>-17.93</sub></td><td>85.24<sup>+71.91</sup><sub>-56.07</sub></td></tr><tr><td>10.48</td><td>11.22</td><td>Band+BB</td><td>1220.39</td><td>-1.17<sup>+0.05</sup><sub>-0.05</sub></td><td>-3.18<sup>+0.31</sup><sub>-0.37</sub></td><td>237.03<sup>+22.45</sup><sub>-22.42</sub></td><td>92.94<sup>+67.45</sup><sub>-59.67</sub></td></tr><tr><td>11.22</td><td>11.86</td><td>Band+BB</td><td>1300.36</td><td>-1.13<sup>+0.2</sup><sub>-0.17</sub></td><td>-2.91<sup>+0.39</sup><sub>-0.48</sub></td><td>205.08<sup>+46.98</sup><sub>-44.85</sub></td><td>42.65<sup>+7.12</sup><sub>-4.66</sub></td></tr><tr><td>11.86</td><td>13.84</td><td>Band+BB</td><td>2861.4</td><td>-0.71<sup>+0.03</sup><sub>-0.03</sub></td><td>-3.51<sup>+0.33</sup><sub>-0.31</sub></td><td>182.16<sup>+5.86</sup><sub>-5.65</sub></td><td>53.39<sup>+73.36</sup><sub>-22.62</sub></td></tr><tr><td>13.84</td><td>14.82</td><td>Band+BB</td><td>1611.61</td><td>-0.82<sup>+0.06</sup><sub>-0.05</sub></td><td>-3.4<sup>+0.31</sup><sub>-0.35</sub></td><td>122.57<sup>+5.45</sup><sub>-5.12</sub></td><td>79.84<sup>+75.9</sup><sub>-51.58</sub></td></tr><tr><td>14.82</td><td>15.64</td><td>Band+BB</td><td>1390.04</td><td>-0.82<sup>+0.08</sup><sub>-0.09</sub></td><td>-3.3<sup>+0.29</sup><sub>-0.34</sub></td><td>97.14<sup>+5.27</sup><sub>-5.32</sub></td><td>35.37<sup>+104.73</sup><sub>-15.27</sub></td></tr><tr><td>15.64</td><td>16.13</td><td>Band+BB</td><td>688.36</td><td>-0.88<sup>+0.12</sup><sub>-0.11</sub></td><td>-3.16<sup>+0.31</sup><sub>-0.31</sub></td><td>86.41<sup>+7.11</sup><sub>-6.34</sub></td><td>79.09<sup>+79.24</sup><sub>-59.24</sub></td></tr><tr><td>16.13</td><td>18.81</td><td>Band+BB</td><td>2890.32</td><td>-1.08<sup>+0.05</sup><sub>-0.05</sub></td><td>-3.24<sup>+0.25</sup><sub>-0.31</sub></td><td>95.55<sup>+4.89</sup><sub>-4.32</sub></td><td>68.28<sup>+75.52</sup><sub>-47.58</sub></td></tr><tr><td>18.81</td><td>21.15</td><td>Band+BB</td><td>2710.11</td><td>-1.06<sup>+0.06</sup><sub>-0.07</sub></td><td>-3.17<sup>+0.3</sup><sub>-0.34</sub></td><td>98.89<sup>+5.99</sup><sub>-5.68</sub></td><td>59.83<sup>+89.53</sup><sub>-38.74</sub></td></tr><tr><td>21.15</td><td>22.38</td><td>Band+BB</td><td>1701.06</td><td>-0.94<sup>+0.13</sup><sub>-0.13</sub></td><td>-2.92<sup>+0.27</sup><sub>-0.35</sub></td><td>76.13<sup>+5.94</sup><sub>-5.78</sub></td><td>79.11<sup>+79.9</sup><sub>-57.9</sub></td></tr><tr><td>22.38</td><td>27.77</td><td>Band+BB</td><td>3957.98</td><td>-0.98<sup>+0.1</sup><sub>-0.09</sub></td><td>-2.95<sup>+0.18</sup><sub>-0.25</sub></td><td>52.58<sup>+2.38</sup><sub>-1.67</sub></td><td>79.37<sup>+75.2</sup><sub>-60.53</sub></td></tr><tr><td>27.77</td><td>30.91</td><td>Band+BB</td><td>3032.73</td><td>-1.3<sup>+0.11</sup><sub>-0.1</sub></td><td>-3.35<sup>+0.29</sup><sub>-0.31</sub></td><td>50.91<sup>+1.18</sup><sub>-0.67</sub></td><td>74.96<sup>+80.0</sup><sub>-64.08</sub></td></tr><tr><td>30.91</td><td>33.62</td><td>Band+BB</td><td>2714.41</td><td>-1.39<sup>+0.1</sup><sub>-0.07</sub></td><td>-3.22<sup>+0.31</sup><sub>-0.35</sub></td><td>51.38<sup>+1.7</sup><sub>-0.97</sub></td><td>72.15<sup>+76.71</sup><sub>-56.63</sub></td></tr><tr><td>33.62</td><td>37.96</td><td>Band+BB</td><td>3425.53</td><td>-1.45<sup>+0.07</sup><sub>-0.04</sub></td><td>-2.87<sup>+0.34</sup><sub>-0.36</sub></td><td>51.64<sup>+2.19</sup><sub>-1.2</sub></td><td>81.73<sup>+73.91</sup><sub>-69.65</sub></td></tr><tr><td>37.96</td><td>47.74</td><td>Band+BB</td><td>4643.79</td><td>-1.43<sup>+0.09</sup><sub>-0.05</sub></td><td>-3.14<sup>+0.33</sup><sub>-0.36</sub></td><td>51.77<sup>+2.63</sup><sub>-1.27</sub></td><td>45.3<sup>+98.24</sup><sub>-38.87</sub></td></tr><tr><td>47.74</td><td>58.90</td><td>Band+BB</td><td>4774.79</td><td>-1.36<sup>+0.17</sup><sub>-0.1</sub></td><td>-2.9<sup>+0.41</sup><sub>-0.42</sub></td><td>54.75<sup>+3.02</sup><sub>-3.57</sub></td><td>43.25<sup>+93.44</sup><sub>-36.18</sub></td></tr></tbody></table>

Note. Band: Band model; BB: blackbody; PL: power law.
ORCID iDs

Shao-Yu Fu https://orcid.org/0009-0002-7730-3985

Dong Xu https://orcid.org/0000-0003-3257-9435

Wei-Hua Lei https://orcid.org/0000-0003-3440-1526

Antonio de Ugarte Postigo https://orcid.org/0000-0001-7717-5085

D. Alexander Kann https://orcid.org/0000-0003-2902-3583

Christina C. Thöne https://orcid.org/0000-0002-7978-7648

José Feliciano Agúi Fernández https://orcid.org/0000-0001-6991-7616

Wei Xie https://orcid.org/0000-0001-5553-4577

Yuan-Chuan Zou https://orcid.org/0000-0002-5400-3261

Zi-Pei Zhu https://orcid.org/0000-0002-9022-1928

Jie Zheng https://orcid.org/0000-0001-6637-6973

Li-Ping Xin https://orcid.org/0000-0002-9422-3437

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