Statistical classification of gamma-ray bursts based on the Amati relation
aa r X i v : . [ a s t r o - ph . H E ] N ov Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 5 September 2018 (MN L A TEX style file v2.2)
Statistical classification of gamma-ray bursts based on theAmati relation
Yi-Ping Qin , , ⋆ , Zhi-Fu Chen , Center for Astrophysics, Guangzhou University, Guangzhou 510006, P. R. China Department of Physics and Telecommunication Engineering, Baise University, Baise, Guangxi 533000, P. R. China Physics Department, Guangxi University, Nanning 530004, P. R. China
ABSTRACT
Gamma-ray bursts (GRBs) are believed to belong to two classes and they are conven-tionally divided according to their durations. This classification scheme is not satisfieddue 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 ofthe logarithmic deviation of the E p value from the Amati relation. The distributionpossesses an obvious bimodality structure and it can be accounted for by the com-bination of two Gaussian curves. Based on this analysis, we propose to statisticallyclassify GRBs in the well-known E p vs. E iso plane with the logarithmic deviation ofthe E p value. This classification scheme divides GRBs into two groups: Amati typebursts and non-Amati type bursts. While Amati type bursts well follow the Amatirelation, non-Amati type bursts do not. It shows that most Amati type bursts arelong duration bursts and the majority of non-Amati type bursts are short durationbursts. In addition, it reveals that Amati type bursts are generally more energeticthan non-Amati type bursts. An advantage of the new classification is that the twokinds of burst are well distinguishable and therefore their members can be identifiedin certainty. Key words: gamma rays: bursts — gamma rays: observations
Gamma-ray bursts (GRBs) are generally divided into twoclasses: short and long-duration classes. The duration con-cerned is always T which is the time interval during whichthe burst integrated counts increases from 5% to 95% ofthe total counts. This classification scheme is based on thebimodality structure of the T distribution of the objects,where all the bursts are likely to be separated at about 2 sec-onds (see, e.g., Kouveliotou et al. 1993). When one replaces T with T (during which the burst integrated counts in-creases from 25% to 75% of the total counts), the bimodal-ity structure also exists (see, e.g., Zhao et al. 2004). Gen-erally, short duration bursts are harder than long durationbursts. In the hardness ratio vs. duration plane, short andlong bursts were observed to distribute in distinct domains( Kouveliotou et al. 1993, Fishman & Meegan 1995). It wasshown that the hardness ratio is correlated to the durationfor the whole GRB sample, but for each of the two classesalone the two quantities are not correlated at all (see Qin et ⋆ E-mail:[email protected] al. 2000). This statistical result strongly suggests that, whileany attempts to consider all GRBs as a single class mightbe questionable, the existence of the two classes of GRBs isconvincing.It is expected that different classes might have differ-ent progenitors. Therefore, the classification of GRBs hasalways been an essential task. Based on many years of in-vestigation, most researchers come to the consent that manyshot bursts are produced in the event of binary neutron staror neutron star-black hole mergers, while many long burstsare caused by the massive star collapsars (e.g., Eichler et al.1989; MacFadyen & Woosley 1999; Paczynski 1986, 1998;Woosley 1993).Thanks to the successful launch of the Swift satellite(Gehrels et al. 2004), many advances in the research of GRBshave been achieved. The most important achievement mightbe the fact that a large body of evidence favors the twoprogenitor proposal for GRBs. It has been continued to bereported that short bursts were found in regions with lowerstar-formation rates, and no evidence of supernovae to ac-company them was detected (Barthelmy et al. 2005; Bergeret al. 2005; Hjorth et al. 2005). Meanwhile, long bursts were c (cid:13) Y.-P. Qin and Z.-F. Chen found to be originated from star-forming regions in galaxies(Fruchter et al. 2006), and in some of these events, super-novae were detected to accompany the bursts (Hjorth et al.2003; Stanek et al. 2003).Short burst class and long burst class are conventionallydivided by T : those their T being larger than 2 secondsare classified as long bursts while the rest are classified asshort bursts. McBreen et al. (1994) showed that, the bimodaldistribution of GRBs can arise from two overlapped lognor-mal distributions. This indicates that each of the two GRBpopulations might possess a single lognormal duration dis-tribution, and due to the overlap, there would be a sufficientnumber of bursts that are mis-classified by simply applyingthe criterion of T = 2 s .The scenario that two overlapped lognormal distribu-tions can account for the duration distribution of the wholeGRB 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 accountfor the duration distribution of all BATSE bursts. Althoughif there exists a third class of GRBs is stills a subject ofdebate, the evidence that the two-Gaussian fit alone cannotaccount for the duration distribution of all GRBs is obvious.In fact, T is not an intrinsic property of a burst or a popu-lation of bursts. For a more robust investigation, one shouldrely on the cosmological rest-frame duration (see the defini-tion of T ,r below), where the effect of cosmological redshifthas been corrected. Unfortunately, the redshift informationis not available for most BATSE bursts, and hence in thecorresponding analysis this effect can not be taken into ac-count. However, in our analysis below, redshifts of the burstsare known, and therefore we will use T ,r instead of T .In fact, voices questioning the duration classificationscheme have become stronger in recent years. Gehrels et al.(2006) reported that the duration of GRB 060614 is long butits behavior is similar to short duration bursts (for example,very deep optical observations of this source exclude an ac-companying supernova). Based on this fact, they even askedif there exists a new GRB classification scheme that strad-dles both long and short duration bursts. Similar observa-tional results were reported by different groups in nearly thesame time (see, e.g., Gal-Yam et al. 2006; Fynbo et al. 2006;Della Valle et al. 2006). For some short duration bursts, softextended emission and late X-ray flares were observed, in-dicating that these sources might not really short (see, e.g.,Barthelmy et al. 2005; Norris & Bonnell 2006).In the recent few years, some attempts of revealing newstatistical properties associated with the classification ofbursts as well as introducing new classification schemes havecontinued to be made. Zhang et al. (2007) proposed thatGRBs should be classified into Type I (typically short andassociated with old populations) and Type II (typically longand associated with young populations) groups. This type ofclassification is charming, but the goal of dividing individ-ual bursts into the distinct groups is hard to realize. Lu etal. (2010) introduced a new parameter to classify GRBs. Intheir efforts, they regarded those long GRBs with “extendedemission” being short ones if the bursts are really “short”without the “extended emission”. In this way, they found aclear bimodal distribution of the parameter. Goldstein et al.(2010) found the distribution of the ratio of Epeak/Fluencebearing a bimodality structure in the complete BATSE 5B spectral catalog, which corresponds directly to the conven-tional short and long burst classes. However, the overlap ofthe distributions of the two groups of bursts is seen to beas heavy as that shown in the duration distributions. Qinet al. (2010) proposed to modify the conventional durationclassification scheme by separating the conventional shortand long duration bursts in different softness (or hardness)groups. While this method seems reasonable, the improve-ment would not be applicable if the size of samples is notlarge enough.Just as was mentioned above, one can verify that, twodistinct smooth curves (e.g., two Gaussian curves) account-ing for the duration distributions of the short and long burstclasses are sufficiently overlapped. This makes the durationclassification scheme an unsatisfied one. Unfortunately, theoverlap of other parameters (e.g., the hardness ratio or thepeak energy) is much heavier than that of the duration. Al-though it is much beyond being satisfactory, the durationclassification scheme is still the most popular one up to day.Thus, It is desirable that a better alternative of the classifi-cation can be established in the near future.Based on a sample of BeppoSAX GRBs with known red-shift, Amati et al. (2002) discovered a tight relation betweenthe cosmological rest-frame spectrum peak energy and theisotropic equivalent radiated energy, which is now known asthe Amati relation. This soon triggered a series of relevantresearches (e.g., Amati 2006, 2010; Amati et al. 2007, 2008,2009; Piranomonte et al. 2008; Ghirlanda et al. 2008, 2009;Gruber et al. 2011; Zhang et al. 2012).There have been debates about the existence of the Am-ati relation as an intrinsic property of GRBs. Some authorspointed out that the relation might arise from observationalselection effects (e.g., Band & Preece 2005; Butler et al.2007, 2009; Nakar & Piran 2005). Other authors arguedthat, to form the relation, selection effects could only playa marginal role (see, e.g., Amati et al. 2009; Bosnjak et al.2008; Ghirlanda et al. 2005, 2008; Krimm et al. 2009; Navaet al. 2008). Recently, Butler et al. (2010) derived a GRBworld model from their data, and based on the model theyreproduced the observables from both Swift and pre-Swiftsatellites. In their analysis, a real, intrinsic correlation be-tween the two quantities is confirmed, but they pointed outthat the correlation is not a narrow log - log relation andits observed appearance is strongly detector-dependent. Ourdata (see the analysis below) show that the Amati relationis real, although it might be, at least in part, introduced byobservational bias.In a subsequent analysis with a much larger sample,Amati (2006) reported that subenergetic GRBs (such asGRB 980425) and short GRBs are found to be inconsistentwith the correlation between the cosmological rest-framespectrum peak energy and the isotropic equivalent radiatedenergy, indicating that this phenomenon might be a power-ful tool for discriminating different classes of GRBs and un-derstanding their nature and differences. Recently, Zhang etal. (2012) selected some short bursts and disregarded thosesubenergetic GRBs concerned by Amati (2006). They re-ported that, for these short bursts alone, there does exista tight relation between the two quantities, which is quitedifferent from the conventional Amati relation.As the Amati relation is real and the number of GRBswith known redshift has become larger and larger in recent c (cid:13) , 000–000 tatistical classification of gamma-ray bursts years, it might be possible now to use the relation to dis-tinguish members of distinct GRB classes statistically. Thismotivates our analysis below.In Section 2, the collection of GRBs with known redshiftis presented and a statistical analysis is performed to checkif there exits an appropriate quantity to separate the burstsinto different groups. Based on this analysis, we presenta new classification scheme in Section 3. In Section 4, wecompare the new classification scheme and the conventionalscheme. A summary and discussion are presented in Section5. Throughout this paper, we adopt the following cosmo-logical parameters: H = 70 kms − Mpc , Ω M = 0 . Λ = 0 . We only consider GRBs with measured redshift, up to May2012, including sources observed by various instruments. Inaddition, some other quantities are required. In fact, in-cluded in our sample are merely those GRBs with the fol-lowing quantities available: redshift z , spectrum peak energy E p , isotropic equivalent radiated energy E iso , and duration T . We get 153 bursts in total. Sources of our sample arelisted in Table 1.Let E p,r ≡ (1 + z ) E p being the cosmological rest-frame νf ν spectrum peak energy (in brief, the rest-frame peak en-ergy), in units of kcV , and E iso being the isotropic equiva-lent radiated energy (in brief, the isotropic energy), in unitsof 10 erg . In the following, when E p,r and E iso are used inany analysis, they stand for their observational values (see,e.g., Table 1). The Amati relation can be expressed as fol-lows (see Amati 2006): E p,r,pre = K × E miso , (1)where subscript pre means “predicted”, K and m are con-stants obtained by fits. In order to avoid notation confusionin the analysis below, we use E p,r,pre to describe the pre-dicted value of the rest-frame peak energy, determined bythe Amati relation when E iso is provided.To check if a burst obey or betray the Amati relation, wefollow Amati (2006) to consider the logarithmic deviation ofthe E p value from the Amati relation that serves as a datumline in the E p vs. E iso plane. The Amati relation adopted asthe datum line in this paper is that obtained by Amati et al.(2008): E p,r,pre = 94 × E . iso . Thus, the logarithmic deviationof the E p value considered in this paper is logE p,r − log − . logE iso , where K = 94 is different from that adopted inFigure 4 of Amati (2006). (Note that, the Amati relation isimproved in Amati et al. 2008 with a much larger samplecompared with that in Amati 2006).Displayed in Fig. 1 is the distribution of the logarithmicdeviation of the E p value of our sample. Unlike that shown inFigure 4 of Amati (2006) (where only long GRBs and X-rayflashes are considered), the distribution in our sample showsan obvious bimodality structure. It reveals that there are twoGaussian distributions that form the bimodality structure,and the overlap of the two distributions is not heavy (seeFig. 7 for a comparison with the T distribution of the samesample).We perform a two-Gaussian fit to the distribution of the Figure 1.
Distribution of the logarithmic deviation of the E p value of our sample (153 sources), where the deviation is calcu-lated by logE p,r − log − . logE iso . The thick dash line rep-resents a two-Gaussian fit, and the two thin solid lines (heavilyoverlapped by the thick dash line) stand for the two Gaussiancurves respectively. There is a dip at about 0.7. The number ofthe sources located at the left hand side of the dip is 137, whilethat of the rest is 16. logarithmic deviation of the E p value (i.e., the distributionof logE p,r − log − . logE iso ), and obtain σ = 0 .
239 and acentral value of -0.044 for the first Gaussian curve, and σ =0 .
300 and a central value of 1.327 for the second Gaussiancurve, with the reduced χ of the fit being χ = 16 . σ range of the first curve, and 91.2 percent (125/137) of thebursts accounted for by the first curve are located beyondthe 3 σ range of the second curve, which indicates that theoverlap of the two Gaussian distributions is very light. The bimodality structure shown in Fig. 1 favors the assump-tion that there are two distinct classes of GRBs. If we believethat each of the two Gaussian distributions obtained abovecorresponds to one of the two classes, then the figure indi-cates that while members of one class clustering around theAmati relation (represented by the zero value of the devia-tion; see Fig. 1), sources of the other class are located faraway from the relation. This encourages us to use a loga-rithmic deviation of the E p value to set apart the classes ofGRBs.According to Fig. 1 and the fitting curve, we assignthe logarithmic deviation of the E p value located at the dipbetween the two peaks of the fitting curve as the criterionto classify members of the two groups. The dip is at 0.72. Itcorresponds to the following curve in the E p vs. E iso plane: E p,r,pre = 10 . × × E . iso . (2)Sources located under this curve in the E p vs. E iso plane areclassified as Amati type bursts, and that located above thiscurve are classified as non-Amati type bursts. Or, in termsof the logarithmic deviation of the E p value, GRBs with c (cid:13) , 000–000 Y.-P. Qin and Z.-F. Chen
Figure 2.
Classification of the 153 GRBs in the E p vs. E iso plane.The dash line represents the Amati relation, and the solid linerepresents the criterion curve of the new classification, equation(2). Filled circles stand for Amati type bursts (137 sources), andopen circles plus pluses reprensent non-Amati type bursts (16sources). logE p,r − log − . logE iso < .
72 are classified as Amatitype bursts, otherwise they are classified as non-Amati typebursts. Shown in Fig. 2 is the result of the classification.To check how different duration (short or long) burstsare influenced by this classification, let us follow the conven-tional method to classify the bursts by duration. Since theredshifts of bursts are available, we modify the conventionalduration classification criterion by replacing T = 2 s with T ,r = 1 s , where T ,r ≡ T / (1+ z ) is the cosmological rest-frame duration (shortly, rest-frame duration). We divideGRBs into two groups by assigning bursts with T ,r > T ,r ≤ T ,r = 1 s as the du-ration criterion is that, it corresponds to T = 2 s when z = 1. In our sample, when bursts are divided by T = 2 s we get 16 short ones. Therefore, to get a sample of shortbursts, the criterion of T ,r = 1 s is more conservative thanthe conventional one, that of T = 2 s .Distributions of these two groups of bursts (short andlong bursts) are displayed in Fig. 3. We find that short burstsare mainly (12/13, 92.3%) located in the non-Amati typeburst region while long bursts are preferentially (136/140,97.1%) distributed in the Amati type burst domain.Shown in Figs. 4, 5, and 6 are the distributions of E iso , E p,r , and T ,r respectively for the two newly classi-fied groups of bursts. We find from these figures that Amatitype bursts are generally longer and more energetic. Un-like in the case of the conventional duration classificationscheme, the two newly classified groups of bursts do notshow significant difference in the distribution of E p,r . Onecan also observe this in Fig. 2. It has been known for a longtime that sources of the conventional short burst class aregenerally harder than those of the conventional long burstclass. At least with the current sample (153 sources), thisdifference is relatively mild if sources are divided with thenew classification scheme. Figure 3.
Distributions of the short (open circles plus pluses)and long (filled circles) bursts of the 153 GRBs in the E p vs. E iso plane. The dash line represents the Amati relation, and thesolid line represents the criterion curve of the new classification,equation (2). Only one short burst (GRB 090426) is located be-low the criterion curve, and four long bursts (GRB 061006,GRB070714B, GRB 071227 and GRB 070809) are located above thecurve. Figure 4.
Distributions of E iso for the two newly classified groupsof bursts. The thick solid line stands for the group of non-Amatitype bursts, and the thin solid line corresponds to the group ofAmati type bursts.
Let us compare the new classification scheme, the schemebased on the logarithmic deviation of the E p value (shortly,the peak energy deviation classification scheme), with theconventional duration classification scheme.Shown in Fig. 7 is the distribution of the rest-frame du-ration, of our sample. The well-known bimodality structureis observed. As is already known, it is unlikely that the bi-modality structure distribution arises from the combinationof two Gaussian distributions.As done in the case of the peak energy deviation classi-fication scheme, we fit the duration distribution of the sam- c (cid:13) , 000–000 tatistical classification of gamma-ray bursts Figure 5.
Distributions of E p , r for the two newly classified groupsof bursts. The meanings of lines are the same as that in Fig. 4. Figure 6.
Distributions of T , r for the two newly classifiedgroups of bursts. The meanings of lines are the same as thatin Fig. 4. ple with the combination of two Gaussian functions and get σ = 0 .
375 and a central value of -0.833 for the first Gaus-sian curve, and σ = 0 .
419 and a central value of 1.017 forthe second Gaussian curve, with the reduced χ of the fitbeing χ = 29 . χ value (29.826) is much larger than that (16.649) of the newclassification scheme. As a key parameter of classification toseparate two groups of sources, one always expects its distri-bution to possess a bimodality structure that arises from thecombination of two perfect Gaussian curves. In this aspect,the logarithmic deviation of the E p value acts much betterthan 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 ,r > s and that with T ,r ≤ s , in our sample. It yields: LogE p,r = (2 . ± .
15) + (0 . ± . LogE iso (3)for bursts with T ,r > s (N = 140 , r = 0 . , P < − ),and Figure 7.
Distribution of T , r , of our sample. The meanings oflines are the same as that in Fig. 1. Figure 8.
Results of correlation analysis between E p,r and E iso for short and long bursts of our sample, divided by T ,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 meanings of the dash line and other symbols. LogE p,r = (2 . ± .
69) + (0 . ± . LogE iso (4)for bursts with T ,r ≤ s (N = 13 , r = 0 . , P = 0 . LogE p,r = (2 . ± .
16) + (0 . ± . LogE iso (5)for Amati type bursts (N = 137 , r = 0 . , P < − ),and LogE p,r = (3 . ± .
65) + (0 . ± . LogE iso (6)for non-Amati type bursts (N = 16 , r = 0 . , P < − ).The results are displayed in Figs. 8 and 9 respectively.It suggests that, if we believe that bursts of the same classshould follow the same relationship between E p,r and E iso ,as hinted by the discovery of Amati et al. (2002), then theduration of bursts cannot appropriately separate the twoclasses. In this aspect and in terms of statistics, the loga- c (cid:13) , 000–000 Y.-P. Qin and Z.-F. Chen
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 newlyclassification scheme. The upper solid line represents the linear fitto the non-Amati type bursts, and the lower solid line representsthe linear fit to the Amati type bursts. See Fig. 2 for the meaningsof the dash line and other symbols. rithmic deviation of the E p value is much more preferentialthan the duration. We collected GRBs with measured redshift, spectrum peakenergy, isotropic equivalent radiated energy, and durationfrom literature up to May 2012, including sources observedby various instruments, and get 153 GRBs in total. Withthis sample, we investigate the distribution of the logarith-mic deviation of the E p value from the Amati relation. Thedistribution exhibits an obvious bimodality structure. A fitto the data shows that the distribution of the deviation canbe accounted for by the combination of two Gaussian curves,and the two curves are well separated. Based on this, we pro-pose to statistically classify GRBs in the E p vs. E iso planewith the logarithmic deviation of the E p value. According tothis classification scheme, bursts are divided into two groups:Amati type bursts and non-Amati type bursts. A statisti-cal interpretation of this classification is that, Amati typebursts well follow the Amati relation, but non-Amati typebursts do not. Our analysis reveals that Amati type burstsare generally longer and more energetic and non-Amati typebursts are generally shorter and less energetic. After com-paring the new classification scheme with the conventionalscheme we find that, in terms of statistics, the logarithmicdeviation of the E p value acts much better in the classifica-tion routine than the duration does. Since the overlap of thedistributions of the logarithmic deviation of the E p value islight, the two groups of bursts so divided are well distin-guishable and therefore their members can be identified incertainty.From Fig. 7, one might observe that, taking T ,r = 1 s as the duration criterion might not be so appropriate sincethe dip between the two peaks of the bimodality structureis located at the position of a much smaller duration value. Figure 10.
Distributions of the short and long bursts of the153 GRBs in the E p vs. E iso plane, classified by the durationcriterion of T ,r = 0 . s . The meanings of the lines and symbolsare the same as that in Fig. 3. There is only one short bursts(GRB 090426) located below the criterion curve, while there aresix long bursts (GRB 051221A, GRB 061006, GRB 061201, GRB070714B, GRB 070809, GRB 070809 and GRB 071227) locatedabove 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 durationcriterion of T ,r = 0 . s . See Fig. 8 for the meanings of the linesand symbols. How the short and long bursts act if we divide them at thisposition?According to Fig. 7, this position is at T ,r = 0 . s .Let us divide bursts into two groups by taking T ,r = 0 . s as the duration criterion. In this way, we get 11 short burstsand 142 long bursts. The distributions of these groups ofbursts in the E p vs. E iso plane are shown in Fig. 10. We findthat 90.9% (10/11) of this kind of short burst are classifiedas non-Amati type bursts, and 95.8% (136/142) of this kindof long burst are classified as Amati type bursts. We repeatthe above linear analysis for these two groups and get LogE p,r = (2 . ± .
15) + (0 . ± . LogE iso (7) c (cid:13) , 000–000 tatistical classification of gamma-ray bursts for bursts with T ,r > . s (N = 142 , r = 0 . , P < − ), and LogE p,r = (2 . ± .
85) + (0 . ± . LogE iso (8)for bursts with T ,r ≤ . s (N = 11 , r = 0 . , P =0 . T ,r = 1 s to T ,r = 0 . s does not give rise to a signifi-cantly different result.We notice that our linear analysis result for short burstsis 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 ,r =0 . s ) is larger than that of Zhang et al. (2012). Note that,short burst GRB 090426 ( T = 1 . s , T ,r = 0 . s ) wasomitted in Zhang et al. (2012), and this burst is just locatedwithin the Amati type burst domain (see Fig. 10).Although certain answers might not be available cur-rently, we still like to raise some questions associated withthe new classification scheme, in order to urge more relevantinvestigations. a) Beside the statistical interpretation men-tioned above, do there exist any mechanisms accounted forthe two classes? What mechanisms or physical conditionsthe Amati relation reveals? b) How about the two newlyclassified groups of bursts are related to the Type 1 and TypeII bursts? c) What is the role this new classification schemeplays? How it relates to the conventional duration classifi-cation scheme? Can both schemes be combined to find in-trinsically different groups? Or, other classification schemesshould be involved?Amati et al. (2009) pointed out that the Amati relationcan be explained by the non-thermal synchrotron radiationscenario, e.g., by assuming that the minimum Lorentz fac-tor, and the normalization of the power-law distribution ofthe radiating electrons do not vary significantly from burstto burst or when imposing limits on the slope of the correla-tion between the fireball bulk Lorentz factor, and the burstluminosity (Lloyd et al. 2000; Zhang & Meszaros 2002). Isthe relation short bursts follow due to the same mechanism?If so, why are the two relations different?As discussed in Amati (2010), those long bursts to beseen off-axis could betray the conventional Amaiti relationand become outliers. The fact that short GRBs do not followthe Amati relation might be due to their different progen-itors (likely mergers) or the difference of the circum-burstenvironment and the main emission mechanisms. Why arethese outliers and short bursts located in the same regionin the E p vs. E iso plane and following the same relation?Perhaps they share some common physical conditions thatare different from what most long bursts possess.GRB 060614 is a typical burst which lasts long enoughbut it is not obviously associated with SN. As this burstis found to be consistent with the Amati relation as mostGRB/SN events, Amati et al. (2007) suggested that the po-sition in the E p vs. E iso plane of long GRBs does not crit-ically depend on the progenitor properties. However, whentaking into account only its first spike, GRB 060614 will shiftfrom the Amati burst domain to non-Amati burst domain(see, e.g., Amati 2010). If one believes that GRB 060614 isa Type I burst, then one must come to this conclusion: atleast in general cases, Type I and Type II bursts are not nec-essarily to be well separated in the E p vs. E iso plane. Or, Figure 12.
Distributions of the bursts detected by various in-struments in the E p,r vs. E iso plane. Amati bursts are not necessary to be Type II sources andnon-Amati bursts are not necessary to be Type I GRBs.Perhaps when special treatment such as considering onlythe first spike of bursts is employed, the conclusion will bechanged.If it is true that Type I and Type II bursts are not nec-essarily to be well separated in the E p vs. E iso plane, thenthe peak energy deviation classification scheme alone wouldnot be able to classify bursts with different progenitors. Inthis case, other classification schemes should be involved.Perhaps one can combine several schemes to set apart thesebursts. If so, combination of both the peak energy deviationclassification scheme and the conventional duration classifi-cation scheme might give rise to a much better result.As mentioned above, the Amati relation might probablybe affected by observational bias. Illustrated in Fig. 12 arethe distributions of the bursts detected by various instru-ments in the E p,r vs. E iso plane. We find that the domainsof the distributions of the bursts observed by different in-struments are not fully coincident. Especially, difference be-tween the domain of the bursts observed by Swift and thatof the bursts observed by other instruments is quite obvi-ous. There does exist instrument bias. A robust analysis ofstatistical classification requires samples without any obser-vational bias, which seems not being available currently.From Fig. 12 we find that the bias introduced by theobservation of Swift comes mainly from the joining of mostof the non-Amati bursts (including the majority of con-ventional short bursts and the outliers of conventional longbursts; see Fig. 3). According to the above analysis, we re-gard this as a contribution of Swift to the new classificationscheme. This is favored by the following fact: when one con-siders only the Amati type bursts (those under the solid linein Fig. 2), one would find that the bias of Swift is mild. Weperform correlation analysis between E p,r and E iso for theAmati type bursts detected by Swift and other instrumentsrespectively. The analysis produces: LogE p,r = (2 . ± .
22) + (0 . ± . LogE iso (9)for the Amati type Swift bursts (N = 67 , r = 0 . , P < − ), and c (cid:13) , 000–000 Y.-P. Qin and Z.-F. Chen
Figure 13.
Results of correlation analysis between E p,r and E iso for the Amati type bursts detected by Swift (Swift sources) andother instruments (non-Swift sources) respectively. The dash linerepresents the Amati relation, the dot dot dash line representsthe linear fit to the Swift sources, and the solid line stands forthe linear fit to the non-Swift sources. LogE p,r = (2 . ± .
22) + (0 . ± . LogE iso (10)for the Amati type non-Swift bursts (N = 70 , r =0 . , P < − ). Presented in Fig. 13 are the results ofthe analysis. It shows that, for the Amati type bursts alone,no significant observational bias of Swift is observed.In fact, for a complete analysis, one cannot rely on thebursts observed only by a single instrument to discuss theclassification scheme. Instead, one should rely on all thebursts that are observed by various instruments over thesame area of sky and during the same interval of time. Thismight be a great task performed later. At present, to in-vestigate the statistical classification, we prefer all avail-able bursts rather than only those observed by a single in-strument, since any instruments might introduce (strong ormild) bias. Currently, no one exactly knows how a completesample would affect the statistical analysis above. Based onFig. 12, we suspect that, when the number of bursts ob-served by all instruments increases, the clustering aroundthe Amati relation might become stronger and this will giverise to a well definition of the Amati type bursts. In return,this will also be helpful to distinguish the non-Amati typebursts.An important difference between the original durationclassification and the one presented here is that the origi-nal was conceived as a discriminator in the observer frame.The observed duration is measured in the observer frameand is influenced by the cosmological redshift. Therefore, toinvestigate intrinsic properties of the sources, one needs toremove this effect from the quantities concerned so that onecan deal with them in the source frame. This is the reasonwhy we use E p,r and T ,r to replace E p and T respectively.In addition, to calculate E iso , one needs to know redshift aswell. Obviously, the information of redshift is essential fora deep investigation of GRBs. We expect more and morebursts with known redshift being well observed in the nearfuture. We thank the anonymous referee for his/her helpfulsuggestions that improve this paper greatly. This work wassupported by the National Natural Science Foundation ofChina (No. 11073007) and the Guangzhou technologicalproject (No. 11C62010685). REFERENCES
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Parameters of prompt emission of GRBs with measured redshifts.GRB z T E iso E p,r Instruments Refs Note10 erg keV970228 0.695 80 1.6 ± ±
64 BeppoSAX 15 A970508 0.835 20 0.612 ± ±
43 BeppoSAX 15 A970828 0.958 146.59 29 ± ±
117 CGROSE 15 A971214 3.42 35 21 ± ±
133 BeppoSAX 15 A980326 1 9 0.482 ± ±
36 BeppoSAX 15 A980613 1.096 20 0.59 ± ±
89 BeppoSAX 15 A980703 0.966 102.37 7.2 ± ±
64 CGROSE 15 A990123 1.6 100 229 ±
37 1724 ±
446 BeppoSAX 15 A990506 1.3 220.38 94 ± ±
156 CGROSE 15 A990510 1.619 75 17 ± ±
42 BeppoSAX 15 A990705 0.843 42 18 ± ±
139 BeppoSAX 15 A990712 0.434 20 0.67 ± ±
15 BeppoSAX 15 A991208 0.706 60 22.3 ± ±
31 Konus 15 A991216 1.02 24.9 67 ± ±
134 GRO/KW 15 A000131 4.5 110.1 172 ±
30 987 ±
416 GRO/KW 15 A000210 0.846 20 14.9 ± ±
26 Konus 15 A000418 1.12 30 9.1 ± ±
21 Konus 15 A000911 1.06 500 67 ±
14 1856 ±
371 Konus 15 A000926 2.07 25 27.1 ± ±
20 Konus 15 A010222 1.48 130 81 ± ±
30 Konus 15 A010921 0.45 24.6 0.95 ± ±
26 HETEC2 15 A011121 0.36 75 7.8 ± ±
265 BeppoSAX 9 A020124 3.198 78.6 27 ± ±
148 HETEC2 15 A020127 1.9 17.6 3.5 ± ±
100 HETEC2 19 A020405 0.695 60 10 ± ±
10 BeppoSAX 15 A020813 1.25 90 66 ±
16 590 ±
151 HETEC2 15 A020819B 0.41 46.9 0.68 ± ±
21 HETEC2 15 A020903 0.25 10 0.0024 ± ± ± ±
117 HETEC2 15 A021211 1.01 2.41 1.12 ± ±
52 HETEC2 15 A030226 1.98 76.8 12.1 ± ±
66 HETEC2 15 A030323 3.37 32.6 2.8 ± ±
113 HETEC2 10 A030328 1.52 140 47 ± ±
55 HETEC2 15 A030329 0.17 23 1.5 ± ±
23 HETEC2 15 A030429 2.65 10.3 2.16 ± ±
26 HETEC2 15 A030528 0.78 49.2 2.5 ± ± ± ±
33 HETEC2 11 A040924 0.859 5 0.95 ± ±
35 HETEC2 15 A041006 0.716 25 3 ± ±
20 HETEC2 15 A050126A 1.29 24.8 0.736 ± ±
110 Swift 16 A050223 0.5915 22.5 0.121 ± ±
54 Swift 16 A050318 1.44 32 2.2 ± ±
25 Swift 15 A050401 2.9 33.3 35 ± ±
110 Swift 15 A050416A 0.65 2.5 0.1 ± ± ± ±
245 Swift 16 A050509B 0.225 0.04 0.00024 +0 . − . ±
10 Swift 18 N050525A 0.606 8.8 2.5 ± ±
10 Swift 15 A050603 2.821 12.4 60 ± ±
107 Konus 15 A050709 0.16 0.07 0.0033 ± ± ± ±
48 Swift 16 A050813 1.8 0.6 0.015 +0 . − . ±
15 Swift 18 N050814 5.3 150.9 11.2 ± ±
47 Swift 16 A050820 2.612 26 97.4 ± ±
277 Konus 15 A050904 6.29 174.2 124 ±
13 3178 ± ± ±
36 Swift 16 A050922C 2.198 4.6 5.3 ± ±
111 HETEC2 15 A051022 0.8 200 54 ± ±
258 HETEC2 15 A051109A 2.346 37.2 6.5 ± ±
200 Konus 15 A051221A 0.547 1.4 0.3 ± ±
144 Swift 18 N060115 3.53 139.6 6.3 ± ±
34 Swift 15 A060124 2.297 750 41 ± ±
285 Konus 15 Ac (cid:13) , 000–000 Y.-P. Qin and Z.-F. Chen
Table 1. — continuedGRB z T E iso E p,r Instruments Refs Note10 erg keV060206 4.048 7.6 4.3 ± ±
46 Swift 15 A060210 3.91 255 41.53 ± ±
186 Swift 16 A060218 0.0331 2100 0.0053 ± ± ± ±
63 Swift 16 A060418 1.489 103.1 13 ± ±
143 Konus 15 A060502B 0.287 0.131 0.003 +0 . − . ±
19 Swift 18 N060510B 4.9 275.2 36.7 ± ±
227 Swift 16 A060522 5.11 71.1 7.77 ± ±
79 Swift 16 A060526 3.21 298.2 2.6 ± ±
21 Swift 15 A060605 3.78 79.1 2.83 ± ±
251 Swift 16 A060607A 3.082 102.2 10.9 ± ±
200 Swift 16 A060614 0.125 108.7 0.21 ± ±
45 Konus 15 A060707 3.43 66.2 5.4 ± ±
28 Swift 15 A060714 2.711 115 13.4 ± ±
109 Swift 16 A060814 0.84 145.3 7 ± ±
155 Konus 15 A060904B 0.703 171.5 0.364 ± ±
41 Swift 16 A060906 3.686 43.5 14.9 ± ±
43 Swift 16 A060908 2.43 19.3 9.8 ± ±
102 Swift 15 A060927 5.6 22.5 13.8 ± ±
47 Swift 15 A061006 0.4377 129.9 0.2 ± ±
267 Swift 1 N061007 1.261 75.3 86 ± ±
124 Konus 15 A061121 1.314 81.3 22.5 ± ±
153 Konus 15 A061126 1.1588 70.8 30 ± ±
410 Swift 17 A061201 0.111 0.76 3 +4 − ±
508 Swift 18 N061217 0.827 0.21 0.03 +0 . − . ±
22 Swift 18 N061222B 3.355 40 10.3 ± ±
28 Swift 16 A070110 2.352 88.4 5.5 ± ±
170 Swift 8 A070125 1.547 70 80.2 ± ±
148 Konus 15 A070429B 0.904 0.47 0.07 +0 . − . ±
81 Swift 18 N070508 0.82 21.2 8 +2 − +138 . − . Swift 14 A070714B 0.92 2 1.1 ± ± +0 . − . ±
12 Swift 18 N070809 0.2187 1.3 0.00131 +0 . − . ± ± ±
286 Swift 19 A071010B 0.947 35.7 1.7 ± ±
20 Konus 15 A071020 2.145 4.2 9.5 ± ±
160 Konus 15 A071117 1.331 6.6 4.1 ± ±
226 Konus 12 A071227 0.383 1.8 0.1 ± ±
277 Swift 3 N080319B 0.937 50 114 ± ±
65 Swift 15 A080319C 1.95 34 14.1 ± ±
272 Swift 15 A080411 1.03 56 15.6 ± ±
70 Konus 13 A080413A 2.433 46 8.1 ± ±
180 Swift 4 A080413B 1.1 8 2.4 ± ±
30 Swift 5 A080514B 1.8 7 17 ± ±
65 Konus 19 A080603B 2.69 60 11 ± ±
100 Konus 19 A080605 1.6398 20 24 ± ±
55 Konus 19 A080607 3.036 79 188 ±
10 1691 ±
226 Konus 19 A080721 2.591 16.2 126 ±
22 1741 ±
227 Swift 19 A080804 2.2 34 11.5 ± ±
45 Swift 8 A080810 3.35 106 45 ± ±
180 Swift 19 A080913 6.7 8 8.6 ± ±
350 Konus 19 A080916A 0.689 60 2.27 ± ± ±
24 Swift 7 A080916C 4.35 62.977 387 ±
46 2268.4 ± ± ±
15 Swift 19 A081028 3.038 260 17 ± ±
93 Swift 19 A081118 2.58 67 4.3 ± ±
14 Swift 19 A081121 2.512 14 26 ± ±
123 Swift 19 A081203A 2.1 294 35 ± ±
757 Swift 8 A081222 2.77 24 30 ± ±
34 Swift 19 A090102 1.547 27 22 ± ±
166 Konus 19 A090323 3.57 135.17 410 ±
50 1901 ±
343 Konus 19 Ac (cid:13) , 000–000 tatistical classification of gamma-ray bursts Table 1. — continuedGRB z T E iso E p,r Instruments Refs Note10 erg keV090328 0.736 61.697 13 ± ±
312 Konus 19 A090418 1.608 56 16 ± ±
384 Swift 19 A090423 8.1 10.3 11 ± ±
200 Swift 19 A090424 0.544 48 4.6 ± ±
50 Swift 19 A090425A 0.544 75.393 4.48 177 ± +0 . − . ±
82 Swift 18 A090510 0.903 0.3 3.75 ± ±
760 Swift 6 N090516 4.109 210 88.5 ± +502 . − . Swift 6 A090618 0.54 113.2 25.4 ± + − . Swift 6 A090812 2.452 66.7 40.3 ± ±
663 Swift 8 A090902B 1.822 19.328 305 ± ± ± ± ± ± ± ± ± ± ± ±
231 Swift 8 A091029 2.752 39.2 7.4 ± ±
66 Swift 8 A091127 0.49 7.1 1.63 ± ± ± +37 . − . Swift 6 A100117A 0.92 0.3 0.09 ± +142 . − Swift 6 N100414A 1.368 26.497 76.6 ± +29 . − . Fermi 6 A100621A 0.542 63.6 4.37 ± ± ± ± ± +33 . − . Swift 6 A100816A 0.8049 2.9 0.73 ± ± ± +47 . − . Swift 6 A101219A 0.718 0.6 0.49 ± +177 . − Swift 2 N101219B 0.55 34 0.59 ± ± ± ±
239 Swift 8 A110213A 1.46 48 6.9 ± +20 . − . Swift 6 A
Note.
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