GRB X-Ray Flare Properties among Different GRB Subclasses

Gamma-ray bursts (GRBs) are violent explosions in the gamma-ray band. They are specified by two types based on the burst duration time, notated as T₉₀ (Kouveliotou et al. 1993). A burst is identified as a long GRB when T₉₀ is more than 2 s, while a burst is identified as a short GRB when T₉₀ is less than 2 s. Besides T₉₀, the hardness ratio is another important parameter for the long/short GRB classification. de Ugarte Postigo et al. (2011) found that some GRBs in the Swift-detected sample are neither long nor short, and these GRBs can be classified as intermediate GRBs. The GRBs detected by BATSE and Fermi-GBM were further examined in the duration-hardness plane (Tarnopolski 2019). On the other hand, the GRB prompt spectrum can be described by the Band function. The Band function has three parameters: low-energy index α, peak energy E_p, and high-energy index β (Band et al. 1993). Preece et al. (2000) found that the peak energy spreads around 250 keV for the GRBs detected by BATSE. We recently classified GRBs into X-Ray Flashes (XRFs), X-Ray Riches (XRRs), and Classical GRBs (C-GRBs) using the latest Swift-BAT3 catalog (Bi et al. 2018). In particular, the peak energy of XRFs is located around 24 keV, which is consistent with the results of Sakamoto et al. (2005). It is also noted that some XRFs are associated with supernovae (Fynbo et al. 2004; Levan et al. 2005; Bersier et al. 2006; Soderberg et al. 2006). The relation between GRB 120422A and SN 2012bz indicates that low-luminosity GRBs are relevant to supernovae at low redshift (Schulze et al. 2014). Bi et al. (2018) took 6 XRFs, 14 XRRs, and 3 C-GRBs that are related to the supernova explosion into account in the Swift-BAT3 catalog.

Some models have been proposed to reveal the physical origins for XRFs. Different baryon loading can have an effect on the GRB bulk Lorentz factor (Dermer et al. 1999). Barraud et al. (2005) suggested the different bulk Lorentz factors of the shock waves for XRFs and C-GRBs. In general, jet off-axis/beaming effects have been accepted to explain the XRF origin (Yamazaki et al. 2002; Granot et al. 2005; Lamb et al. 2005; Salafia et al. 2016). Matzner et al. (2013) proposed that the nonradial motion of the GRB outflow near the progenitor stellar surface can suppress the photon flash so that the low energetic GRBs can be discovered. Ciolfi (2016) suggested that XRF 020903 can originate from the neutron star spindown if this XRF was formed by the binary neutron star or the core-collapse supernova, because the modeling spectrum mainly falls in the X-ray band and the modeling luminosity is similar to the XRF luminosity. This suggests that XRFs can be related to Poynting-dominated jets. Moreover, photospheric radiation can also be applied for the explanation of the XRF properties (e.g., Pe'er et al. 2006).

X-ray flares are the rebrightening emission shown in some GRB X-ray afterglows (Falcone et al. 2006). Some statistical analysis results from the Swift samples have been achieved. Chinacarini et al. (2007) performed one temporal investigation on 69 X-ray flares, and they concluded that the X-ray flare and the prompt emission have the same origin. Falcone et al. (2007) performed one spectral investigation on 77 X-ray flares, and the Band function can be a good fitting to the X-ray flare spectra. Chincarini et al. (2010) systematically studied the temporal properties of the X-ray flares with a large sample. They found that the X-ray flare duration decreases with the energy as w ∝ E^−0.5 and linearly increases with the X-ray flare peak time as w ∼ 0.2t_p, where w is the duration, E is the isotropic energy in the 0.3–10 keV band, and t_p is the peak time. Yi et al. (2016) enlarged the X-ray flare sample from the updated Swift-XRT data set. From a statistical point of view, about 30% of GRBs have X-ray flares (Chincarini et al. 2010; Margutti et al. 2011; Yi et al. 2016).

There are some models to explain X-ray flare origin. X-ray flares that are contemporaneous with the early X-ray afterglow are likely due to a late time manifestation of the same emission mechanism as the prompt emission (Zhang et al. 2006). Ioka et al. (2005) and Lazzati & Perna (2007) proposed several possibilities to explain the GRB X-ray flare. Chincarini et al. (2010) put the data on the log(ΔF/F)-log(w/t_pk) plane to examine the different models suggested by Ioka et al. (2005), where ΔF is the fluence of the X-ray flare, and F is the underlying fluence. It looks like that X-ray flares have an internal origin from a long-active central engine. Mu et al. (2018) indicated that the X-ray flares of short GRBs may also have an internal origin. Jin et al. (2010) estimated the Lorentz factor of the X-ray flare in their model, and the Lorentz factor of the X-ray flare is smaller than that of the general GRB outflow. Mu et al. (2016) took use of the curvature effect to further constrain the Lorentz factor of the X-ray flare. It indicated long-time activity from the GRB central engine to explain the observed GRB X-ray flares. Jia et al. (2016) examined the temporal decay index and the spectral index of the X-ray flares, and the results suggested a Poynting-dominated outflow for the X-ray flare production (Uhm & Zhang 2016). Geng et al. (2017) further calculated an anisotropic effect in the X-ray flare radiation. Lazzati et al. (2011) simulated GRB jet propagation. It was inferred that the X-ray flare originates from some jet propagation instabilities in different cases of the jet opening angle. Giannios (2012) built a dissipative photospheric model to obtain the bulk Lorentz factor that could be used to explain both the spectrum and the light curve for the X-ray flares. Beniamini & Kumar (2016) examined the small emission radius of the X-ray flares and further considered the photosphere model for the X-ray flare origin. It is also possible for a remnant disk accretion to produce X-ray flares if the magnetic coupling is involved between the inner disk and the central black hole (Luo et al. 2013).

We attempt to comprehensively examine the X-ray flare properties among XRF, XRR, and C-GRB subclasses using the Swift samples in this paper. We utilize our statistical results presented by Bi et al. (2018), in which XRFs, XRRs, and C-GRBs were classified from the latest Swift-BAT3 catalog. We collect the X-ray flare data from both Chincarini et al. (2010) and Yi et al. (2016) for the temporal analysis and the X-ray flare data from Falcone et al. (2007) for the spectral analysis. Because some similar explanations in the former descriptions have been proposed for both XRFs and X-ray flares, it indicates that X-ray flares may have some special associations to XRFs. In fact, some GRBs, such as GRB 040916, GRB 050502B, and GRB 050406, with prominent X-ray flares, were identified as XRFs or XRRs (Burrows et al. 2005; Arimoto et al. 2007). We expect some statistical differences of the X-ray flare properties between XRF and C-GRB subclasses in this paper. However, the long/short GRB identification and the XRF/XRR/C-GRB classification are important to our results in this paper. For example, GRB 050502B is classified as an XRR, but its prompt emission has a power-law spectral index of 1.6 over the primary time of 6 s. Thus, it is very similar to a C-GRB. We provide a comprehensive discussion on the GRB classifications in this paper.

We present the data selection in Section 2. In Section 3, we show some general properties of XRFs, XRRs, and C-GRBs. Then, we illustrate the properties of the X-ray flare fluence for XRFs, XRRs, and C-GRBs. We investigate the temporal properties of the X-ray flares for XRFs, XRRs, and C-GRBs. Some properties of the redshift-corrected parameters are presented. The linear correlation between the duration and the peak time of the X-ray flares for XFRs, XRRs, and C-GRBs are given. We plot the $\mathrm{log}({\rm{\Delta }}F/F)-\mathrm{log}(w/{t}_{p}$) distribution of the X-ray flares for XRFs, XRRs, and C-GRBs. Finally, the spectral properties of the X-ray flares among XRF, XRR, and C-GRB subclasses are illustrated. In Section 4, we comprehensively discuss some issues, such as sample classification, selection effect, and instrument bias, which affect our results. We list the conclusions in Section 5.

We use the standard cosmological parameters: H₀ = 72 km s⁻¹ Mpc⁻¹, Ω_Λ = 0.7, and Ω_M = 0.3.

We utilize the GRB X-ray flare temporal data from both Chincarini et al. (2010) and Yi et al. (2016). The X-ray flares presented by Chincarini et al. (2010) were observed from 2005 April to 2008 March, while those of Yi et al. (2016) were observed from 2005 April to 2015 March. The two samples cover the same observational period, from 2005 April to 2008 March. In this period, some GRBs having X-ray flares identified in Yi et al. (2016) are not shown in Chincarini et al. (2010). These GRBs are GRB 050712, GRB 050724, GRB 050803, GRB 050820A, GRB 050904, GRB 050915A, GRB 050916, GRB 060124, GRB 060223A, GRB 060510B, GRB 060522, GRB 060926, GRB 061121, GRB 070103, GRB 070129, GRB 070616, GRB 070714A, GRB 071112C, GRB 071122, GRB 080229A, GRB 080319A, and GRB 080325. In the same period, some GRBs having X-ray flares identified in Chincarini et al. (2010) are not shown in Yi et al. (2016). These GRBs are GRB 051210, GRB 051227, GRB 060729, GRB 060814, GRB 060908, GRB 070220, GRB 070306, and GRB 070621.

We also consider the spectral properties of the X-ray flares among XRF, XRR, and C-GRB subclasses. We utilize the data from Falcone et al. (2007). Thirty-three GRBs were observed from 2005 February to 2006 January, and 77 X-ray flares with the spectral analysis are included in the sample.

We have classified GRBs into XRFs, XRRs, and C-GRBs from the Swift-BAT3 catalog (Bi et al. 2018). The criteria for the classification of XRFs, CRRs, and C-GRBs were introduced by Sakamoto et al. (2008). We select the XRFs, XRRs, and C-GRBs that have the X-ray flares identified from Falcone et al. (2007), Chincarini et al. (2010), and Yi et al. (2016) to be the data sample in this paper. We list each GRB having the X-ray flare temporal properties in Table 1. In general, we have 7 XRFs, 34 XRRs, and 15 C-GRBs having X-ray flares from the sample of Chincarini et al. (2010), where 1 XRR and 1 C-GRB are short bursts. We have 16 XRFs, 118 XRRs, and 64 C-GRBs having X-ray flares from the sample of Yi et al. (2016), where 1 XRR and 2 C-GRBs are short bursts.

Table 1.  Temporal Properties of X-Ray Flares among XRFs, XRRs, and C-GRBs

GRB	GRB	GRB	z	T90	Epa	αPL	αCPL	Sp(25–50 keV)	Sp(50–100 keV)	Spf(15–350 keV)	${t}_{p}^{b}$	wc	Sid(0.2–10 keV)	Ste(0.2–10 keV)	${r}_{i}^{g}$	${r}_{t}^{h}$	ri	rt	Ref.k
Name	Type	Type		s	102 keV			10−8 erg cm−2	10−8 erg cm−2	10−8 erg cm−2	s	s	10−8 erg cm−2	10−8 erg cm−2			≥0.2i	≥0.2j
GRB 050406	XRF	⋯	2.7	5.8 ± 1.4	0.3 ± 6.1e−2	2.4 ± 0.3	−4.2e−1 ± 2.4	2.5 ± 0.5	1.9 ± 0.7	142.0 ± 26.4	218.1 ± 7.3	401.8 ± 28.9	1.3 ± 0.1	1.3 ± 0.1	9.2e−3	9.2e−3			Yi16
											209.6 ± 4.0	70.1 ± 7.1	0.9 ± 0.6	0.9 ± 0.6	6.3e−3	6.3e−3			Ch10
GRB 050714B	XRF	⋯	2.438	49.4 ± 11.3	0.3 ± 8.3e−2	2.4 ± 0.3	9.2e−3 ± 1.8	26.2 ± 4.7	10.8 ± 5.8	75.1 ± 17.0	382.9 ± 7.7	484.3 ± 42.5	2.2 ± 0.3	2.2 ± 0.3	3.0e−2	3.0e−2			Yi16
											⋯	⋯	⋯	⋯	⋯	⋯			Ch10
GRB 050822	XRF	⋯	1.434	104.3 ± 15.8	0.1 ± 0.1	2.3 ± 0.1	1.8 ± 0.5	85.4 ± 4.9	59.9 ± 10.7	306.0 ± 29.5	235.7 ± 3.8	269.9 ± 11.3	3.0 ± 0.4	15.8 ± 0.6	9.6e−3	5.2e−2			Yi16
											447.6 ± 2.5	634.5 ± 26.8	12.9 ± 0.5		4.2e−2
											136.7 ± 4.9	53.3 ± 5.2	18.0 ± 14.0	45.7 ± 14.7	5.9e−2	1.5e−1			Ch10
											239.6 ± 9.8	35.4 ± 6.2	2.7 ± 3.6		8.8e−3
											436.0 ± 2.6	104.0 ± 3.9	25.0 ± 2.4		8.2e−2
GRB 060512	XRF	Int.	2.1	8.4 ± 1.7	0.2 ± 1.9e−3	2.4 ± 0.3	1.6 ± 1.3	⋯	⋯	27.8 ± 6.6	206.5 ± 4.2	78.6 ± 13.6	1.8 ± 0.5	1.8 ± 0.5	6.6e−2	6.6e−2			Yi16
											197.2 ± 4.3	79.2 ± 7.8	4.5 ± 1.1	4.5 ± 1.1	1.6e−1	1.6e−1			Ch10
GRB 060926	XRF	Int.	3.2086	8.8 ± 1.1	4.2e−2 ± 4.2e−4	2.5 ± 0.2	1.9 ± 1.9e−2	7.7 ± 0.8	5.5 ± 1.2	27.0 ± 4.2	443.3 ± 26.1	3.3e3 ± 366.0	2.8 ± 0.4	2.8 ± 0.4	1.0e−1	1.0e−1			Yi16
GRB 070330	XRF	⋯	⋯	6.6 ± 0.7	0.4 ± 6.2e−2	1.9 ± 0.2	-6.7e−1 ± 1.7	7.9 ± 1.1	4.8 ± 2.0	30.3 ± 5.8	215.9 ± 4.2	149.0 ± 18.7	1.9 ± 0.3	1.9 ± 0.3	6.3e−2	6.3e−2			Yi16
											210.7 ± 5.9	94.6 ± 9.6	2.4 ± 0.9	2.4 ± 0.9	7.9e−2	7.9e−2			Ch10
GRB 070714A	XRF	⋯	⋯	3.0 ± 1.4	1.8e−2 ± 2.9e−3	2.6 ± 0.2	2.0 ± 0.5	5.2 ± 0.5	3.5 ± 0.7	17.7 ± 2.4	303.4 ± 54.7	709.0 ± 573.8	0.5 ± 0.2	3.2 ± 1.5	2.9e−2	1.8e−1			Yi16
											869.8 ± 185.5	1.5e4 ± 6.5e3	2.7 ± 1.5		1.5e−1
GRB 071031	XRF	⋯	2.6918	180.6 ± 30.3	2.1e−2 ± 0.8	2.4 ± 0.3	2.0 ± 0.2	21.1 ± 8.0	12.3 ± 9.9	108.0 ± 22.1	158.0 ± 1.5	201.0 ± 10.4	59.4 ± 3.1	106.9 ± 4.0	5.5e−1	9.9e−1	$\surd$	$\surd$	Yi16
											200.9 ± 1.7	468.8 ± 107.6	16.3 ± 2.3		1.5e−1
											258.3 ± 1.8	331.8 ± 55.2	7.0 ± 0.8		6.5e−2
											448.8 ± 3.9	2.7e3 ± 106.7	24.3 ± 0.8		2.2e−1		$\surd$
											146.8 ± 1.1	61.2 ± 4.2	28.0 ± 11.0	60.4 ± 11.4	2.6e−1	5.6e−1	$\surd$	$\surd$	Ch10
											200.7 ± 1.8	44.0 ± 4.9	8.0 ± 1.9		7.4e−2
											255.6 ± 2.2	51.9 ± 6.3	5.4 ± 1.3		5.0e−2
											447.8 ± 4.4	276.1 ± 10.0	19.0 ± 1.9		1.8e−1

Note. "Int." in the second column of GRB type means that the GRB belongs to the intermediate class. ${E}_{p}^{a}$ indicates the GRB peak energy. ${t}_{p}^{b}$ is the peak time of the X-ray flare. w^c is the duration of the X-ray flare. S^d(0.2–10 keV) is the fluence of the single X-ray flare. ${S}_{t}^{e}$(0.2–10 keV) is the total fluence of all X-ray flares corresponding to one GRB. S_p^f(15–350 keV) is the fluence of the GRB prompt emission. ${r}_{i}^{g}$ is equal to S(0.2–10 keV)/S_p(15–350 keV). ${r}_{t}^{h}$ is equal to S_t(0.2–10 keV)/S_p(15–350 keV). ${r}_{i}\geqslant 0.2$ⁱ represents that the ratio of the individual flare is greater than 0.2. If it is greater than the threshold, this column is marked as $\surd$. r_t ≥ 0.2^j represents whether the ratio of total flare is greater than 0.2. If it is greater than the threshold, this column is marked as $\surd$. Ref.^k lists two samples from which the parameters of the flare are obtained. The sample of Yi16 ranges from 2005 April to 2015 March for Yi et al. (2016). The sample of Ch10 ranges from 2005 April to 2008 March for Chincarini et al. (2010).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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We note that some GRBs do not have fluence values in the Swift-BAT sample. They are GRB 060602, GRB 071112C, GRB 081028, GRB 090516, GRB 090807, and GRB 090809. In addition, the GRB 050714B X-ray flare has no measurements on the peak time and the duration in Chincarini et al. (2010).

3.1. General Properties of XRFs, XRRs, and C-GRBs

3.1.1. T₉₀ Distributions

We examine the T₉₀ distributions for the XRFs, XRRs, and C-GRBs with the temporal properties of the X-ray flares. We show the results in Figure 1. Although it seems that all the XRFs with X-ray flares are long GRBs, we may consider some XRFs with X-ray flares that are short bursts found in future observations. We also note that some XRFs are identified as intermediate GRBs that are neither short nor long (Horváth et al. 2010). We list the intermediate GRBs in Table 1. The sources were identified by de Ugarte Postigo et al. (2011).⁵

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In order to examine the T₉₀ distribution differences among XRF, XRR, and C-GRB subclasses, we further perform the Kolmogorov–Smirnov (K-S) test on the T₉₀ distributions. We first take the GRBs that have the X-ray flares from Chincarini et al. (2010). We obtain the p-value 0.11 that indicates the T₉₀ distribution difference between XRF and C-GRB subclasses. The p-value 0.84 is obtained to indicate the T₉₀ distribution difference between XRR and C-GRB subclasses, and the p-value 0.26 is obtained to indicate the T₉₀ distribution difference between XRR and XRF subclasses. If we exclude the short bursts in XRFs, XRRs, and C-GRBs, the numbers of the p-value are 0.06, 0.67, and 0.21 to indicate T₉₀ distribution differences of XRF and C-GRB subclasses, XRR and C-GRB subclasses, and XRF and XRR subclasses, respectively. Then, we take the GRBs that have the X-ray flares from Yi et al. (2016). We obtain the numbers of the p-value as 0.10, 0.82, and 0.08 to indicate the T₉₀ distribution differences of XRF and C-GRB subclasses, XRR and C-GRB subclasses, and XRF and XRR subclasses, respectively. If we exclude short GRBs in XRFs, XRRs, and C-GRBs, we obtain the numbers of the p-value as 0.06, 0.63, and 0.07 to indicate the T₉₀ distribution differences of XRF and C-GRB subclasses, XRR and C-GRB subclasses, and XRF and XRR subclasses, respectively. We write the p-value numbers for the difference cases in Table 2.

Table 2.  K-S Test for the Distributions of T₉₀, E_grb,p, r_i, r_t, ${S}_{{\mathrm{flare}}_{i}}$, ${S}_{{\mathrm{flare}}_{t}}$, ${E}_{{\mathrm{flare}}_{{\rm{i}}},\mathrm{iso}}$, ${E}_{{\mathrm{flare}}_{{\rm{t}}},\mathrm{iso}}$, w, w_z, t_p, and t_{p, z} among XRFs, XRRs, and C-GRBs

		C-GRB versus XRF	C-GRB versus XRR	XRF versus XRR	Reference
T90	sample size	C-GRB:15 XRF:7	C-GRB:15 XRR:34	XRF:7 XRR:34	Ch10
	p-value	0.11	0.84	0.26
	sample size	C-GRB:64 XRF:16	C-GRB:64 XRR:118	XRF:16 XRR:118	Yi16
	p-value	0.10	0.82	0.08
Egrb,p	sample size	C-GRB:45 XRF:15	C-GRB:45 XRR:102	XRF:15 XRR:102	Bi18
	p-value	1.2 × 10−10	1.7 × 10−5	3.1 × 10−10
ri	sample size	C-GRB:31 XRF:12	C-GRB:31 XRR:69	XRF:12 XRR:69	Ch10
	p-value	2.35 × 10−5	1.27 × 10−6	0.09
	sample size	C-GRB:151 XRF:36	C-GRB:151 XRR:265	XRF:36 XRR:265	Yi16
	p-value	2.60 × 10−8	5.82 × 10−8	8.68 × 10−4
rt	sample size	C-GRB:15 XRF:6	C-GRB:15 XRR:34	XRF:6 XRR:34	Ch10
	p-value	5.39 × 10−3	0.01	0.53
	sample size	C-GRB:61 XRF:16	C-GRB:61 XRR:118	XRF:16 XRR:118	Yi16
	p-value	1.15 × 10−3	1.08 × 10−3	0.19
${S}_{{\mathrm{flare}}_{i}}$	sample size	C-GRB:32 XRF:12	C-GRB:32 XRR:69	XRF:12 XRR:69	Ch10
	p-value	0.26	2.57 × 10−3	0.43
	sample size	C-GRB:167 XRF:36	C-GRB:167 XRR:265	XRF:36 XRR:265	Yi16
	p-value	0.02	0.38	1.14 × 10−3
${S}_{{\mathrm{flare}}_{t}}$	sample size	C-GRB:15 XRF:6	C-GRB:15 XRR:34	XRF:6 XRR:34	Ch10
	p-value	0.63	0.07	0.46
	sample size	C-GRB:59 XRF:16	C-GRB:59 XRR:119	XRF:16 XRR:119	Yi16
	p-value	0.04	0.74	0.06
${E}_{{\mathrm{flare}}_{{\rm{i}}},\mathrm{iso}}$	sample size	C-GRB:16 XRF:9	C-GRB:16 XRR:33	XRF:9 XRR:33	Ch10
	p-value	0.98	0.10	0.13
	sample size	C-GRB:67 XRF:11	C-GRB:67 XRR:129	XRF:11 XRR:129	Yi16
	p-value	0.97	0.13	0.65
${E}_{{\mathrm{flare}}_{{\rm{t}}},\mathrm{iso}}$	sample size	C-GRB:7 XRF:4	C-GRB:7 XRR:19	XRF:4 XRR:19	Ch10
	p-value	0.90	0.84	0.98
	sample size	C-GRB:28 XRF:7	C-GRB:28 XRR:56	XRF:7 XRR:56	Yi16
	p-value	0.19	0.55	0.18
w	sample size	C-GRB:32 XRF:12	C-GRB:32 XRR:69	XRF:12 XRR:69	Ch10
	p-value	0.11	0.45	0.42
	sample size	C-GRB:168 XRF:36	C-GRB:168 XRR:265	XRF:36 XRR:265	Yi16
	p-value	0.79	0.07	0.81
wz	sample size	C-GRB:16 XRF:9	C-GRB:16 XRR:33	XRF:9 XRR:33	Ch10
	p-value	0.75	0.89	0.24
	sample size	C-GRB:74 XRF:11	C-GRB:74 XRR:129	XRF:11 XRR:129	Yi16
	p-value	0.29	0.01	0.07
tp	sample size	C-GRB:32 XRF:12	C-GRB:32 XRR:69	XRF:12 XRR:69	Ch10
	p-value	0.38	0.49	0.36
	sample size	C-GRB:168 XRF:36	C-GRB:168 XRR:265	XRF:36 XRR:265	Yi16
	p-value	0.09	0.11	0.24
tp,z	sample size	C-GRB:16 XRF:9	C-GRB:16 XRR:33	XRF:9 XRR:33	Ch10
	p-value	0.63	0.99	0.45
	sample size	C-GRB:74 XRF:11	C-GRB:74 XRR:129	XRF:11 XRR:129	Yi16
	p-value	0.07	0.01	0.23

Note. We list two references of the X-ray flare data in the Reference column. "Ch10" indicates Chincarini et al. (2010), and "Yi16" indicates Yi et al. (2016). E_grb,p indicates the GRB peak energy.

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It seems that T₉₀ distributions among XRF, XRR, and C-GRB subclasses have high similarity. Thus, there are no significant differences of T₉₀ distribution among XRF, XRR, and C-GRB subclasses. This result is consistent with that of Sakamoto et al. (2005).

3.1.2. Hardness-duration and Peak Energy Distributions of XRFs, XRRs, and C-GRBs

In order to further examine the classification of XRFs, XRRs, and C-GRBs in our sample, we first investigate the hardness-duration distribution for XRFs, XRRs, and C-GRBs in Figure 2. Although the classification can successfully separate XRFs from C-GRBs, we see the overlaps between XRR and C-GRB subclasses, and between XRF and XRR subclasses.

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We then investigate the peak energy of XRFs, XRRs, and C-GRBs in our sample. The peak energy distributions are shown in Figure 3. We perform the K-S test for the distributions of XRF and C-GRB subclasses, XRF and XRR subclasses, and XRR and C-GRB subclasses, respectively. The results are given in Table 2. We clearly see that the E_p distributions among XRF, XRR, and C-GRB subclasses are different. However, we note that the distribution overlaps are also shown in Figure 3.

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3.2. X-Ray Flare Fluence Properties among XRF, XRR, and C-GRB Subclasses

3.2.1. Fluence Ratio between X-Ray Flare and Prompt Emission

We perform a detailed analysis on the X-ray flare fluence properties for XRFs, XRRs, and C-GRBs in this subsection. We obtain the fluence of each individual X-ray flare S_i,flare from Chincarini et al. (2010) and Yi et al. (2016). The fluence of the GRB prompt emission S_prompt can be obtained from the Swift-BAT3 Catalog. In order to properly understand the energy released from the X-ray flare that can be compared to the energy released from the prompt emission, we define a parameter of r_i, and it can be identified as the fluence ratio between one single flare and the prompt emission for each GRB. Some GRBs have multiple X-ray flares, then we accumulate all the S_i,flare numbers to get the total fluence of the X-ray flares S_t,flare in a single GRB. A parameter of r_t can be identified as the fluence ratio between the total flares and the prompt emission for each of these GRBs. Thus, we write the following formula for a certain GRB as:

$$\begin{eqnarray}&&{r}_{i}={S}_{i,\mathrm{flare}}/{S}_{\mathrm{prompt}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{S}_{t,\mathrm{flare}}=\displaystyle \sum _{i}{S}_{i,\mathrm{flare}},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{r}_{t}={S}_{t,\mathrm{flare}}/{S}_{\mathrm{prompt}}.\end{eqnarray} \tag{ 3 }$$

We select the X-ray flare data of Chincarini et al. (2010) and investigate the r_i and r_t distributions for XRFs, XRRs, and C-GRBs. The distributions are shown in Figure 4. We further perform the K-S test, and the results are written in Table 2. We also take the X-ray flare data of Yi et al. (2016) to investigate the r_i and r_t distributions for XRFs, XRRs, and C-GRBs. The distributions are shown in Figure 5, and the K-S test results are also written in Table 2. Although different p-value numbers are obtained among different distributions, we clearly identify that XRF and C-GRB subclasses are different on either r_i or r_t distributions.

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We attempt to directly compare the X-ray flare fluence among C-GRB, XRR, and XRF subclasses using the X-ray flare data from Chincarini et al. (2010) and Yi et al. (2016). We show the fluence distributions of the X-ray flares for C-GRBs, XRRs and XRFs in Figures 6 and 7. We also perform the K-S test, and the results are written in Table 2. However, because some GRBs have no redshift measurements, we caution the direct fluence comparison of the X-ray flares among XRF, XRR, and C-GRB subclasses.

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3.2.2. Bright X-Ray Flares

Some XRFs and XRRs have prominent X-ray flares (Burrows et al. 2005; Arimoto et al. 2007). We have compared the X-ray flare fluence to the prompt emission fluence in each GRB and performed the statistics on the fluence ratio in Section 3.2.1. Here, we define a threshold ratio between the X-ray flare fluence and the prompt emission fluence. The bright X-ray flare is satisfied with the condition of r_i ≥ 0.2. When a GRB has multiple X-ray flares, the bright X-ray flares with the accumulated fluence is satisfied with the condition of r_t ≥ 0.2. We take notes on the GRBs having the bright X-ray flares in Figures 4, 5, 8, and 9.

We take the XRFs, XRRs, and C-GRBs that have the bright X-ray flares into account, and we define three ratios as

$$\begin{eqnarray}&&{\varepsilon }_{{\rm{C}} \mbox{-} \mathrm{GRB}}=\displaystyle \frac{{N}_{{\rm{C}} \mbox{-} \mathrm{GRB},{r}_{t}\geqslant 0.2}}{{N}_{{\rm{C}} \mbox{-} \mathrm{GRB}}},\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{\varepsilon }_{\mathrm{XRF}}=\displaystyle \frac{{N}_{\mathrm{XRF},{r}_{t}\geqslant 0.2}}{{N}_{\mathrm{XRF}}},\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{\varepsilon }_{\mathrm{XRR}}=\displaystyle \frac{{N}_{\mathrm{XRR},{r}_{t}\geqslant 0.2}}{{N}_{\mathrm{XRR}}}.\end{eqnarray} \tag{ 6 }$$

We first examine the bright X-ray flares from the data of Chincarini et al. (2010). We do not find any bright X-ray flares in C-GRBs. The fraction of the XRRs that have the bright X-ray flares to the total XRRs is 29.4%, and the fraction of the XRFs that have the bright X-ray flares to the total XRFs is 28.6%. When we consider only the bright X-ray flares, the mean values of r_t are 0.39 and 0.53 for XRFs and XRRs, respectively. We then examine the bright X-ray flares from the data of Yi et al. (2016). The fraction of the C-GRBs that have bright X-ray flares out of the total C-GRBs is 4.5%, the fraction of the XRRs that have bright X-ray flares out of the total XRRs is 24.6%, and the fraction of the XRFs that have bright X-ray flares out of the total XRFs is 37.5%. When we consider only the bright X-ray flares, the mean values of r_t are 0.46, 0.51, and 0.73 for XRFs, XRRs, and C-GRBs, respectively. Therefore, for the GRBs that have bright X-ray flares, the fluence of the X-ray flare is comparable to the fluence of the prompt emission. In our sample, it seems that XRFs and XRRs have more bright X-ray flares than C-GRBs.

3.2.3. Relation between X-Ray Flare Fluence and Prompt Emission Fluence

In order to examine energy release of the GRB X-ray flare that is related to GRB prompt emission, we further investigate the X-ray flare fluence and the prompt emission fluence among XRF, XRR, and C-GRB subclasses. The X-ray flare data samples are taken from Chincarini et al. (2010) and Yi et al. (2016). We obtain four panels of X-ray flare fluence versus prompt emission fluence in Figure 10. We cannot find a reliable correlation between the X-ray flare fluence and the prompt emission fluence due to the large data scattering.

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If X-ray flares in the GRB early X-ray afterglow are originally from a late time manifestation of the same emission mechanism as the prompt emission, we may consider a correlation between the X-ray flare fluence and the prompt emission fluence. However, we cannot find a significant correlation. It seems that the correlation is not straightforward if it really exists.

3.2.4. Isotropic Energy Release of X-Ray Flares

We calculate the isotropic energy of the X-ray flare in each GRB if we have GRB redshift measurements. The distributions of the isotropic energy for XRFs, XRRs, and C-GRBs are shown in Figures 11 and 12. The X-ray flare data samples are taken from Chincarini et al. (2010) and Yi et al. (2016). We perform the K-S test for the distributions. It seems that the distributions of the X-ray flare energy release have no significant differences among XRF, XRR, and C-GRB subclasses.

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We note that a direct comparison of X-ray flare energy release among XRF, XRR, and C-GRB subclasses cannot reveal the relation between X-ray flare and prompt emission for one GRB. The results from the fluence ratios of XRFs, XRRs, and C-GRBs properly present the energy release of X-ray flare compared to the energy release of prompt emission (see Figures 4 and 5).

3.3. Temporal Properties of X-Ray Flares among XRF, XRR, and C-GRB Subclasses

3.3.1. Distributions of Duration and Peak Time of X-Ray Flares among XRF, XRR, and C-GRB Subclasses

A detailed analysis of the X-ray flare temporal properties among XRF, XRR, and C-GRB subclasses is also an important issue in this paper. Here, we ignore the Lorentz factor of the X-ray flare, and we do not have the redshift correction to the X-ray flare temporal properties.

We identify the width of the X-ray flare w to be the X-ray flare duration. We present the distributions of the X-ray flare duration for XRFs, XRRs, and C-GRBs. The results from the X-ray flare data of Chincarini et al. (2010) and Yi et al. (2016) are shown in Figure 8. The K-S test results are listed in Table 2.

We also use the X-ray flare data from Chincarini et al. (2010) and Yi et al. (2016) to analyze the distributions of the X-ray flare peak time t_p for XRFs, XRRs, and C-GRBs. The results are in Figure 9. The K-S test results are listed in Table 2.

We do not find any differences in the duration distribution and the peak time distribution of the X-ray flares among XRF, XRR, and C-GRB subclasses. However, we ignore the effect of the bulk Lorentz factor on these temporal properties, and we do not perform the redshift correction to these temporal properties. We caution the direct comparison of the X-ray flare temporal properties among XRF, XRR, and C-GRB subclasses.

3.3.2. Distributions of Redshift-corrected Duration and Peak Time of X-Ray Flares among XRF, XRR, and C-GRB Subclasses

In order to directly compare the temporal properties of the X-ray flares among XRF, XRR, and C-GRB classes, we perform the redshift-corrected duration and peak time of the X-ray flares in our sample. The distributions of the duration and the peak time of the X-ray flares are shown in Figures 13 and 14.

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The distributions of the duration and the peak time do not have significant differences among XRF, XRR, and C-GRB subclasses in general. Yi et al. (2016) have larger X-ray flare duration values than Chincarini et al. (2010) because some late X-ray flares were included in Yi et al. (2016). However, we note that the issues mentioned above might have strong bias because the data samples in our statistical analysis are small. We hope that more X-ray flare data with the redshift measurements are available in the future to further investigate the distributions of the temporal properties.

3.3.3. Correlation between Duration and Peak Time of X-Ray Flare Among XRF, XRR, and C-GRB Subclasses

We can examine the correlation between the duration and the peak time of the X-ray flares for XRFs, XRRs, and C-GRBs. When we usually perform the least-square method for a linear fitting of observational data, the data errors are not included. Thus, the extrinsic scatter of the linear fitting may exist due to the large data error, and the fitting results are not reliable. In order to consider the effect from the large data error and obtain reliable fitting results, we perform the maximum likelihood method suggested by Amati et al. (2008) to obtain the linear correlation fitting between the duration and the peak time of the X-ray flares.

We use the X-ray flare data of Chincarini et al. (2010) to perform the $w-{t}_{p}$ correlations for XRFs, XRRs, and C-GRBs. We find the correlation of $\mathrm{log}w=(-{0.42}_{-0.87}^{+0.87})\,+({0.97}_{-0.37}^{+0.36})\mathrm{log}{t}_{p}$ with $\sigma ={0.19}_{-0.04}^{+0.06}$ for XRFs, the correlation of $\mathrm{log}w=(-{0.34}_{-0.23}^{+0.24})+({0.89}_{-0.09}^{+0.09})\mathrm{log}{t}_{p}$ with $\sigma ={0.21}_{-0.02}^{+0.02}$ for XRRs, and the correlation of $\mathrm{log}w=({0.05}_{-0.46}^{+0.46})\,+({0.71}_{-0.19}^{+0.19})\mathrm{log}{t}_{p}$ with $\sigma ={0.19}_{-0.04}^{+0.05}$ for C-GRBs, where σ is the extrinsic scatter. The results are shown in Figure 15.

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We also use the X-ray flare data of Yi et al. (2016) to perform the $w-{t}_{p}$ correlations for XRFs, XRRs, and C-GRBs. We find the correlation of $\mathrm{log}w=(-{1.41}_{-0.73}^{+0.73})\,+({1.59}_{-0.29}^{+0.30})\mathrm{log}{t}_{p}$ with $\sigma ={0.40}_{-0.05}^{+0.06}$ for XRFs, the correlation of $\mathrm{log}w=(-{0.36}_{-0.15}^{+0.14})+({1.12}_{-0.05}^{+0.06})\mathrm{log}{t}_{p}$ with $\sigma ={0.45}_{-0.02}^{+0.02}$ for XRRs, and the correlation of $\mathrm{log}w=(-{0.16}_{-0.18}^{+0.19})\,+({1.04}_{-0.07}^{+0.06})\mathrm{log}{t}_{p}$ with $\sigma ={0.57}_{-0.03}^{+0.04}$ for C-GRBs. The results are shown in Figure 16.

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It seems that the $w-{t}_{p}$ correlation of XRFs and that of C-GRBs are different, although the fitting errors and the extrinsic scatters are relatively large. We note that the fitting results from the data of Chincarini et al. (2010) and Yi et al. (2016) are significantly different.

3.4. XRFs, XRRs, and C-GRBs in the $\mathrm{log}({\rm{\Delta }}F/F)-\mathrm{log}(w/{t}_{p})$ Plane

The GRB X-ray flare has been explained by some physical models. Ioka et al. (2005) and Lazzati & Perna (2007) suggested both internal and external shocks to explain GRB X-ray flares. The excess flux ΔF to the underlying flux F can be identified as the X-ray flare flux. It seems that most GRB X-ray flares provided by Chincarini et al. (2010) favor the internal origin of the central engine model.

We can use the X-ray flare data of Chincarini et al. (2010) to examine the X-ray flare distribution in the log ΔF/F–log w/t_p plane for XRF, XRR, and C-GRB subclasses. The results are shown in Figure 17. The constraints of some models are also shown.⁶ It seems that there is no difference among XRF, XRR, and C-GRB subclasses on the X-ray flare distribution in the $\mathrm{log}{\rm{\Delta }}F/F$–$\mathrm{log}w/{t}_{p}$ plane.

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3.5. Spectral Properties of X-Ray Flares among XRF, XRR, and C-GRB Subclasses

Falcone et al. (2007) presented one detailed spectral analysis on GRB X-ray flares. Here, we select the results of the X-ray flare spectra fitting from the power-law, the cutoff power-law, and the Band function models. Thus, the spectral indices and the peak energy values of the X-ray flares are provided. We obtain the distributions of α_pl and α_cpl from the power-law and the cutoff power-law model fittings among XRF, XRR, and C-GRB subclasses in Figure 18. We also obtain the distributions of α, β, and E_p from the Band function fitting among XRF, XRR, and C-GRB subclasses in Figures 19 and 20. Due to the small sample from Falcone et al. (2007), it is hard to distinguish the differences of the X-ray flare spectral properties among XRF, XRR, and C-GRB subclasses.

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In order to examine the spectral correlation between the prompt emission and the X-ray flare, we show the spectral index of the X-ray flare versus the spectral index of the prompt emission in Figure 21. The spectral indices are obtained from the power-law model fitting and the cutoff power-law modeling fitting. We do not find any possible correlation between the spectral index of the X-ray flare and that of the prompt emission. We also show the X-ray flare peak energy versus the prompt emission peak energy in Figure 20. We do not find any possible correlation between the X-ray flare peak energy and the prompt emission peak energy. A large data sample is required for further investigations.

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When we mention that GRBs are associated with supernovae, we find only three GRBs that have X-ray flares in this paper. They are XRR 060729, XRR 060904, and C-GRB 111209A. Thus, we do not find any XRFs with X-ray flares to be associated with supernovae. However, a few XRFs without X-ray flares have associations with supernovae. For example, XRF 060218 is associated with SN 2006aj, XRF 081007 is associated with SN 2008hw, and XRF 100316D is associated with 2010bh (Bi et al. 2018). We expect a large sample in the future to further investigate this issue.

The X-ray flares that are contemporaneous with the early X-ray afterglow are likely due to a late time manifestation of the same emission mechanism as the prompt emission (Zhang et al. 2006). Godet et al. (2007) found that the prompt emission of XRF 050822 was followed by three X-ray flares, and the X-ray flares are shown in the deep decay phase of the X-ray light curve. Kazanas et al. (2015) comprehensively investigated the BAT-to-XRT flux ratio of the Swift-detected GRBs. From the X-ray flare sample of Chincarini et al. (2010), it was suggested that the GRB X-ray flares can be generated by the central engine, and this suggestion seems to be also valid for the X-ray flares in some short GRBs (Mu et al. 2018). Thus, we indicate a possible energy contribution from the bright X-ray flare to the total GRB emission, and these GRBs might be identified as XRFs. In this paper, we identify some observational properties of the X-ray flares among XRF, XRR, and C-GRB subclasses. We find that XRFs and XRRs have more bright X-ray flares than C-GRBs. When we calculate the fluence ratio between the X-ray flare and the prompt emission for each GRB, we identify that XRFs are different from C-GRBs. The $w-{t}_{p}$ correlations are also different between XRF and C-GRB subclasses. However, the X-ray flares observed by Swift-XRT are in the energy range of 0.2–10 keV, while the XRFs identified by Swift-BAT are in the energy range of 15 to 350 keV. Therefore, when we indicate that there is an inclination to identify the GRBs with bright X-ray flares as XRFs, we should consider that X-ray flare and XRF are detected in different energy bands. Falcone et al. (2006) examined the spectral properties of the X-ray flare in GRB 090502B from the Swift-XRT data, and one hardening signature was clearly seen during the giant flare duration. Although we perform a detailed analysis of the X-ray flare spectral properties among XRF, XRR, and C-GRB subclasses in this paper, we expect large samples of the X-ray flare spectral analysis in the future.

The intrinsic X-ray flare properties, such as fluence, width, and peak time, should be corrected by both bulk Lorentz factor and redshift. When we compare the X-ray flare properties among XRF, XRR, and C-GRB subclasses, we do not consider the effect from the bulk Lorentz factor of the X-ray flares. Thus, we note the bias related to the comparison of fluence, width, and peak time of X-ray flares among XRF, XRR, and C-GRB subclasses, even these temporal parameters are redshift-corrected. However, when we consider r_i, r_t, and $w-{t}_{p}$ correlation for each GRB, the results are not affected by the bulk Lorentz factor and the redshift.

The selection criteria of the X-ray flare can be different among different X-ray flare samples. The flares with S/Ns larger than 5 were selected in Chinacarini et al. (2007) and the flares with S/Ns larger than 3 were selected in Falcone et al. (2007), such that the low-signal X-ray flares were excluded. However, some fluctuations in GRB X-ray light curves were identified as X-ray flares in Chincarini et al. (2010). We list the different sources between Chincarini et al. (2010) and Yi et al. (2016) in Section 2. Moreover, in the sample of Chincarini et al. (2010), some blended flares are included. The blended X-ray flares of one certain GRB in Chincarini et al. (2010) were identified in a different way by Yi et al. (2016). Thus, judging the blended structure of the X-ray flare is a challenge. Compared to Chincarini et al. (2010), Yi et al. (2016) considered the X-ray flares with the redshift measurements, and small fluctuations shown in light curves were also identified as X-ray flares. Chincarini et al. (2010) selected only the early-time (occurring less than 10³ s after the trigger) X-ray flares, while Yi et al. (2016) considered both the early-time and the late-time X-ray flares. Therefore, systematic bias can be induced in our results. In this paper, we consider the temporal samples of Chincarini et al. (2010) and Yi et al. (2016), because the two samples have more X-ray flare data than Chinacarini et al. (2007).

Different fitting functions have been applied to the temporal structure of the X-ray flare. Chinacarini et al. (2007) simply used a Gaussian function to fit the X-ray flare temporal structure. The profile proposed by Norris et al. (2005) was applied in Chincarini et al. (2010). This profile consists of two combined exponentials to be flexible for the fitting of pulse shapes. Yi et al. (2016) performed the fitting with a smooth broken power-law function. Comparison of the different fitting functions is out of the scope of this paper, but different fitting functions may lead to a systematic bias on the fitting results. We list the temporal results of the X-ray flares given by Chinacarini et al. (2007), Chincarini et al. (2010), and Yi et al. (2016) in Table 3. We see some X-ray flares with different fitting results and different blended X-ray flare identification in one GRB. However, we note that the $\mathrm{log}({\rm{\Delta }}F/F)-\mathrm{log}(w/{t}_{p}$) plane shown in Chinacarini et al. (2007) and that shown in this paper (see 17) have no significant differences. This restates the indication that GRB X-ray flares have a central engine origin.

Although GRBs are usually classified as long/short GRBs, some evidence has shown that GRBs may have an intermediate class. Horváth et al. (2010) performed one analysis on the Swift-detected GRBs, in which the GRB hardness ratio was considered. de Ugarte Postigo et al. (2011) further examined some GRBs that belong to the intermediate class. Zitouni et al. (2015) suggested the existence of the intermediate group due to the asymmetric distribution of the GRB duration from the Swift-BAT sample. However, Koen & Bere (2012) performed a careful analysis by the autocorrelation function with the Swift-BAT data, and the results seem to incline the two-class (long/short) GRB classification. Tarnopolski (2019) examined the GRB data from BATSE and Fermi observations, and the results infer that the intermediate class is not physical.

It is important to note that the long/short GRB classification takes effect on the classification of XRFs, XRRs, and C-GRBs, although the investigation of the GRB hardness-duration is not a major topic in this paper. For example, Veres et al. (2010) found that intermediate GRBs have soft spectra. This indicates that intermediate GRBs are related to XRFs. From the Swift-BAT3 catalog, Bi et al. (2018) found that a few XRFs are short GRBs. In this paper, we do not find any XRFs having X-ray flares that are short GRBs, but a large data sample is required to further confirm this issue.

The XRF, XRR, and C-GRB samples of Bi et al. (2018) adopted in this paper follow the selection criteria by Sakamoto et al. (2008). Some XRRs are likely to be extensions of C-GRBs: the selection criteria may induce the overlaps of XRFs/XRRs and CRRs/C-GRBs that are shown in the hardness-duration distribution (Figure 2). The overlaps are also shown in the E_p distributions among XRF, XRR, and C-GRB subclasses (Figure 3). When we further examine the spectral properties of the X-ray flares among XRF, XRR, and C-GRB subclasses, the E_p overlaps of XRFs/XRRs and XRRs/C-GRBs are clearly shown in Figure 20. Meanwhile, we note that the E_p values of both X-ray flare and prompt emission are derived in narrow spectral ranges. This creates large uncertainty on the E_p values. However, the overlaps of XRFs/XRRs and XRRs/C-GRBs are not shown in the spectral index distributions (Figure 21). Further investigations are useful when we have more data from the spectral analysis in the future.

Different detectors and instruments have bias on the GRB classification. In the literature, Tarnopolski (2015) summarized long/short classification by several GRB detectors. Tarnopolski (2019) further noted that the Swift-BAT detection is more sensitive to soft bands. Thus, some Swift-detected GRBs might be identified as XRFs by the biased detection, and even the intermediate class is elusive. Spectral cross-calibration from different detectors to simultaneously observe the same GRB should be performed to give a reliable conclusion after enough data are accumulated (Sakamoto et al. 2011).

GRB X-ray flares may have internal origin. In the paper, we investigate the different temporal and spectral properties of the X-ray flares among XRF, XRR, and C-GRB subclasses. We find that (1) XRFs and XRRs have more bright X-ray flares than GRBs; (2) the ratio between the X-ray flare fluence and the prompt emission fluence has different distributions between XRF and C-GRB subclasses; (3) and the linear correlations between the duration and the peak time of the X-ray flares are different between XRF and C-GRB subclasses. We infer that there is an inclination to identify the GRBs with bright X-ray flares as XRFs. We caution that the classifications of XRFs, XRRs, and C-GRBs may affect our results. Our results might also be affected by the selection effects and the instrument bias. We expect more observational data to further investigate our results in the future, and some theoretical explanations are also required.

We utilize the Swift-BAT/XRT databases and the related webpages for further data analysis in this paper. J.M. is supported by the National Natural Science Foundation of China (11673062), the Hundred Talent Program of the Chinese Academy of Sciences, and the Oversea Talent Program of Yunnan Province.