Statistical classification of gamma-ray bursts based on the Amati relation

Abstract

Gamma-ray bursts (GRBs) are believed to belong to two classes and they are conventionally divided according to their durations. This classification scheme is not satisfied due to the fact that duration distributions of the two classes are heavily overlapped. We collect a new sample (153 sources) of GRBs and investigate the distribution of the logarithmic deviation of the E_p value from the Amati relation. The distribution possesses an obvious bimodality structure and it can be accounted for by the combination of two Gaussian curves. Based on this analysis, we propose to statistically classify GRBs in the well-known E_p versus E_iso plane with the logarithmic deviation of the E_p value. This classification scheme divides GRBs into two groups: Amati type bursts and non-Amati type bursts. While Amati type bursts follow the Amati relation, non-Amati type bursts do not. It shows that most Amati type bursts are long duration bursts and the majority of non-Amati type bursts are short duration bursts. In addition, it reveals that Amati type bursts are generally more energetic than non-Amati type bursts. An advantage of the new classification is that the two kinds of burst are well distinguishable and therefore their members can be identified in certainty.

methods: statistical, gamma-ray burst: general, stars: late-type, stars: massive, supernovae: general, gamma-rays: general

1 INTRODUCTION

Gamma-ray bursts (GRBs) are generally divided into two classes: short and long-duration classes. The duration concerned is always T₉₀ which is the time interval during which the burst integrated counts increases from 5 to 95 per cent of the total counts. This classification scheme is based on the bimodality structure of the T₉₀ distribution of the objects, where all the bursts are likely to be separated at about 2 s (see, e.g. Kouveliotou et al. 1993). When one replaces T₉₀ with T₅₀ (during which the burst integrated counts increases from 25 to 75 per cent of the total counts), the bimodality structure also exists (see, e.g., Zhao et al. 2004). Generally, short duration bursts are harder than long duration bursts. In the hardness ratio versus duration plane, short and long bursts were observed to distribute in distinct domains(Kouveliotou et al. 1993; Fishman & Meegan 1995). It was shown that the hardness ratio is correlated to the duration for the whole GRB sample, but for each of the two classes alone the two quantities are not correlated at all (see Qin et al. 2000). This statistical result strongly suggests that, while any attempts to consider all GRBs as a single class might be questionable, the existence of the two classes of GRBs is convincing.

It is expected that different classes might have different progenitors. Therefore, the classification of GRBs has always been an essential task. Based on many years of investigation, most researchers come to the consent that many shot bursts are produced in the event of binary neutron star or neutron star–black hole mergers, while many long bursts are caused by the massive star collapsars (e.g. Paczynski 1986, 1998; Eichler et al. 1989; Woosley 1993; MacFadyen & Woosley 1999).

Thanks to the successful launch of the Swift satellite (Gehrels et al. 2004), many advances in the research of GRBs have been achieved. The most important achievement might be the fact that a large body of evidence favours the two progenitor proposal for GRBs. It has been continued to be reported that short bursts were found in regions with lower star formation rates, and no evidence of supernovae (SNe) to accompany them was detected (Barthelmy et al. 2005; Berger et al. 2005; Hjorth et al. 2005). Meanwhile, long bursts were found to be originated from star-forming regions in galaxies (Fruchter et al. 2006), and in some of these events, SNe were detected to accompany the bursts (Hjorth et al. 2003; Stanek et al. 2003).

Short burst class and long burst class are conventionally divided by T₉₀: those whose T₉₀ being larger than 2 s are classified as long bursts while the rest are classified as short bursts. McBreen et al. (1994) showed that, the bimodal distribution of GRBs can arise from two overlapped log normal distributions. This indicates that each of the two GRB populations might possess a single log normal duration distribution, and due to the overlap, there would be a sufficient number of bursts that are misclassified by simply applying the criterion of T₉₀ = 2 s.

The scenario that two overlapped log normal distributions can account for the duration distribution of the whole GRB sample was challenged later by other investigations. Horvath (1998) found that, instead of the two-Gaussian fit, the three-Gaussian fit is more likely to be able to account for the duration distribution of all BATSE bursts. Although if there exists a third class of GRBs is still a subject of debate, the evidence that the two-Gaussian fit alone cannot account for the duration distribution of all GRBs is obvious. In fact, T₉₀ is not an intrinsic property of a burst or a population of bursts. For a more robust investigation, one should rely on the cosmological rest-frame duration (see the definition of T_{90, r} below), where the effect of cosmological redshift has been corrected. Unfortunately, the redshift information is not available for most BATSE bursts, and hence in the corresponding analysis this effect cannot be taken into account. However, in our analysis below, redshifts of the bursts are known, and therefore we will use T_{90, r} instead of T₉₀.

In fact, voices questioning the duration classification scheme have become stronger in recent years. Gehrels et al. (2006) reported that the duration of GRB 060614 is long but its behaviour is similar to short duration bursts (for example, very deep optical observations of this source exclude an accompanying SN). Based on this fact, they even asked if there exists a new GRB classification scheme that straddles both long and short duration bursts. Similar observational results were reported by different groups in nearly the same time (see, e.g., Della Valle et al. 2006; Fynbo et al. 2006; Gal-Yam et al. 2006). For some short duration bursts, soft extended emission and late X-ray flares were observed, indicating that these sources might not be really short (see, e.g. Barthelmy et al. 2005; Norris & Bonnell 2006).

In the recent few years, some attempts of revealing new statistical properties associated with the classification of bursts as well as introducing new classification schemes have continued to be made. Zhang et al. (2007) proposed that GRBs should be classified into Type I (typically short and associated with old populations) and Type II (typically long and associated with young populations) groups. This type of classification is charming, but the goal of dividing individual bursts into the distinct groups is hard to realize. Lu et al. (2010) introduced a new parameter to classify GRBs. In their efforts, they regarded those long GRBs with ‘extended emission’ being short ones if the bursts are really ‘short’ without the ‘extended emission’. In this way, they found a clear bimodal distribution of the parameter. Goldstein, Preece & Briggs (2010) found the distribution of the ratio of Epeak/fluence bearing a bimodality structure in the complete BATSE 5B spectral catalogue, which corresponds directly to the conventional short and long burst classes. However, the overlap of the distributions of the two groups of bursts is seen to be as heavy as that shown in the duration distributions. Qin et al. (2010) proposed to modify the conventional duration classification scheme by separating the conventional short and long duration bursts in different softness (or hardness) groups. While this method seems reasonable, the improvement would not be applicable if the size of samples is not large enough.

Just as was mentioned above, one can verify that, two distinct smooth curves (e.g. two Gaussian curves) accounting for the duration distributions of the short and long burst classes are sufficiently overlapped. This makes the duration classification scheme an unsatisfied one. Unfortunately, the overlap of other parameters (e.g. the hardness ratio or the peak energy) is much heavier than that of the duration. Although it is much beyond being satisfactory, the duration classification scheme is still the most popular one up to day. Thus, It is desirable that a better alternative of the classification can be established in the near future.

Based on a sample of BeppoSAX GRBs with known redshift, Amati et al. (2002) discovered a tight relation between the cosmological rest-frame spectrum peak energy and the isotropic equivalent radiated energy, which is now known as the Amati relation. This soon triggered a series of relevant researches (e.g. Amati 2006, 2010; Amati et al. 2007, 2008; Ghirlanda et al. 2008, 2009; Piranomonte et al. 2008; Amati, Frontera & Guidorzi 2009; Gruber et al. 2011; Zhang et al. 2012).

There have been debates about the existence of the Amati relation as an intrinsic property of GRBs. Some authors pointed out that the relation might arise from observational selection effects (e.g. Band & Preece 2005; Nakar & Piran 2005; Butler et al. 2007; Butler, Kocevski & Bloom 2009). Other authors argued that, to form the relation, selection effects could only play a marginal role (see, e.g. Ghirlanda et al. 2005, 2008; Bosnjak et al. 2008; Nava et al. 2008; Amati et al. 2009; Krimm et al. 2009). Recently, Butler, Bloom & Poznanski (2010) derived a GRB world model from their data, and based on the model they reproduced the observables from both Swift and pre-Swift satellites. In their analysis, a real, intrinsic correlation between the two quantities is confirmed, but they pointed out that the correlation is not a narrow log–log relation and its observed appearance is strongly detector dependent. Our data (see the analysis below) show that the Amati relation is real, although it might be, at least in part, introduced by observational bias.

In a subsequent analysis with a much larger sample, Amati (2006) reported that subenergetic GRBs (such as GRB 980425) and short GRBs are found to be inconsistent with the correlation between the cosmological rest-frame spectrum peak energy and the isotropic equivalent radiated energy, indicating that this phenomenon might be a powerful tool for discriminating different classes of GRBs and understanding their nature and differences. Recently, Zhang et al. (2012) selected some short bursts and disregarded those subenergetic GRBs concerned by Amati (2006). They reported that, for these short bursts alone, there does exist a tight relation between the two quantities, which is quite different from the conventional Amati relation.

As the Amati relation is real and the number of GRBs with known redshift has become larger and larger in recent years, it might be possible now to use the relation to distinguish members of distinct GRB classes statistically. This motivates our analysis below.

In Section 2, the collection of GRBs with known redshift is presented and a statistical analysis is performed to check if there exits an appropriate quantity to separate the bursts into different groups. Based on this analysis, we present a new classification scheme in Section 3. In Section 4, we compare the new classification scheme and the conventional scheme. A summary and discussion are presented in Section 5.

Throughout this paper, we adopt the following cosmological parameters: H₀ = 70 km s⁻¹ Mpc, Ω_M = 0.3 and Ω_Λ = 0.7.

2 DATA AND ANALYSIS

We only consider GRBs with measured redshift, up to 2012 May, including sources observed by various instruments. In addition, some other quantities are required. In fact, included in our sample are merely those GRBs with the following quantities available: redshift z, spectrum peak energy E_p, isotropic equivalent radiated energy E_iso and duration T₉₀. We get 153 bursts in total. Sources of our sample are listed in Table 1.

Let E_{p, r} ≡ (1 + z)E_p be the cosmological rest-frame νf_ν spectrum peak energy (in brief, the rest-frame peak energy), in units of kcV, and E_iso be the isotropic equivalent radiated energy (in brief, the isotropic energy), in units of 10⁵² erg. In the following, when E_{p, r} and E_iso are used in any analysis, they stand for their observational values (see, e.g. Table 1). The Amati relation can be expressed as follows (see Amati 2006):

\begin{equation} E_{{\rm p},{\rm r},{\rm pre}}=K\times E^{m}_{\rm iso}, \end{equation}

(1)

where subscript pre means ‘predicted’, K and m are constants obtained by fits. In order to avoid notation confusion in the analysis below, we use E_{p, r, pre}, to describe the predicted value of the rest-frame peak energy determined by the Amati relation when E_iso is provided.

Table 1.

Parameters of prompt emission of GRBs with measured redshifts.

GRB	z	T90	Eiso 1052 erg	Ep, r keV	Instruments	Refs	Note
970228	0.695	80	1.6 ± 0.12	195 ± 64	BeppoSAX	15	A
970508	0.835	20	0.612 ± 0.13	145 ± 43	BeppoSAX	15	A
970828	0.958	146.59	29 ± 3	586 ± 117	CGROSE	15	A
971214	3.42	35	21 ± 3	685 ± 133	BeppoSAX	15	A
980326	1	9	0.482 ± 0.09	71 ± 36	BeppoSAX	15	A
980613	1.096	20	0.59 ± 0.09	194 ± 89	BeppoSAX	15	A
980703	0.966	102.37	7.2 ± 0.7	503 ± 64	CGROSE	15	A
990123	1.6	100	229 ± 37	1724 ± 446	BeppoSAX	15	A
990506	1.3	220.38	94 ± 9	677 ± 156	CGROSE	15	A
990510	1.619	75	17 ± 3	423 ± 42	BeppoSAX	15	A
990705	0.843	42	18 ± 3	459 ± 139	BeppoSAX	15	A
990712	0.434	20	0.67 ± 0.13	93 ± 15	BeppoSAX	15	A
991208	0.706	60	22.3 ± 1.8	313 ± 31	Konus	15	A
991216	1.02	24.9	67 ± 7	648 ± 134	GRO/KW	15	A
000131	4.5	110.1	172 ± 30	987 ± 416	GRO/KW	15	A
000210	0.846	20	14.9 ± 1.6	753 ± 26	Konus	15	A
000418	1.12	30	9.1 ± 1.7	284 ± 21	Konus	15	A
000911	1.06	500	67 ± 14	1856 ± 371	Konus	15	A
000926	2.07	25	27.1 ± 5.9	310 ± 20	Konus	15	A
010222	1.48	130	81 ± 9	766 ± 30	Konus	15	A
010921	0.45	24.6	0.95 ± 0.1	129 ± 26	HETE..C2	15	A
011121	0.36	75	7.8 ± 2.1	1060 ± 265	BeppoSAX	9	A
020124	3.198	78.6	27 ± 3	448 ± 148	HETE..C2	15	A
020127	1.9	17.6	3.5 ± 0.1	290 ± 100	HETE..C2	19	A
020405	0.695	60	10 ± 0.9	354 ± 10	BeppoSAX	15	A
020813	1.25	90	66 ± 16	590 ± 151	HETE..C2	15	A
020819B	0.41	46.9	0.68 ± 0.017	70 ± 21	HETE..C2	15	A
020903	0.25	10	0.0024 ± 0.0006	3.37 ± 1.79	HETE..C2	15	A
021004	2.3	77.1	3.3 ± 0.4	266 ± 117	HETE..C2	15	A
021211	1.01	2.41	1.12 ± 0.3	127 ± 52	HETE..C2	15	A
030226	1.98	76.8	12.1 ± 1.3	289 ± 66	HETE..C2	15	A
030323	3.37	32.6	2.8 ± 0.9	270 ± 113	HETE..C2	10	A
030328	1.52	140	47 ± 3	328 ± 55	HETE..C2	15	A
030329	0.17	23	1.5 ± 0.3	100 ± 23	HETE..C2	15	A
030429	2.65	10.3	2.16 ± 0.26	128 ± 26	HETE..C2	15	A
030528	0.78	49.2	2.5 ± 0.3	57 ± 9	HETE..C2	10	A
040912	1.563	143	1.3 ± 0.3	44 ± 33	HETE..C2	11	A
040924	0.859	5	0.95 ± 0.09	102 ± 35	HETE..C2	15	A
041006	0.716	25	3 ± 0.9	98 ± 20	HETE..C2	15	A
050126A	1.29	24.8	0.736 ± 0.16	263 ± 110	Swift	16	A
050223	0.5915	22.5	0.121 ± 0.0177	110 ± 54	Swift	16	A
050318	1.44	32	2.2 ± 0.16	115 ± 25	Swift	15	A
050401	2.9	33.3	35 ± 7	467 ± 110	Swift	15	A
050416A	0.65	2.5	0.1 ± 0.01	25.1 ± 4.2	Swift	15	A
050505	4.27	58.9	17.6 ± 2.61	661 ± 245	Swift	16	A
050509B	0.225	0.04	0.00024 + 0.00044− 0.0001	102 ± 10	Swift	18	N
050525A	0.606	8.8	2.5 ± 0.43	127 ± 10	Swift	15	A
050603	2.821	12.4	60 ± 4	1333 ± 107	Konus	15	A
050709	0.16	0.07	0.0033 ± 0.0001	97.4 ± 11.6	HETE-2	1	N
050803	0.422	87.9	0.186 ± 0.0399	138 ± 48	Swift	16	A
050813	1.8	0.6	0.015 + 0.0025− 0.008	150 ± 15	Swift	18	N
050814	5.3	150.9	11.2 ± 2.43	339 ± 47	Swift	16	A
050820	2.612	26	97.4 ± 7.8	1325 ± 277	Konus	15	A
050904	6.29	174.2	124 ± 13	3178 ± 1094	Swift	15	A
050908	3.344	19.4	1.97 ± 0.321	195 ± 36	Swift	16	A
050922C	2.198	4.6	5.3 ± 1.7	415 ± 111	HETE..C2	15	A
051022	0.8	200	54 ± 5	754 ± 258	HETE..C2	15	A
051109A	2.346	37.2	6.5 ± 0.7	539 ± 200	Konus	15	A
051221A	0.547	1.4	0.3 ± 0.04	621 ± 144	Swift	18	N
060115	3.53	139.6	6.3 ± 0.9	285 ± 34	Swift	15	A
060124	2.297	750	41 ± 6	784 ± 285	Konus	15	A
060206	4.048	7.6	4.3 ± 0.9	394 ± 46	Swift	15	A
060210	3.91	255	41.53 ± 5.7	575 ± 186	Swift	16	A
060218	0.0331	2100	0.0053 ± 0.0003	4.9 ± 0.3	Swift	15	A
060223A	4.41	11.3	4.29 ± 0.664	339 ± 63	Swift	16	A
060418	1.489	103.1	13 ± 3	572 ± 143	Konus	15	A
060502B	0.287	0.131	0.003 + 0.005− 0.002	193 ± 19	Swift	18	N
060510B	4.9	275.2	36.7 ± 2.87	575 ± 227	Swift	16	A
060522	5.11	71.1	7.77 ± 1.52	427 ± 79	Swift	16	A
060526	3.21	298.2	2.6 ± 0.3	105 ± 21	Swift	15	A
060605	3.78	79.1	2.83 ± 0.45	490 ± 251	Swift	16	A
060607A	3.082	102.2	10.9 ± 1.55	575 ± 200	Swift	16	A
060614	0.125	108.7	0.21 ± 0.09	55 ± 45	Konus	15	A
060707	3.43	66.2	5.4 ± 1	279 ± 28	Swift	15	A
060714	2.711	115	13.4 ± 0.912	234 ± 109	Swift	16	A
060814	0.84	145.3	7 ± 0.7	473 ± 155	Konus	15	A
060904B	0.703	171.5	0.364 ± 0.0743	135 ± 41	Swift	16	A
060906	3.686	43.5	14.9 ± 1.56	209 ± 43	Swift	16	A
060908	2.43	19.3	9.8 ± 0.9	514 ± 102	Swift	15	A
060927	5.6	22.5	13.8 ± 2	475 ± 47	Swift	15	A
061006	0.4377	129.9	0.2 ± 0.03	955 ± 267	Swift	1	N
061007	1.261	75.3	86 ± 9	890 ± 124	Konus	15	A
061121	1.314	81.3	22.5 ± 2.6	1289 ± 153	Konus	15	A
061126	1.1588	70.8	30 ± 3	1337 ± 410	Swift	17	A
061201	0.111	0.76	3 + 4− 2	969 ± 508	Swift	18	N
061217	0.827	0.21	0.03 + 0.04− 0.02	216 ± 22	Swift	18	N
061222B	3.355	40	10.3 ± 1.6	200 ± 28	Swift	16	A
070110	2.352	88.4	5.5 ± 1.5	370 ± 170	Swift	8	A
070125	1.547	70	80.2 ± 8	934 ± 148	Konus	15	A
070429B	0.904	0.47	0.07 + 0.11− 0.02	813 ± 81	Swift	18	N
070508	0.82	21.2	8 + 2− 1	378.56 + 138.32− 74.62	Swift	14	A
070714B	0.92	2	1.1 ± 0.1	2150 ± 1113	Swift	1	N
070724A	0.457	0.4	0.00245 + 0.00175− 0.0055	119 ± 12	Swift	18	N
070809	0.2187	1.3	0.00131 + 0.00103− 0.00285	91 ± 9	Swift	18	N
071003	1.604	150	36 ± 4	2077 ± 286	Swift	19	A
071010B	0.947	35.7	1.7 ± 0.9	101 ± 20	Konus	15	A
071020	2.145	4.2	9.5 ± 4.3	1013 ± 160	Konus	15	A
071117	1.331	6.6	4.1 ± 0.9	647 ± 226	Konus	12	A
071227	0.383	1.8	0.1 ± 0.02	1384 ± 277	Swift	3	N
080319B	0.937	50	114 ± 9	1261 ± 65	Swift	15	A
080319C	1.95	34	14.1 ± 2.8	906 ± 272	Swift	15	A
080411	1.03	56	15.6 ± 0.9	524 ± 70	Konus	13	A
080413A	2.433	46	8.1 ± 2	584 ± 180	Swift	4	A
080413B	1.1	8	2.4 ± 0.3	150 ± 30	Swift	5	A
080514B	1.8	7	17 ± 4	627 ± 65	Konus	19	A
080603B	2.69	60	11 ± 1	376 ± 100	Konus	19	A
080605	1.6398	20	24 ± 2	650 ± 55	Konus	19	A
080607	3.036	79	188 ± 10	1691 ± 226	Konus	19	A
080721	2.591	16.2	126 ± 22	1741 ± 227	Swift	19	A
080804	2.2	34	11.5 ± 2	810 ± 45	Swift	8	A
080810	3.35	106	45 ± 5	1470 ± 180	Swift	19	A
080913	6.7	8	8.6 ± 2.5	710 ± 350	Konus	19	A
080916A	0.689	60	2.27 ± 0.76	184.101 ± 15.201	Swift	6	A
080916B	4.35	32	563	424 ± 24	Swift	7	A
080916C	4.35	62.977	387 ± 46	2268.4 ± 128.4	Fermi	6	A
081007	0.5295	10	0.16 ± 0.03	61 ± 15	Swift	19	A
081028	3.038	260	17 ± 2	234 ± 93	Swift	19	A
081118	2.58	67	4.3 ± 0.9	147 ± 14	Swift	19	A
081121	2.512	14	26 ± 5	871 ± 123	Swift	19	A
081203A	2.1	294	35 ± 3	1541 ± 757	Swift	8	A
081222	2.77	24	30 ± 3	505 ± 34	Swift	19	A
090102	1.547	27	22 ± 4	1149 ± 166	Konus	19	A
090323	3.57	135.17	410 ± 50	1901 ± 343	Konus	19	A
090328	0.736	61.697	13 ± 3	1028 ± 312	Konus	19	A
090418	1.608	56	16 ± 4	1567 ± 384	Swift	19	A
090423	8.1	10.3	11 ± 3	491 ± 200	Swift	19	A
090424	0.544	48	4.6 ± 0.9	273 ± 50	Swift	19	A
090425A	0.544	75.393	4.48	177 ± 3	Fermi	7	A
090426	2.609	1.2	0.42 + 0.38− 1.14	177 ± 82	Swift	18	A
090510	0.903	0.3	3.75 ± 0.25	8370 ± 760	Swift	6	N
090516	4.109	210	88.5 ± 19.2	948.2304 + 502.73− 217.1325	Swift	6	A
090618	0.54	113.2	25.4 ± 0.6	239.47 +− 16.94	Swift	6	A
090812	2.452	66.7	40.3 ± 4	2023 ± 663	Swift	8	A
090902B	1.822	19.328	305 ± 2	2187.05 ± 31.042	Fermi	6	A
090926A	2.1062	13.76	186 ± 5	975.3468 ± 12.4248	Fermi	6	A
090926B	1.24	109.7	3.55 ± 0.12	203.84 ± 4.48	Swift	6	A
091003A	0.8969	20.224	10.6 ± 0.1	922.2728 ± 44.76684	Fermi	6	A
091020	1.71	34.6	12.2 ± 2.4	129.809 ± 19.241	Swift	6	A
091024	1.092	109.8	28 ± 3	794 ± 231	Swift	8	A
091029	2.752	39.2	7.4 ± 0.74	230 ± 66	Swift	8	A
091127	0.49	7.1	1.63 ± 0.02	53.64 ± 2.98	Swift	6	A
091208B	1.063	14.9	2.01 ± 0.07	297.4846 + 37.13− 28.6757	Swift	6	A
100117A	0.92	0.3	0.09 ± 0.01	551 + 142.00− 96	Swift	6	N
100414A	1.368	26.497	76.6 ± 1.2	1486.157 + 29.60− 28.6528	Fermi	6	A
100621A	0.542	63.6	4.37 ± 0.5	146 ± 23.1	Swift	8	A
100728B	2.106	12.1	2.66 ± 0.11	406.886 ± 46.59	Swift	6	A
100814A	1.44	174.5	14.8 ± 0.5	259.616 + 33.92− 30.744	Swift	6	A
100816A	0.8049	2.9	0.73 ± 0.02	246.7298 ± 8.48303	Swift	6	A
100906A	1.727	114.4	28.9 ± 0.3	289.062 + 47.72− 55.0854	Swift	6	A
101219A	0.718	0.6	0.49 ± 0.07	842 + 177.00− 136	Swift	2	N
101219B	0.55	34	0.59 ± 0.04	108.5 ± 12.4	Swift	6	A
110205A	2.22	257	56 ± 6	715 ± 239	Swift	8	A
110213A	1.46	48	6.9 ± 0.2	242.064 + 20.91− 16.974	Swift	6	A

Notes. The ‘Note’ column: ‘A’ represents Amati type bursts, and ‘N’ represents non-Amati type bursts. References: (1) Ghirlanda et al. (2008) and references therein; (2) Golenetskii et al. (2010); (3) Golenetskii et al. (2007b); (4) Ohno et al. (2008); (5) Barthelmy et al. (2008); (6) Zhang et al. (2012) and references therein; (7) Ghirlanda, Nava & Ghisellini (2010) and references therein; (8) Ghirlanda et al. (2012) and references therein; (9) Ulanov et al. (2005); (10) Sakamoto et al. (2005) and references therein; (11) Stratta et al. (2007); (12) Golenetskii et al. (2007a); (13) Golenetskii et al. (2008); (14) Nava et al. (2008); (15) Amati et al. (2008) and references therein; (16) Cabrera et al. (2007) and references therein; (17) Perley et al. (2008); (18) Butler et al. (2007) and references therein; (19) Amati et al. (2009) and references therein.

To check if a burst obey or betray the Amati relation, we follow Amati (2006) to consider the logarithmic deviation of the E_p value from the Amati relation that serves as a datum line in the E_p versus E_iso plane. The Amati relation adopted as the datum line in this paper is that obtained by Amati et al. (2008): E_{p, r, pre} = 94 × E^0.57_iso. Thus, the logarithmic deviation of the E_p value considered in this paper is log E_{p, r} − log 94 − 0.57 log E_iso, where K = 94 is different from that adopted in fig. 4 of Amati (2006). (Note that, the Amati relation is improved in Amati et al. 2008 with a much larger sample compared with that in Amati 2006.)

Displayed in Fig. 1 is the distribution of the logarithmic deviation of the E_p value of our sample. Unlike that shown in fig. 4 of Amati (2006, where only long GRBs and X-ray flashes are considered), the distribution in our sample shows an obvious bimodality structure. It reveals that there are two Gaussian distributions that form the bimodality structure, and the overlap of the two distributions is not heavy (see Fig. 7 for a comparison with the T₉₀ distribution of the same sample).

Figure 1.

Distribution of the logarithmic deviation of the E_p value of our sample (153 sources), where the deviation is calculated by log E_{p, r} − log 94 − 0.57log E_iso. The thick dash line represents a two-Gaussian fit and the two thin solid lines (heavily overlapped by the thick dash line) stand for the two Gaussian curves, respectively. There is a dip at about 0.7. The number of the sources located at the left-hand side of the dip is 137, while that of the rest is 16.

We perform a two-Gaussian fit to the distribution of the logarithmic deviation of the E_p value (i.e. the distribution of log E_{p, r} − log 94 − 0.57log E_iso), and obtain σ = 0.239 and a central value of −0.044 for the first Gaussian curve, and σ = 0.300 and a central value of 1.327 for the second Gaussian curve, with the reduced χ² of the fit being χ²_dof = 16.649.

We find that, 100 per cent (16/16) of the bursts accounted for by the second curve are located beyond the 3σ range of the first curve, and 91.2 per cent (125/137) of the bursts accounted for by the first curve are located beyond the 3σ range of the second curve, which indicate that the overlap of the two Gaussian distributions is very light.

3 NEW CLASSIFICATION

The bimodality structure shown in Fig. 1 favours the assumption that there are two distinct classes of GRBs. If we believe that each of the two Gaussian distributions obtained above corresponds to one of the two classes, then the figure indicates that while members of one class are clustering around the Amati relation (represented by the zero value of the deviation; see Fig. 1), sources of the other class are located far away from the relation. This encourages us to use a logarithmic deviation of the E_p value to set apart the classes of GRBs.

According to Fig. 1 and the fitting curve, we assign the logarithmic deviation of the E_p value located at the dip between the two peaks of the fitting curve as the criterion to classify members of the two groups. The dip is at 0.72. It corresponds to the following curve in the E_p versus E_iso plane:

\begin{equation} E_{{\rm p},{\rm r},{\rm pre}}=10^{0.72} \times 94 \times E^{0.57}_{\rm iso}. \end{equation}

(2)

Sources located under this curve in the E_p versus E_iso plane are classified as Amati type bursts, and that located above this curve are classified as non-Amati type bursts. Or, in terms of the logarithmic deviation of the E_p value, GRBs with log E_{p, r} − log 94 − 0.57log E_iso < 0.72 are classified as Amati type bursts, otherwise they are classified as non-Amati type bursts. Shown in Fig. 2 is the result of the classification.

Figure 2.

Classification of the 153 GRBs in the E_p versus E_iso plane. The dash line represents the Amati relation and the solid line represents the criterion curve of the new classification, equation (2). The filled circles stand for Amati type bursts (137 sources) and the open circles plus pluses represent non-Amati type bursts (16 sources).

To check how different duration (short or long) bursts are influenced by this classification, let us follow the conventional method to classify the bursts by duration. Since the redshifts of bursts are available, we modify the conventional duration classification criterion by replacing T₉₀ = 2 s with T_{90, r} = 1 s, where T_{90, r} ≡ T₉₀/(1 + z) is the cosmological rest-frame duration (shortly, rest-frame duration). We divide GRBs into two groups by assigning bursts with T_{90, r} > 1 for one group (long bursts) and bursts with T_{90, r} ≤ 1 for the other group (short bursts). In this way, we get 13 short bursts in total. The reason for taking T_{90, r} = 1 s as the duration criterion is that, it corresponds to T₉₀ = 2 s when z = 1. In our sample, when bursts are divided by T₉₀ = 2 s we get 16 short ones. Therefore, to get a sample of short bursts, the criterion of T_{90, r} = 1 s is more conservative than the conventional one, that of T₉₀ = 2 s.

Distributions of these two groups of bursts (short and long bursts) are displayed in Fig. 3. We find that short bursts are mainly (12/13, 92.3 per cent) located in the non-Amati type burst region while long bursts are preferentially (136/140, 97.1 per cent) distributed in the Amati type burst domain.

Figure 3.

Distributions of the short (open circles plus pluses) and long (filled circles) bursts of the 153 GRBs in the E_p versus E_iso plane. The dash line represents the Amati relation and the solid line represents the criterion curve of the new classification, equation (2). Only one short burst (GRB 090426) is located below the criterion curve and four long bursts (GRB 061006,GRB 070714B, GRB 071227 and GRB 070809) are located above the curve.

Shown in Figs 4–6 are the distributions of E_iso, E_{p, r} and T_{90, r}, respectively, for the two newly classified groups of bursts. We find from these figures that Amati type bursts are generally longer and more energetic. Unlike in the case of the conventional duration classification scheme, the two newly classified groups of bursts do not show significant difference in the distribution of E_{p, r}. One can also observe this in Fig. 2. It has been known for a long time that sources of the conventional short burst class are generally harder than those of the conventional long burst class. At least with the current sample (153 sources), this difference is relatively mild if sources are divided with the new classification scheme.

Figure 4.

Distributions of E_iso for the two newly classified groups of bursts. The thick solid line stands for the group of non-Amati type bursts and the thin solid line stands for the group of Amati type bursts.

Figure 5.

Distributions of E_{p, r} for the two newly classified groups of bursts. The meaning of lines is the same as that in Fig. 4.

Figure 6.

Distributions of T_{90, r} for the two newly classified groups of bursts. The meaning of lines is the same as that in Fig. 4.

4 COMPARISON

Let us compare the new classification scheme, the scheme based on the logarithmic deviation of the E_p value (shortly, the peak energy deviation classification scheme), with the conventional duration classification scheme.

Shown in Fig. 7 is the distribution of the rest-frame duration of our sample. The well-known bimodality structure is observed. As is already known, it is unlikely that the bimodality structure distribution arises from the combination of two Gaussian distributions.

Figure 7.

Distribution of T_{90, r}, of our sample. The meaning of lines is the same as that in Fig. 1.

As done in the case of the peak energy deviation classification scheme, we fit the duration distribution of the sample with the combination of two Gaussian functions and get σ = 0.375 and a central value of −0.833 for the first Gaussian curve, and σ = 0.419 and a central value of 1.017 for the second Gaussian curve, with the reduced χ² of the fit being χ²_dof = 29.826. We find that the resulting reduced χ² value (29.826) is much larger than that (16.649) of the new classification scheme. As a key parameter of classification to separate two groups of sources, one always expects its distribution to possess a bimodality structure that arises from the combination of two perfect Gaussian curves. In this aspect, the logarithmic deviation of the E_p value acts much better than the duration does.

In addition, we perform a linear fit to the E_{p, r} and E_iso data of the two kinds of duration bursts, those with T_{90, r} > 1 s and T_{90, r} ≤ 1 s, in our sample. This yields

\begin{equation} {\rm log}\,E_{{\rm p},{\rm r}}=(2.12\pm 0.15) + (0.46\pm 0.11) \, {\rm log}\,E_{\rm iso} \end{equation}

(3)

for bursts with T_{90, r} > 1 s (N = 140, r = 0.754, P < 10⁻²⁷) and

\begin{equation} {\rm log}\,E_{{\rm p},{\rm r}}=(2.95\pm 0.69) + (0.32\pm 0.36){\rm log}\,E_{\rm iso} \end{equation}

(4)

for bursts with T_{90, r} ≤ 1 s (N = 13, r = 0.846, P = 0.0003).

As a comparison, the same analysis is performed in the case of the new classification scheme, which produces

\begin{equation} {\rm log}\,E_{{\rm p},{\rm r}}=(2.06\pm 0.16) + (0.51\pm 0.12){\rm log}\,E_{\rm iso} \end{equation}

(5)

for Amati type bursts (N = 137, r = 0.831, P < 10⁻³⁶) and

\begin{equation} {\rm log}\,E_{{\rm p},{\rm r}}=(3.16\pm 0.65) + (0.39\pm 0.33){\rm log}\,E_{\rm iso} \end{equation}

(6)

for non-Amati type bursts (N = 16, r = 0.912, P < 10⁻⁷).

The results are displayed in Figs 8 and 9, respectively. The results suggest that, if we believe that bursts of the same class should follow the same relationship between E_{p, r} and E_iso, as hinted by the discovery of Amati et al. (2002), then the duration of bursts cannot appropriately separate the two classes. In this aspect and in terms of statistics, the logarithmic deviation of the E_p value is much more preferential than the duration.

Figure 8.

Results of correlation analysis between E_{p, r} and E_iso for short and long bursts of our sample, divided by T_{90, r} = 1 s. The upper solid line represents the linear fit to the short bursts and the lower solid line represents the linear fit to the long bursts. See Fig. 3 for the meaning of the dash line and other symbols.

Figure 9.

Results of correlation analysis between E_{p, r} and E_iso for the two groups of bursts of our sample, divided by the newly classification scheme. The upper solid line represents the linear fit to the non-Amati type bursts and the lower solid line represents the linear fit to the Amati type bursts. See Fig. 2 for the meaning of the dash line and other symbols.

5 SUMMARY AND DISCUSSION

We collected GRBs with measured redshift, spectrum peak energy, isotropic equivalent radiated energy and duration from the literature up to 2012 May, including sources observed by various instruments and get 153 GRBs in total. With this sample, we investigate the distribution of the logarithmic deviation of the E_p value from the Amati relation. The distribution exhibits an obvious bimodality structure. A fit to the data shows that the distribution of the deviation can be accounted for by the combination of two Gaussian curves, and the two curves are well separated. Based on this, we propose to statistically classify GRBs in the E_p versus E_iso plane with the logarithmic deviation of the E_p value. According to this classification scheme, bursts are divided into two groups: Amati type bursts and non-Amati type bursts. A statistical interpretation of this classification is that, Amati type bursts follow the Amati relation, but non-Amati type bursts do not. Our analysis reveals that Amati type bursts are generally longer and more energetic and non-Amati type bursts are generally shorter and less energetic. After comparing the new classification scheme with the conventional scheme we find that, in terms of statistics, the logarithmic deviation of the E_p value acts much better in the classification routine than the duration does. Since the overlap of the distributions of the logarithmic deviation of the E_p value is light, the two groups of bursts so divided are well distinguishable and therefore their members can be identified in certainty.

From Fig. 7, one might observe that, taking T_{90, r} = 1 s as the duration criterion might not be so appropriate since the dip between the two peaks of the bimodality structure is located at the position of a much smaller duration value. How the short and long bursts act if we divide them at this position?

According to Fig. 7, this position is at T_{90, r} = 0.63 s. Let us divide bursts into two groups by taking T_{90, r} = 0.63 s as the duration criterion. In this way, we get 11 short bursts and 142 long bursts. The distributions of these groups of bursts in the E_p versus E_iso plane are shown in Fig. 10. We find that 90.9 per cent (10/11) of this kind of short burst are classified as non-Amati type bursts and 95.8 per cent (136/142) of this kind of long burst are classified as Amati type bursts. We repeat the above linear analysis for these two groups and get

\begin{equation} {\rm log}\,E_{{\rm p},{\rm r}}=(2.13\pm 0.15) + (0.46\pm 0.11){\rm log}\,E_{\rm iso} \end{equation}

(7)

for bursts with T_{90, r} > 0.45 s (N = 142, r = 0.731, P < 10⁻²⁵) and

\begin{equation} {\rm log}\,E_{{\rm p},{\rm r}}=(2.98\pm 0.85) + (0.33\pm 0.41){\rm log}\,E_{\rm iso} \end{equation}

(8)

for bursts with T_{90, r} ≤ 0.45 s (N = 11, r = 0.809, P = 0.003). The correlation analysis results are shown in Fig. 11. The results suggest that the duration criterion changing from T_{90, r} = 1 to T_{90, r} = 0.63 s does not give rise to a significantly different result.

Figure 10.

Distributions of the short and long bursts of the 153 GRBs in the E_p versus E_iso plane, classified by the duration criterion of T_{90, r} = 0.63 s. The meaning of the lines and symbols is the same as that in Fig. 3. There is only one short burst (GRB 090426) located below the criterion curve, while there are six long bursts (GRB 051221A, GRB 061006, GRB 061201, GRB 070714B, GRB 070809, GRB 070809 and GRB 071227) located above the curve.

Figure 11.

Results of correlation analysis between E_{p, r} and E_iso for short and long bursts of our sample, classified by the duration criterion of T_{90, r} = 0.63 s. See Fig. 8 for the meaning of the lines and symbols.

We note that our linear analysis result for short bursts is quite different from that obtained by Zhang et al. (2012). This must be due to the fact that our short burst sample (even in the case of adopting the duration criterion of T_{90, r} = 0.63 s) is larger than that of Zhang et al. (2012). Note that, short burst GRB 090426 (T₉₀ = 1.2 s, T_{90, r} = 0.33 s) was omitted in Zhang et al. (2012), and this burst is just located within the Amati type burst domain (see Fig. 10).

Although certain answers might not be available currently, we still like to raise some questions associated with the new classification scheme, in order to urge more relevant investigations. (a) Beside the statistical interpretation mentioned above, do there exist any mechanisms accounted for the two classes? What mechanisms or physical conditions the Amati relation reveals? (b) How the two newly classified groups of bursts are related to the Type 1 and Type II bursts? (c) What is the role this new classification scheme plays? How it relates to the conventional duration classification scheme? Can both schemes be combined to find intrinsically different groups? Or, other classification schemes should be involved?

Amati et al. (2009) pointed out that the Amati relation can be explained by the non-thermal synchrotron radiation scenario, e.g., by assuming that the minimum Lorentz factor and the normalization of the power-law distribution of the radiating electrons do not vary significantly from burst to burst or when imposing limits on the slope of the correlation between the fireball bulk Lorentz factor and the burst luminosity (Lloyd, Petrosian & Mallozzi 2000; Zhang & Meszaros 2002). Do short and long bursts follow the same mechanism? If so, why are the two relations different?

As discussed in Amati (2010), those long bursts to be seen off-axis could betray the conventional Amaiti relation and become outliers. The fact that short GRBs do not follow the Amati relation might be due to their different progenitors (likely mergers) or the difference of the circumburst environment and the main emission mechanisms. Why are these outliers and short bursts located in the same region in the E_p versus E_iso plane and following the same relation? Perhaps they share some common physical conditions that are different from what most long bursts possess.

GRB 060614 is a typical burst which lasts long enough but it is not obviously associated with SN. As this burst is found to be consistent with the Amati relation as most GRB/SN events, Amati et al. (2007) suggested that the position in the E_p versus E_iso plane of long GRBs does not critically depend on the progenitor properties. However, when taking into account only its first spike, GRB 060614 will shift from the Amati burst domain to non-Amati burst domain (see, e.g. Amati 2010). If one believes that GRB 060614 is a Type I burst, then one must come to this conclusion: at least in general cases, Type I and Type II bursts are not necessarily to be well separated in the E_p versus E_iso plane. Or, Amati bursts are not necessary to be Type II sources and non-Amati bursts are not necessary to be Type I GRBs. Perhaps, when special treatment such as considering only the first spike of bursts is employed, the conclusion will be changed.

If it is true that Type I and Type II bursts are not necessarily to be well separated in the E_p versus E_iso plane, then the peak energy deviation classification scheme alone would not be able to classify bursts with different progenitors. In this case, other classification schemes should be involved. Perhaps one can combine several schemes to set apart these bursts. If so, combination of both the peak energy deviation classification scheme and the conventional duration classification scheme might give rise to a much better result.

As mentioned above, the Amati relation might probably be affected by observational bias. Illustrated in Fig. 12 are the distributions of the bursts detected by various instruments in the E_{p, r} versus E_iso plane. We find that the domains of the distributions of the bursts observed by different instruments are not fully coincident. Especially, difference between the domain of the bursts observed by Swift and that of the bursts observed by other instruments is quite obvious. There does exist instrument bias. A robust analysis of statistical classification requires samples without any observational bias, which seems not being available currently.

From Fig. 12 we find that the bias introduced by the observation of Swift comes mainly from the joining of most of the non-Amati bursts (including the majority of conventional short bursts and the outliers of conventional long bursts; see Fig. 3). According to the above analysis, we regard this as a contribution of Swift to the new classification scheme. This is favoured by the following fact: when one considers only the Amati type bursts (those under the solid line in Fig. 2), one would find that the bias of Swift is mild. We perform correlation analysis between E_{p, r} and E_iso for the Amati type bursts detected by Swift and other instruments, respectively. The analysis produces

\begin{equation} {\rm log}\,E_{{\rm p},{\rm r}}=(2.08\pm 0.22) + (0.49\pm 0.18){\rm log}\,E_{\rm iso} \end{equation}

(9)

for the Amati type Swift bursts (N = 67, r = 0.798, P < 10^{− 16}) and

\begin{equation} {\rm log}\,E_{{\rm p},{\rm r}}=(2.04\pm 0.22) + (0.53\pm 0.16){\rm log}\,E_{\rm iso} \end{equation}

(10)

for the Amati type non-Swift bursts (N = 70, r = 0.847, P < 10^{− 20}). Presented in Fig. 13 are the results of the analysis. It shows that, for the Amati type bursts alone, no significant observational bias of Swift is observed.

Figure 12.

Distributions of the bursts detected by various instruments in the E_{p, r} versus E_iso plane.

Figure 13.

Results of correlation analysis between E_{p, r} and E_iso for the Amati type bursts detected by Swift (Swift sources) and other instruments (non-Swift sources), respectively. The dash line represents the Amati relation, the dot–dot dash line represents the linear fit to the Swift sources, and the solid line represents the linear fit to the non-Swift sources.

In fact, for a complete analysis, one cannot rely on the bursts observed only by a single instrument to discuss the classification scheme. Instead, one should rely on all the bursts that are observed by various instruments over the same area of sky and during the same interval of time. This might be a great task performed later. At present, to investigate the statistical classification, we prefer all available bursts rather than only those observed by a single instrument, since any instruments might introduce (strong or mild) bias. Currently, no one exactly knows how a complete sample would affect the statistical analysis above. Based on Fig. 12, we suspect that, when the number of bursts observed by all instruments increases, the clustering around the Amati relation might become stronger and this will give rise to a well-defined definition of the Amati type bursts. In return, this will also be helpful to distinguish the non-Amati type bursts.

An important difference between the original duration classification and the one presented here is that the original was conceived as a discriminator in the observer frame. The observed duration is measured in the observer frame and is influenced by the cosmological redshift. Therefore, to investigate intrinsic properties of the sources, one needs to remove this effect from the quantities concerned so that one can deal with them in the source frame. This is the reason why we use E_{p, r} and T_{90, r} to replace E_p and T₉₀, respectively. In addition, to calculate E_iso, one needs to know redshift as well. Obviously, the information of redshift is essential for a deep investigation of GRBs. We expect more and more bursts with known redshift being well observed in the near future.

We thank the anonymous referee for his/her helpful suggestions that improved this paper greatly. This work was supported by the National Natural Science Foundation of China (no. 11073007) and the Guangzhou technological project (no. 11C62010685).