Multiwavelength Analysis of the Supernova-associated Low-luminosity GRB 171205A

Multiwavelength properties of the nearby supernova (SN)-associated low-luminosity GRB 171205A are investigated in depth to constrain its physical origin synthetically. The pulse width is found to be correlated with energy with a power-law index of −0.24 ± 0.07, which is consistent with the indices of other SN-associated gamma-ray bursts (SN/GRBs) but larger than those of long GRBs. By analyzing the overall light curve of its prompt gamma rays and X-ray plateaus simultaneously, we infer that the early X-rays together with the gamma-rays should reflect the activities of the central engine, while the late X-rays may be dominated by the interaction of external shocks with circumburst material. In addition, we find that the host radio flux and offset of GRB 171205A are similar to those of other nearby low-luminosity GRBs. We adopt nine SN/GRBs with measured offset to build a relation between peak luminosity (L γ,p ) and spectral lag (τ) as L γ,p ∝ τ −1.91±0.33. The peak luminosity and the projected physical offset of 12 SN/GRBs and 10 kilonova-associated GRBs are found to be moderately correlated, suggesting their different progenitors. The multiwavelength afterglow fitted with a top-hat jet model indicates that the jet half-opening angle and the viewing angle of GRB 171205A are ∼34.°4 and 41.°8, respectively, which implies that the off-axis emissions are dominated by the peripheral cocoon rather than the jet core.


Introduction
Gamma-ray bursts (GRBs) are the most energetic gamma-ray flashes in the universe.They consist of two stages: an initial prompt gamma-ray emission phase, and a long-lasting multiwavelength afterglow emission phase (Zhang & Mészáros 2004;Zhang 2007;Kumar & Zhang 2015;Zhang 2018).Physically, the prompt emissions are considered to originate from internal shocks due to the interactions between ejected materials inside the fireball, while the broadband afterglows are produced by external shocks due to ejecta-medium interactions (e.g., Mészáros & Rees 1997;Sari 1997;Huang et al. 2000;Zhang 2018).In general, the collapsar model is thought to account for long GRBs (LGRBs) with a duration of T 90 > 2 s (Paczyński 1998;Woosley & Heger 2006).So far, a handful of LGRBs are observed to be associated with energetic, broadlined, stripped-envelope supernovae (SNe).These SN-associated GRBs (SN/GRBs) usually have a luminosity 3-4 orders of magnitude lower than normal LGRBs (e.g., Galama et al. 1998;Pian et al. 2006).
The light curves of prompt emissions are variable and highly irregular, reflecting the temporal properties of the internal energy dissipation and the activities of the cental engine (e.g., Rees & Meszaros 1994;Li et al. 2020).Besides, the spectral properties of GRBs contain the key information of radiative mechanisms (Norris et al. 1996).For example, the time lags of light curves between different energy bands can be used to understand the emission mechanism of prompt emissions (Zhang et al. 2006a;Wei et al. 2017).Generally, when the higher-energy photons arrive earlier than lower-energy photons, we call it a positive time lag.Otherwise, it is called a negative lag.Norris et al. (2000) reported an anticorrelation between the peak luminosity (L γ,p ) and the time lag (τ) for six BATSE LGRBs, which can be described by a power-law function as L γ,p ∝ τ −1.14 .At the same time, they found that the SN/GRB GRB 980425 falls below the extrapolated power-law function by a factor of 400-700.Subsequently, the anticorrelation between L γ,p and τ was further investigated and confirmed with different samples (e.g., Norris 2002;Schaefer & Collazzi 2007;Hakkila et al. 2008;Arimoto et al. 2010;Ukwatta et al. 2010Ukwatta et al. , 2012;;Bernardini et al. 2015).However, whether the L γ,p -τ relation existed for the SN/GRBs was unknown until Li et al. (2023) recently built the luminosity relation L γ,p ∝ τ −1.43±0.33 by using 16 SN/GRBs.In addition, they also utilized 14 kilonova-associated GRBs (KN/GRBs) to build a power-law relation of L γ,p ∝ τ −2.17±0.57 .
Two leading types of central engines, i.e., (1) a hyperaccreting black hole (BH) and (2) a rapidly spinning, strongly magnetized neutron star (NS), have been proposed to power the GRB outflows (e.g., Usov 1992;Popham et al. 1999;Zhang & Mészáros 2001).Long-lasting emissions of GRBs in the form of extended emissions and X-ray afterglows are crucial to reveal the physical origin of the central engines (Norris & Bonnell 2006;Zhang et al. 2006;Rowlinson et al. 2013;Lü et al. 2015;Kisaka et al. 2017;Lü et al. 2018Lü et al. , 2020;;Sharma et al. 2021).Based on the dipole spin-down model, Lü et al. (2015) confirmed the hypothesis of the magnetar central engine model for short GRBs (SGRBs) with an "internal plateau" followed by a very rapid decay.In view of the energetics of GRBs, the central engines of LGRBs with energies larger than 10 52 erg are preferentially identified as BHs (Sharma et al. 2021).Nevertheless, the unusual observations of low-Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Several nearby LLGRBs, such as GRB 980425/SN 1998bw, GRB 031203/SN 2003lw, GRB 060218/SN 2006aj, GRB 100316D/SN 2010bh, GRB 171205A/SN 2017iuk, and GRB 190829A/SN 2019oyu, are identified to be associated with SNe (e.g., Galama et al. 1998;Malesani et al. 2004;Campana et al. 2006;Pian et al. 2006;Starling et al. 2011;Terreran et al. 2019).A systematic study of the time lags in the prompt emissions of both the SN/GRBs and KN/GRBs (Li et al. 2023) and the similarity between SN/GRB 171205A and KN/ GRB 170817A motivate us to undertake further analysis in more detail.In fact, the properties of GRB 171205A were found to be different from other energetic GRBs and other LLGRBs in many respects (e.g., D'Elia & Campana 2018; Wang et al. 2018;Izzo et al. 2019;Zhang et al. 2023).Therefore, it is necessary for us to go further to compare this burst with other nearby LLGRBs systematically in this study.This paper is organized as follows.Data analysis and methods are given in Section 2. The main results are presented in Section 3. Finally, the discussion and conclusions are presented in Sections 4 and 5, respectively.photons cm −2 s −1 , respectively (Lien et al. 2016).The afterglow observations of GRB 171205A were carried out in multiple wavelengths from X-rays to radio bands up to 1000 days (e.g., Butler et al. 2017;Chandra et al. 2017bChandra et al. , 2017a;;Choi et al. 2017;Cobb 2017;Izzo et al. 2017;Kennea et al. 2017;D'Elia & Campana 2018;Urata et al. 2019;Leung et al. 2021;Maity & Chandra 2021).Spectroscopic observations revealed that GRB 171205A is associated with a Type Ic SN, SN 2017iuk (Izzo et al. 2017;D'Elia & Campana 2018;Wang et al. 2018).It is also found that GRB 171205A occurred in the outskirts of the bright spiral galaxy 2MASX J11093966-1235116 located at z = 0.037, which is an early-type (S0), high-mass, star-forming galaxy with a low specific star formation rate and a low metallicity (Izzo et al. 2017;Wang et al. 2018).Throughout this study, a flat ΛCDM Universe with Ω m = 0.286, Ω Λ = 0.714, and H 0 = 69.6 km s −1 Mpc −1 is assumed (Bennett et al. 2014).

Data Analysis
To study the relation between luminosity and spectral lag for GRB 171205A, we first compare three different kinds of lags including the cross-correlation function (CCF) lag τ (Band 1997), the centroid delay τ c , and the peak time delay τ p (Norris et al. 2000) between channel 1 (15-25 keV), channel 2 (25-50 keV), channel 3 (50-100 keV), and channel 4 (100-350 keV).This proves that the CCF method can provide the best lags with relatively smaller scatter (see Figure 1 for details).Consequently, the CCF lag will be calculated and applied for all GRBs in our sample herein.The mask-weighted light-curve data with a 10 s resolution are taken from the Swift website6 (Lien et al. 2016).We take two steps to obtain the more accurate spectral lags.First, in order to obtain the smooth CCF curves, we follow Zhang et al. (2006aZhang et al. ( , 2006bZhang et al. ( , 2008) ) to fit the light-curve data using the "KRL" function of individual GRB pulses and obtain four smooth light-curve pulses (Li et al. 2020(Li et al. , 2021a(Li et al. , 2022a)).Then, we perform the CCF analysis with the Stingray Python package (Huppenkothen et al. 2019b(Huppenkothen et al. , 2019a)). 7wo distinct components could be observed following the prompt emission of many GRBs.One is a high-level extended emission, and the other is a low-level plateau stage.Kisaka et al. (2017) used a phenomenological formula to depict these two components, which essentially synthesizes two functions (each has a constant flux stage followed by a subsequent power-law decay).Considering that the two power-law indices could be different for the two components, we modify their empirical formula as where L EX,iso , L PL,iso , T EX , and T PL are the luminosities and durations of the extended and plateau emissions, and α 1 and α 2 are the temporal indices.Note that the extended emission is defined as emission with a timescale of 10 3 s, some of which are not detected by Swift/BAT.A longer timescale component (10 3 s) is defined as plateau emission (Kisaka et al. 2017).
The identification of the extended and plateau emission is purely phenomenological (Kisaka et al. 2017).

Dependence of Pulse Width on Energy
We now examine the dependence of the FWHM on the averaged photon energy (E).The FWHM versus photon energy is plotted in Figure 2.Here the errors of FWHM are estimated by considering the error propagation, using the method proposed in our previous study (Zhang et al. 2006a).Considering the fact that a larger bin size of light curve can improve the signal-tonoise ratio (S/N) level but also can smooth the pulse structures (Li et al. 2021a), we here use the observed light curves with a time resolution of 10 s.This is feasible since GRB 171205A is a very long burst and it can be divided into sufficient bin numbers to ensure its essential temporal profiles.
It could be seen that the negative power-law correlation, FWHM ∼ E α , still holds for GRB 171205A, with a Pearson coefficient of ρ = 0.92 and a chance probability of P = 0.08.Our best-fit power-law index is α = − 0.24 ± 0.07, which is coincident with those observed in GRB 980425 (α = − 0.20 ± 0.04) and GRB 060218 (α = − 0.31 ± 0.03) (Liang et al. 2006;Zhang 2008) but is significantly larger than the value of −0.4 for normal LGRBs (Fenimore 1995; Norris et al. 1996).In addition, we find that the power-law index of GRB 171205A is marginally consistent with the mean value of α = −0.32 ± 0.03 for single-peaked BATSE SGRBs (Li et al. 2020) and α = −0.32 ± 0.02 for Swift SGRBs (Li et al. 2021a).Physically, the energydependent burst duration is related to the evolution of peak energy across the observing band (Campana et al. 2006;Uhm et al. 2018).Considering the fact that most KN/GRBs are short in duration, one can conclude that SN/GRB GRB 171205A shares the partial properties of KN/GRBs, which has also been illustrated on the plane of luminosity versus spectral lag (Li et al. 2023).The overlapping features of SN/GRBs and KN/ GRBs add more complexity to the GRB classification.The best solution is to assort GRBs with more physical parameters jointly (e.g., Zhang et al. 2009).

Peak Luminosity versus Time Lag
To check whether GRB 171205A matches the L γ,p -τ relation, one needs to precisely measure the time lags of light curves across different energy channels.The CCF lag was adopted more frequently than either the peak lag or the centroid lag since these basic techniques were proposed in the past (Band 1997;Norris et al. 2000).Three types of lags between distinct energy channels in diverse time resolutions are compared for GRB 171205A in Figure 1, where it can be found that the CCF lags with a bin size of 10 s have relatively smaller errors and the centroid lags are larger than the others.Therefore, the CCF lag τ 31 between energy channels 1 and 3 is chosen to compare GRB 171205A with other SN/GRBs and KN/GRBs in the plot of L γ,p versus τ 31 .The three types of lags are listed in Table 1.
Figure 3 is plotted to examine whether SN/GRBs and KN/GRBs with known offsets in our sample obey the powerlaw relations of L p , 31 . Here D L is the luminosity distance, P γ,bolo = P γ K c is the bolometric peak flux, and K c is the K-correction factor (Zhang et al. 2018b(Zhang et al. , 2020)).The lags have been corrected by the factor (1 + z) −1 to compensate for the cosmological time dilation.The spectral lag is proportional to the pulse width with a factor of (1 + z) for the cosmological time dilation and a factor of (1 + z) −0.33 for the frequency shift (Li et al. 2020(Li et al. , 2021a)).As a result, the ratio of the intrinsic time lag to the observed one is (1 + z) −0.67 (see also Gehrels et al. 2006).The errors of lag are calculated by considering the error propagation process as done in our previous study (Zhang et al. 2006a).We find that the lags of the SN/GRBs are longer than those of the KN/GRBs, which can be understood if the time lags are related to the burst durations through the emission radius and Lorentz factor (Zhang et al. 2009) 2008).Note that the inferred errors of the centroid lags are large and we just take 10% of the centroid lags as an error estimation in our calculations.c The CCF lags.d The signal in the corresponding bin size is too weak to be well fitted by a pulse function.
Figure 2. The FWHM and the averaged photon energy of GRB 171205A in the four energy channels are anticorrelated.The solid line stands for the best power-law fit to the data.
be seen that most lags are nearly zero, which is very close to previous results for SGRBs (e.g., Norris & Bonnell 2006;Zhang et al. 2006b;Bernardini et al. 2015).However, it is hard to obtain a firm conclusion owing to the limited sample of KN/ GRBs with measured offset.In addition, we caution that GRB 171205A exhibits a time lag close to the averaged one of normal LGRBs (see, e.g., Norris et al. 2000;Zhang et al. 2006aZhang et al. , 2006b)), and it lies near the fitting line of SN/GRBs, which further strengthens its association with an SN.Since most bight GRBs are found to have narrower pulses and smaller lags (Band 1997;Norris et al. 2000), it is straightforward to expect the power-law relation between luminosity and spectral lag as shown in Equation (2).Because SGRBs have zero lags owing to very fast variability (Zhang et al. 2006b), the luminosity-lag/time correlation could be insignificant among them, while the power-law relation is quite significant for LGRBs (Norris et al. 2000;Zhang et al. 2006a).

Extended Emission and Plateau Emission
By jointly analyzing both the Swift/BAT8 and XRT9 data, we now investigate the potential connection between the extended emission and the plateau component.The X-ray luminosity of GRB 171205A can be calculated as (Tang et al. 2019;Xu et al. 2021), where Γ = 1.63 is the photon spectral index taken from the Swift GRB table. 10The prompt γ-ray light curves in the four BAT energy channels and the X-ray plateau emissions of GRB 171205A are presented in Figure 4, where we find that the Swift/BAT light curves in all energy bands perfectly bridge with the XRT afterglow.This indicates that both γ-ray and early X-ray components should reflect the activities of the central engine together and could share the same radiation mechanism.
Furthermore, we perform a temporal fit to the X-ray light curve of GRB 171205A by adopting Equation (1).The best-fit results are L EX,iso = (3.86 ± 0.11) × 10 46 erg s −1 , L PL,iso = (2.95 ± 0.24) × 10 42 erg s −1 , T EX = (840.03± 241.66) s, T PL = (2.40 ± 0.08) × 10 6 s, α 1 = −9.0 ± 2.2, and α 2 = −1.5 ± 0.2, with a reduced χ 2 of 1.37 2  c n (see Figure 4).The late X-ray plateau followed by a shallower decay could be mainly contributed by the energy injection from a magntar (e.g., Zhang & Mészáros 2001;Fan & Xu 2006;Tang et al. 2019), the jet viewed off-axis (Beniamini et al. 2020), or the fallback accretion process of a BH (Yu et al. 2015), which reflects the multiple activities of the central engine.Of course, the possibility that the X-ray plateau is contributed by SN 2017iuk cannot be fully ruled out (D'Elia & Campana 2018;Li et al. 2023).Interestingly, GRB 171205A favors a magnetar origin, although it has an external plateau in X-rays (Wang et al. 2023).The power-law index of α 2 = −1.5 ± 0.2 of the second decay segment at late time (tens of days after trigger) is very close to the expected value of (4 − 3p)/2 ∼ 1.6 for an electronic spectral index of p = 2.4 in the standard afterglow theory (Gao et al. 2013), which demonstrates that the late-time decay should be dominated by the interaction of external shocks with circumburst material.This does not conflict with the magnetar origin that can be dominant in the early X-ray phase.Very recently, we analyzed those GRBs with internal X-ray plateaus and found that the prompt gamma-ray durations are tightly correlated with the plateau lasting times (Du et al. 2023), which indicates that the early X-ray emissions including plateaus should originate from some internal processes, such as the dissipation of magnetars.

The Host and Offset
For standard GRBs and high-luminosity GRBs, Zhang et al. (2018a) found a similar redshift independence of the flux for host galaxies.Only three nearby LLGRBs deviate from the relation.Li et al. (2015) statistically investigated the relation between the host flux density (F host ) and the peak afterglow flux density (F o,peak ) in radio bands and derived a useful tight correlation as F ν,host = (b 1 + b 2 ν)F o,peak for LLGRBs, with b 1 = 0.27 ± 0.02 and b 2 = − 0.016 ± 0.002, where ν is the observing frequency.Using this correlation, we can estimate the F ν,host of GRB 171205A at frequencies with F o,peak available.Using the radio data provided in Leung et al. (2021) and Maity & Chandra (2021), we have calculated the radio flux density of the host galaxy of GRB 171205A.The result is illustrated in Figure 5 and is compared with several other GRB hosts.It can be seen that the host spectral index (β h < − 1) of GRB 171205A is significantly less than the average spectral index 〈β h 〉 ∼ −0.75 of spiral galaxies (Condon 1992), which is similar to other nearby LLGRBs but differs from the high-luminosity or standard GRBs.In addition, we find that GRB 170817A, as a peculiar SGRB associated with both a gravitational wave and a kilonova, is located in the region with a lower spectral index of β h < −1.It is worth noting that some selection effects, including the instrumental threshold and the galaxy identification as emphasized by Zhang et al. (2018a), have been neglected in the work.
The offsets of GRBs in their host galaxies can help reveal the populations of unusual GRB progenitors (Bloom et al. 2002).Dainotti et al. (2020) reported 22 SN/GRBs and 8 KN/GRBs.Jin et al. (2021) provided another sample including 9 KN/GRBs.Here we choose these SN/GRBs and KN/GRBs with projected physical offset (R phys ) or angular offset (R ang ) available to examine their similarity in depth.In total, we have a sample consisting of 12 SN/GRBs and 10 KN/GRBs.Table 2 lists the key parameters of these SN/GRBs and KN/GRBs and relevant references.The overall distribution of offsets can provide a robust clue to the nature of the progenitors (Bloom et al. 2002).Zhang et al. (2017) have checked the possible correlations between the luminosities of SGRBs with/without extended emission and their offsets to examine the underlying physical origins.Here similar studies are made to diagnose the possible difference of underlying physical origins between SN/GRBs and KN/GRBs.Figure 6 illustrates their one-dimensional and two-dimensional distributions on the L γ,p −R phys plane.We see that the offsets of SN/GRBs tend to be smaller than those of KN/GRBs.This result is consistent with the fact that SGRBs typically have a larger offset than LGRBs (e.g., Fong et al. 2010;Fong & Berger 2013).
We have performed the Kolmogorov-Smirnov (K-S) test to analyze the difference between the two distributions of KN/GRBs and SN/GRBs.In panel (a), we get D = 0.64 from the K-S test, with a p-value of 0.01.Adopting the critical value of D α = 0.74 at a significance level of α = 0.005, we conclude that the distribution of SN/GRBs is different from that of KN/GRBs.It is further noticed that four LLGRBs, i.e., Figure 5. Radio flux densities of GRB host galaxies vs. their redshifts.The lines correspond to different spectrum indices of β h = −1 (solid), −1/3 (dashed), 0 (dotted), 1/3 (dashed-dotted), 2 (dot-dotted-dashed), and 2.5 (short dashed) in Zhang et al. (2018a).The F ν,host values of GRB 060218, GRB 980425, and GRB 031203 are also taken from Zhang et al. (2018a).The F ν,host values of GRB 171205A (yellow circle) and GRB 170817A (red star) are estimated in this study, at the frequencies of 3.5 and 7.1 GHz, respectively.GRB 171205A, GRB 170817A, GRB 060218, and GRB 980425, are generally located in the lower section and obviously deviate from the other GRBs owing to their very low luminosities.Additionally, we find that there is a moderate correlation between the isotropic prompt luminosity and the offset, with the Pearson correlation coefficient being ρ = −0.44 (−0.30) and a chance probability of P = 0.23 (0.43) for SN/GRBs (KN/GRBs) after excluding the four LLGRBs.This is similar to the result of Zhang et al. (2017).Since the offset distributions of SN/GRBs and KN/GRBs with longer and shorter durations are obviously distinct as illustrated by Troja et al. (2008), their luminosities should be related with offsets.However, due to the limited number of LLGRBs, no general conclusion on the correlation between luminosity and offset can be drawn currently.

Modeling Multiwavelength Afterglows
We adopt an overall dynamic evolution and radiation process of a jetted GRB ejecta model (Huang et al. 1999(Huang et al. , 2000(Huang et al. , 2006) ) to fit the multiwavelength afterglow of GRB 171205A on the condition that a simple top-hat jet model is assumed.We use the Markov Chain Monte Carlo (MCMC) algorithm to get the best-fitting result for the multiwavelength GRB afterglow.The corresponding corner plot of some typical parameters is shown in Figure 7 and Table 3, in which the jet half-opening angle and the viewing angle are found to be ∼34°.4and 41°.8, respectively, confirming that GRB 171205A was viewed off-axis (see, e.g., Maity & Chandra 2021;Kumar et al. 2022).Consequently, the large θ j should correspond to the angular size of a cocoon rather than the jet core (Li et al. 2020;Maity & Chandra 2021).In addition, we present the observed data of multiwavelength afterglows and the best-fitting light curves in Figure 8.
The Karl G. Jansky Very Large Array Sky Survey (VLASS) revealed that the spectral luminosity of GRB 171205A lies between normal LGRBs and SNe with an H-poor prompt spectrum (Stroh et al. 2021).In addition, Arabsamani et al. (2022) presented a detailed study on the distribution and kinematics of atomic hydrogen in the host galaxy of GRB 171205A through the Hi 21 cm emission-line observation with the Very Large Array.Its unusual Hi features indicate that GRB 171205A could be ignited under extreme conditions with rare dynamics.Here we find that GRB 171205A is located close to other SN/GRBs in the plane of peak luminosities versus spectral lags, which is consistent with the result of all SN/GRBs and KN/GRBs (Li et al. 2023).The host galaxy spectrum of GRB 171205A, like other nearby LLGRBs, has a spectral index lower than −1.Meanwhile, we notice in the plot of L γ,iso against R phys that GRB 171205A is located between SN/GRBs and KN/GRBs.However, the result is somewhat  ambiguous owing to a limited number of KN/GRBs with measured offsets.

Discussion
The central engine of GRBs may be a magnetar, especially those GRBs with a plateau component in the X-ray afterglow (Xu & Huang 2012;Tang et al. 2019).The total rotational energy of a millisecond magnetar can be written as ´--, where I is the moment of inertia and P 0 = 2π/Ω 0 is the initial spin period.M and R are the mass and radius of the NS, respectively.The magnetar spins down owing to magnetic dipole radiation, and the spin-down luminosity evolves with time as ) , where is the characteristic spin-down timescale (Lü et al. 2015(Lü et al. , 2018)).To diagnose the center engine of GRB 171205A, we use the Swift X-ray data to constrain the initial spin period and the dipolar surface magnetic field to test whether the results match the spin-up line predictions for a typical NS (Stratta et al. 2018).In this way, we constrain the initial spin period as P 0 ∼ 117.6 ± 0.4 ms, with the dipolar surface magnetic field being B p ∼ (3.73 ± 0.33) × 10 15 G.The magnetic field deviates from the bounding of the B p -P 0 parameters corresponding to the range of mass accretion rates 10 −4 M e s −1 < M˙< 0.1M e s −1 (Stratta et al. 2018).Note that M = 1.35M e and R = 11.9 km (Deibel et al. 2013;Lattimer & Prakash 2016;Most et al. 2018) have been adopted in our calculations.
In contrast to those normal GRBs produced from an ultrarelativistic jet driven by a compact central engine, LLGRBs may be powered by shock breakouts (e.g., Kulkarni et al. 1998;Nakar & Sari 2012).For example, Starling & Page (2012) argued that two LLGRBs (GRB 060218 and GRB 100316D) with thermal spectrum and emitting radius much smaller than those of the normal energetic GRBs can be interpreted by the shock breakout model.However, GRB 171205A, as a typical low-luminosity burst, has a thermal spectral component but with a temperature close to that of the thermal component in the energetic SN/GRB GRB 101219B (D'Elia & Campana 2018).This hints that both low-and highluminosity SN/GRBs may have a thermal spectrum universally.Izzo et al. (2019) studied the multiepoch spectrum of GRB 171205A/SN 2017iuk and argued that the high-speed emission features should originate from a mildly relativistic hot cocoon generated as a result of the breakout of an ultrarelativistic jet (see also Suzuki & Maeda 2022).The geometric feature of outflow is quite similar to that of the KN/GRB GRB 170817A on the basis of multiple-facility radio observations (Mooley et al. 2018(Mooley et al. , 2018)).Interestingly, we found that the special structure of a relativistic jet surrounded by a nonrelativistic cocoon of GRB 170817A-like events can also be distinguished by the temporal evolution of prompt γ-ray light curves (Li et al. 2020).Subsequently, Maity & Chandra (2021) utilized the upgraded Giant Meter-wave Radio Telescope (uGMRT) to monitor the late radio afterglow (∼1000 days after burst) of GRB 171205A in a frequency range of 250-1450 MHz and further inferred GRB 171205A to originate from an off-axis jet enveloped by a wide cocoon.Kumar et al. (2022) used the latest XRT data to constrain the jet half-opening angle to be θ j > 51°.3.For such a large jet half-opening angle, the X-ray afterglow under the off-axis condition is expected to peak dozens (or even hundreds) of days after the GRB detection, and the X-ray flux would be very low.However, its X-ray afterglow peaks within ∼1 day, which resembles other GRB X-ray light curves viewed on-axis.
In general, GRBs can be physically classified as short-hard (type I) and long-soft (type II) groups according to the multiple classification standards (Zhang et al. 2009).The type I and II bursts are produced by the compact star merger and corecollapse processes, respectively.We notice from Li et al. (2023) that almost all SN/GRBs (except GRB 200826A) have   durations longer than 2 s, while most KN/GRBs are short ones with T 90 < 2 s.There are four long KN/GRBs (GRB 050724, GRB 060614A, GRB 070714B, and GRB 080503) challenging the traditional classification scheme on the basis of durations (Kouveliotou et al. 1993;Zhang & Choi 2008).This means that a fraction of LGRBs should originate from compact binary collisions instead of core-collapse processes.For example, a recent striking LGRB associated with a kilonova, GRB 211211A, provides compelling evidence of a compact binary merger origin (e.g., Troja et al. 2022;Yang et al. 2022).On the other hand, Li et al. (2023) systematically compared the temporal and spectral properties of 53 SN/GRBs and 15 KN/ GRBs and found a heavy overlap in the plots of luminositylag, Amati relation, and plateau duration-luminosity between both types of GRBs.In practice, most GRBs do not have an SN or KN detected, but they still could be SN/GRBs or KN/ GRBs.In these cases, the SN or KN signals are not detectable because either the signals are too faint or they are buried beneath the brighter GRB afterglow.As a nearby SN/GRB, GRB 171205A exhibits both differences and similarities with normal LGRBs, nearby LLGRBs, and SGRBs, indicating that the SN/LLGRB populations might be more complex than what we thought before.Hopefully, our statistical results can shed new light on the nature of GRB 171205A and provide some useful clues for further investigations in the field.

Conclusions
We find that the pulse width and energy of GRB 171205A have a power-law relation with an index of -0.24 ± 0.07, which is on average larger than those of normal LGRBs.The early X-rays and gamma-rays may reflect the activities of the central engine, while the late X-rays should result from the interaction of the external shock with the circumburst material.Using the nine SN/GRBs with measured offset, we found that L γ,p ∝ τ −1.91 , which is different from the L γ,p ∝ τ −1.15 derived by Norris et al. (2000) for normal LGRBs.The MCMC method is engaged to fit the multiwavelength afterglow of GRB 171205A.The jet half-opening angle and the viewing angle are found to be ∼34°.4and 41°.8, respectively, confirming the offaxis geometry of this event.
5 at 07:20:43.9UT, the Swift Burst Alert Telescope (Swift/BAT) triggered and located GRB 171205A (D'Elia et al. 2017), whose duration is long, T 90 = 190.5 ± 33.9 s, as measured from T − 26.2 s to T + 164.3 s (Izzo et al. 2017), and the time-averaged spectrum is best fit by a powerlaw function with a photon index of 1fluence and the peak photon flux in the 15-350 keV band are 6

Figure 1 .
Figure 1.The CCF lags (crosses), the peak lags (filled symbols), and the centroid lags (open symbols) measured between different energy channels in time bins of 64 ms, 1 s, and 10 s, respectively.

Figure 4 .
Figure4.The joint light curves of the prompt multi-wave-band γ-ray emissions (gray diamonds) and the X-ray emissions (green circles) of GRB 171205A.Note that the data points in BAT bands are chosen with high S/N (S/N 2).The solid line stands for the best fit to the XRT data with Equation (1).The dotted lines show the total luminosity of the Blandford-Znajek (BZ) jet launched by an evolving BH with a power-law timing index of α = −5/3(Rosswog 2007;Kisaka & Ioka 2015;Kisaka et al. 2017).

Figure 7 .
Figure 7. Physical parameters derived by using a top-hat jet model (1σ-3σ confidence levels) for GRB 171205A.The best-fitting results are marked with 1σ uncertainties above the panel of their posterior distributions.
. In particular, we find that the new luminosity relation is The centroid lags.We calculate the centroid as t centoid = ∑I(t)tΔt/∑I(t)Δt , where Δt is the time bin of the observed data and I(t) is the pulse intensity (Zhang Norris et al. (2000)icient of ρ = 0.91 and a chance probability of P = 7.11 × 10 −4 for the SN/GRBs, which is consistent with those based on a large sample of SN/GRBs and KN/ GRBs(Li et al. 2023)but differs from the one given byNorris et al. (2000)for six normal LGRBs.For the KN/GRBs, it can a The peak lags.b

Table 2
Physical Parameters of the SN/GRBs and KN/GRBs

Table 3
The Best-fit Results of GRB 171205A for a Top-hat Jet Model