Discerning the physical origins of cosmological Gamma-ray bursts based on multiple observational criteria: the cases of z=6.7 GRB 080913, z=8.3 GRB 090423, and some short/hard GRBs
Bing Zhang, Bin-Bin Zhang, Francisco J. Virgili, En-Wei Liang, D. Alexander Kann, Xue-Feng Wu, Daniel Proga, Hou-Jun Lv, Kenji Toma, Peter Meszaros, David N. Burrows, Peter W. A. Roming, Neil Gehrels
aa r X i v : . [ a s t r o - ph . H E ] A ug Preprint typeset using L A TEX style emulateapj v. 08/22/09
DISCERNING THE PHYSICAL ORIGINS OF COSMOLOGICAL GAMMA-RAY BURSTS BASED ONMULTIPLE OBSERVATIONAL CRITERIA: THE CASES OF Z = 6 . Z = 8 . Bing Zhang , Bin-Bin Zhang , Francisco J. Virgili , En-Wei Liang , D. Alexander Kann , Xue-Feng Wu ,Daniel Proga , Hou-Jun Lv , Kenji Toma , Peter M´esz´aros , David N. Burrows , Peter W. A. Roming , NeilGehrels Draft version October 2, 2018
ABSTRACTThe two high-redshift gamma-ray bursts, GRB 080913 at z = 6 . z = 8 . z ≤
1. In order to address their physi-cal origin, we perform a more thorough investigation on two physically distinct types (Type I/II) ofcosmological GRBs and their observational characteristics. We reiterate the definitions of Type I/IIGRBs and then review the following observational criteria and their physical motivations: supernovaassociation, specific star forming rate of the host galaxy, location offset, duration, hardness, spectrallag, statistical correlations, energetics and collimation, afterglow properties, redshift distribution, lu-minosity function, and gravitational wave signature. Contrary to the traditional approach of assigningthe physical category based on the gamma-ray properties (duration, hardness, and spectral lag), wetake an alternative approach to define the Type I and Type II Gold Samples using several criteriathat are more directly related to the GRB progenitors (supernova association, host galaxy type, andspecific star forming rate). We then study the properties of the two Gold Samples and compare themwith the traditional long/soft and short/hard samples. We find that the Type II Gold Sample reason-ably tracks the long/soft population, although it includes several intrinsically short (shorter than 1sin the rest frame) GRBs. The Type I Gold Sample only has 5 GRBs, 4 of which are not strictly shortbut have extended emission. Other short/hard GRBs detected in the Swift era represent the BATSEshort/hard sample well, but it is unclear whether all of them belong to Type I. We suggest that some(probably even most) high-luminosity short/hard GRBs instead belong to Type II. Based on multipleobservational criteria, we suggest that GRB 080913 and GRB 090423 are more likely Type II events.In general, we acknowledge that it is not always straightforward to discern the physical categories ofGRBs, and re-emphasize the importance of invoking multiple observational criteria. We cautiouslypropose an operational procedure to infer the physical origin of a given GRB with available multipleobservational criteria, with various caveats laid out.
Subject headings: gamma-rays: bursts—gamma rays: observations—gamma rays: theory INTRODUCTION
Phenomenologically, gamma-ray bursts (GRBs) havebeen generally classified into the long-duration, soft-spectrum class and the short-duration, hard-spectrumclass in the CGRO/BATSE era based on the bimodaldistribution of GRBs in the duration-hardness diagram(Kouveliotou et al. 1993) . There is no clear boundaryline in this diagram to separate the two populations. Department of Physics and Astronomy, University of NevadaLas Vegas, Las Vegas, NV 89154, USA. Department of Physics, Guangxi University, Guangxi 530004,China. Th¨uringer Landessternwarte Tautenburg, D-07778, Tauten-burg, Germany. Department of Astronomy & Astrophysics, Pennsylvania StateUniversity, University Park, PA 16802, USA. Purple Mountain Observatory, Chinese Academy of Sciences,Nanjing 210008, China. Department of Physics, Pennsylvania State University, Univer-sity Park, PA 16801, USA. NASA Goddard Space Flight Center, Greenbelt, MD 20771,USA. Several analyses have suggested the existence of an inter-mediate duration group (Mukherjee et al. 1998; Horvath 1998;Hakkila et al 2000). However, as discussed in the bulk of the textbelow, there is so far no strong indication of the existence of a
Traditionally, an observer-frame BATSE-band duration T ∼ T >
2s are “long” and bursts with T <
2s are“short”.The journey was long to uncover the physical ori-gins of these two phenomenologically different classesof GRBs. The discoveries and the routine observa-tions of the broad band afterglows of long GRBs re-veal that their host galaxies are typically irregular (ina few cases spiral) galaxies with intense star formation(Fruchter et al. 2006). In a handful of cases these GRBsare firmly associated with Type Ib/c supernovae (e.g.Hjorth et al. 2003; Stanek et al. 2003; Campana et al.2006; Pian et al. 2006). This strongly suggests that theyare likely related to deaths of massive stars. Theoreti-cally, the “collapsar” model of GRBs has been discussedover the years as the standard scenario for long GRBs(Woosley 1993; Pacz´ynski 1998; MacFadyen & Woosley1999; Woosley & Bloom 2006).The breakthrough to understand the nature of some third, physically distinct category of cosmological GRBs based onmultiple observational data. So we will focus on the two mainphenomenological categories of GRBs in the rest of the paper.
Zhang et al.short GRBs was made in 2005 after the launch ofthe Swift satellite (Gehrels et al. 2004). Prompt lo-calizations and deep afterglow searches for a hand-ful of short GRBs (Gehrels et al. 2005; Bloom et al.2006; Fox et al. 2005; Villasenor et al. 2005; Hjorth et al.2005a; Barthelmy et al. 2005a; Berger et al. 2005) sug-gest that some of them are associated with nearby early-type galaxies with little star formation. Deep searchesof associated supernovae from these events all led tonon-detections (e.g. Kann et al. 2008 and referencestherein, see also Appendix for more references). Theseare in stark contrast to the bursts detected in the pre-Swift era (mostly long-duration). On the other hand, theobservations are consistent with (although not a directproof of) the long-sought progenitor models that invokemergers of two compact stellar objects, leading candi-dates being NS-NS and NS-BH systems (Pacz´ynski 1986;Eichler et al. 1989; Pacz´ynski 1991; Narayan et al. 1992).Although the sample with secure host galaxies is small,a general trend in the community is to accept that theBATSE short/hard population bursts are of this compactstar merger origin .The clean dichotomy of the two populations (bothphenomenological and physical) was soon muddled bythe detection of a nearby long-duration GRB with-out SN association (Gehrels et al. 2006; Gal-Yam et al.2006; Fynbo et al. 2006; Della Valle et al. 2006a).GRB 060614 has T ∼ ∼ E p ∝ E / γ,iso relation (Amati et al.2002; Liang et al. 2004) to GRB 060614 and makes itas energetic as GRB 050724, the pseudo-burst wouldbe detected as a marginal short/hard burst by BATSE,and would be very similar to GRB 050724 if detectedby Swift/BAT. In particular, the soft gamma-ray tailwould appear as the “extended emission” detected insome “short/hard” GRBs including GRB 050724. Asecond, much shorter (with T ∼ It is widely accepted that at least a fraction of short/hardGRBs are the giant flares of soft gamma-ray repeaters in nearbygalaxies (Palmer et al. 2005; Tanvir et al. 2005). The observationssuggest that the contribution from such a population is not signif-icant (Nakar et al. 2006), but see Chapman et al. (2009). We donot discuss these bursts in this paper.
In any case, duration and hardness are not neces-sarily reliable indicators of the physical nature of aGRB any more. In order to determine whether ornot a GRB can be associated with a particular phys-ical model, one is forced to appeal to multiple obser-vational criteria (Donaghy et al. 2006). Prompted bythe detection of GRB 060614, we (Zhang et al. 2007b;Zhang 2006) suggested naming the bursts that are con-sistent with the massive-star origin and the compact-star-merger origin models as Type II and Type I, respec-tively , and attempted to invoke a set of multiple obser-vational criteria to judge the physical category of a GRB.A more developed physical categorization scheme wasproposed by Bloom et al. (2008), who also introducedSGR giant-flare-like (non-destructive and likely repeat-ing) events. Within the destructive events, Bloom et al.(2008) agreed that there are two major model types (de-generate and non-degenerate), which correspond to TypeI and Type II in the Zhang et al. (2007b)’s classificationscheme. Throughout this paper we will adopt the nomen-clature of Type I/II to denote the two physically distinctcategories of cosmological GRB models.The recently detected two high- z GRBs, GRB 080913at z = 6 . z = 8 . T / (1 + z )] shorter than 2 seconds,with a hard spectrum typical for short/hard GRBs.This naturally raises the interesting question regard-ing the progenitor system of the burst (Greiner et al.2009a; Perez-Ramirez et al. 2008; Belczynski et al. 2008;Tanvir et al. 2009; Salvaterra et al. 2009). More gener-ally, it again raises the difficult question regarding how touse the observed properties to judge the physical originof a GRB. In this paper, we make some attempts to ad-dress this difficult problem. The structure of the paper isthe following. In §
2, we present the observational prop-erties of GRB 080913 and GRB 090423, and show thatif the identical bursts had occurred at z <
1, they couldhave been recognized as short hard GRBs based on theirobserved properties. In §
3, we comment on the strengthsand weaknesses of classifying GRBs based on physicallymotivated criteria. We then reiterate the definitions ofType I/II GRBs in §
4, and critically review a list of ob-servational criteria as well as their physical motivationsas discussed in the literature. In order to address the pro-found questions of whether “Type I = short/hard/shortlag” and “Type II = long/soft/long lag”, in § a priori based on its gamma-ray properties (duration, hardness, spectral lag), we useseveral observational properties that are more directlyrelevant to the GRB progenitors to define the Gold Sam- The idea was to make a connection to the Type II and TypeIa SNe (not including Type Ib/c), which correspondingly have themassive star and compact star origins, respectively. This is howevernot related to the original definitions of Type II and Type I SNs,which are based on whether or not there are hydrogen lines in thespectrum. hysical origins of GRBs 3ples of Type II and Type I GRBs. We then turn aroundto evaluate the various observational properties (dura-tion, hardness, spectral lag, afterglow properties, empir-ical correlations, etc) of these Gold Samples, and checkwhether these properties are useful criteria to judge thephysical category of the bursts. In §
6, we discuss theintriguing question whether all short/hard GRBs are ofthe Type I origin, and raise the possibility that a fractionof (probably even most) high-luminosity short GRBs areof the Type II origin. We then dedicate § §
8, and cautiously proposean operational procedure to associate a GRB with a spe-cific model based on multiple observational criteria. Ourresults are summarized in § GRB 080913 AND GRB 090423: INTRINSICALLYSHORT/HARD GRBS AT HIGH- Z The light curve of GRB 080913 as detected bySwift/BAT is shown as the black solid curve in Fig.1a.The burst duration T (the time interval during which90% of the fluence is measured) in the BAT (15-150 keV)band is 8 ± E p = 93 ±
56 keV (Greiner et al.2009a). A combined Swift/BAT and Konus/Wind (20-1300 keV) fit using the Band-function spectrum gives E p = 121 +232 − keV (Palshin et al. 2008). Given the mea-sured redshift z = 6 . T rest ∼ E restp ∼
710 keV and E restp ∼
930 keV for the cutoff power law and Band-function spectra, respectively. Although being recog-nized as a long duration burst phenomenologically, thisburst has an intrinsically short duration and an intrinsi-cally hard spectrum.In order to compare this burst with other phenomeno-logically classified short hard GRBs, we simulate a“pseudo” GRB by placing GRB 080913 at z = 1. Weconsider three factors. First, the specific photon flux N ( E p ) at E p is proportional to (1 + z ) /D L , where D L is the luminosity distance. This can be translated to anincrease of a factor of ∼ . N ( E p ) from z = 6 . z = 1. Second, we consider the BAT band (15-150 keV)emission of the pseudo GRB, which corresponds to anenergy band lower by a factor of (1 + 6 . / (1 + 1) ∼ . ∼ .
85 to account for the cosmologi-cal time dilation effect. After applying these transforma-tions, we are able to construct the BAT-band light curveof the pseudo GRB at z = 1 as shown in Fig.1a.GRB 080913 displays a series of early X-ray flares(Greiner et al. 2009a). It is interesting to check whetherthey would show up in the BAT band for the pseudoGRB to mimic the “extended emission” seen in a sub-group of Swift “short/hard” GRBs (Norris & Bonnell2006; Troja et al. 2008) . We therefore manipulate the Rigorously based on the T criterion, the fraction of Swift Fig. 1.—
The simulated 15-150 keV light curves of the pseudoGRBs obtained by placing GRB 080913 and GRB 090423 at z = 1.The red curves display the extrapolated BAT data, and the bluedata points show the extrapolated XRT data. Inset: a comparisonof the light curve of the pseudo GRBs (red) and the observed GRBs(black). (a) GRB 080913; (b) GRB 090423. XRT (Burrows et al. 2005b) data of GRB 080913 to sim-ulate the BAT band extended emission of the pseudoburst. We first extrapolate the GRB 080913 XRT datato the BAT band according to the measured XRT pho-ton spectral index. We then follow the three steps men-tioned above to shift this BAT-band “virtual” emissionto the BAT band emission of the pseudo burst. Thisis shown as blue data points in Fig.1a. By addingthe appropriate noise level for the BAT observation,we show that these extrapolated XRT emission compo-nents stick out the background, which would appear asthe extended emission in the BAT band for the pseudo bursts that have T < T up toseveral 10s to even more than 100 seconds. The current approachin the community is to define a burst “short/hard” if it appearsshort in the BATSE band. A growing trend is to also include somebursts with extended emission even in the BATSE band to the“short/hard” category. Zhang et al.burst. We note that our method is based on the as-sumption of the power law extension of the X-ray flarespectrum (0 . −
10 keV) to the BAT band of the pseudoburst (1 . −
39 keV). On the other hand, since X-rayflares are generally believed to be due to GRB late cen-tral engine activities (Burrows et al. 2005a; Zhang et al.2006; Lazzati & Perna 2007; Chincarini et al. 2007),they may have a Band-function or cutoff power lawspectrum (Falcone et al. 2007). If the E p ’s of the X-ray flares are within or not far above the XRT win-dow, the extrapolated extended emission would be de-graded. We should therefore regard the level of theextended emission of the pseudo burst as an upperlimit. We estimate the BAT-band duration of the pseudoGRB as T (pseudo) ∼ . T (pseudo , EE) ∼
140 s with extended emis-sion. In any case, the observational properties of thispseudo burst are very similar to some “short/hard”GRBs detected in the Swift era. By comparing theflux level of the pseudo GRB with other short/hardGRBs, we find that it belongs to the bright end ofthe short/hard GRB flux distribution, similar to, e.g.GRB 051221A (Burrows et al. 2006; Soderberg et al.2006), GRB 060313 (Roming et al. 2006), GRB 060121(Donaghy et al. 2006), and the recent GRB 090510 de-tected by Fermi LAT/GBM and Swift (Hoversten et al2009; Ohno et al. 2009; Guiriec et al. 2009; Rau et al.2009).GRB 090423 at z = 8 . T ∼ . z = 8 . +0 . − . (Tanvir et al. 2009), the corre-sponding rest-frame duration is ∼ T / (1 + z ) ∼ . E p = 48 . ± . E restp = 451 ± T / (1 + z ), and the duration ofthe corresponding pseuodo GRB at z = 1 is definedas 2 T / (1 + z ). These calculated durations correspondto different energy bands in the rest frame (the sameobserved band after redshifting). Strictly speaking, inorder to derive the durations of the pseudo GRBs inthe observed energy band, one needs to know the time-dependent spectral information, which is not availablefor these bursts. Observationally, pulse widths at highenergies tend to be narrower than those at low ener-gies (Ford et al 1995; Romano et al. 2006; Page et al.2007). An empirical relation w ∝ E − a with a ∼ . w ∝ (1 + z ) − a , which would correspond toa correction factor of (1 + z ) a − rather than (1 + z ) − to derive the intrinsic duration. However, GRB promptemission is usually composed of multiple pulses. Theseparations between the pulses, which are more relevantfor the T definition, may not follow the same energy-dependence of the pulse widths. We therefore do notintroduce this extra correction factor of T throughoutthe paper. For GRB 080913 and GRB 090423, if onetakes the (1 + z ) a − correction factor, the derived in- Fig. 2.—
The T − HR diagram of GRBs. The backgroundorange dots are BATSE GRBs. Overplotted are Type II GoldSample (blue), Type I Gold Sample (red), and other short/hardGRBs (green), mostly detected by Swift. Open symbols are forthe observed values, while the filled symbols are the rest-framevalues. For short GRBs with extended emission, those with theshort spike only are denoted as circles, while those including theextended emission are denoted as squares. The same bursts (withdifferent T with or without extended emission) are connected bylines. GRB 080913, GRB 090423, their pseudo counterparts at z = 1, and their rest-frame counterparts are marked with specialcolors/symbols. trinsic durations are in the marginal regime between thephenomenologically-defined long and short GRBs.Figure 2 displays the locations of GRB 080913, GRB090423, their corresponding pseudo GRBs at z = 1,and their rest-frame counterparts in the traditional T − HR (hardness ratio) two-dimensional distributionplane. Also plotted are the BATSE GRB sample (or-ange), the Gold samples of Type II (blue) and Type I(red) GRBs, and the Other SGRB Sample (green) (see § z ≤ PHENOMENOLOGICAL VS. PHYSICALCLASSIFICATION SCHEMES: WEAKNESSES ANDSTRENGTHS
The eventual goal of GRB studies is to identify thephysical origins of every observed GRB, including its pro-genitor system, central engine, energy dissipation mech-anism, and radiation mechanism. To achieve this goal,a combination of observations and theoreical modeling isneeded. The number of competive models and the al-lowed parameter space steadily reduce as more and moreobservational data are accumulated. This is evident inthe history of GRB studies: while more than 100 mod-els were proposed before 1992 (Nemiroff 1994), only twobroad categories of progenitor models remain competi-tive at the time when this paper is written. A group ofGRBs are hosted by active star-forming dwarf galaxies(Fruchter et al. 2006), some of which have clear (Type Ic)supernova associations (Hjorth et al. 2003; Stanek et al.2003; Campana et al. 2006; Pian et al. 2006). Thispoints towards a massive star origin of this group ofhysical origins of GRBs 5bursts. At least a few bursts were discovered to be as-sociated with galaxies with a very low star forming rate(Gehrels et al. 2005; Bloom et al. 2006; Barthelmy et al.2005a; Berger et al. 2005), which point towards a non-massive-star origin of the bursts, likely due to mergers ofcompact objects. Therefore it is now justified to discussat least two physically distinct categories of GRB modelsas well as how to associate a particular burst with eithercategory based on certain observational criteria.In the literature, some physical classification schemesof GRBs have been discussed (Zhang et al. 2007b;Bloom et al. 2008). Strictly speaking, these are not clas-sifications of GRBs, but are classifications of models thatinterpret GRB data. A scientific classification scheme isbased on statistical formalisms, which make use of a uni-form set of observational data with instrumental biasesproperly corrected, and classify objects based on statisti-cally significant clustering of some measured properties.Examples include to classify supernovae broadly intoType II/I based on whether there are/are not hydrogenlines in the optical spectrum, and to classify GRBs intotwo (Kouveliotou et al. 1993) or three (Mukherjee et al.1998; Horvath 1998) classes based on BATSE T anal-yses. The classes defined by the phenomenological datado not carry physical meanings, and theoretical model-ing is needed to clarify whether different phenomenolog-ical classes of objects are of different physical origins.Compared with the SN classification schemes, which arebased on the “yes/no” criteria regarding the existenceof spectral lines and therefore are relatively insensitiveto the instrumental details, the GRB phenomenolog-ical classification schemes suffer another major draw-back, i.e. every parameter that one can directly mea-sure is strongly instrument-dependent. For example, T is strongly energy-dependent, and sensitivity-dependent,so that a “short” GRB in a hard energy band would be-come a “long” GRB in softer bands or if the detectorsensitivity is increased. The membership of a particularGRB to a particular category (e.g. long vs. short) isnot guaranteed. As a result, such classification schemescannot be compared from one mission to another, andare of limited scientific value.A physical classification scheme, on the other hand,is on theoretical models that interpret the data. As aresult, it suffers the great difficulty of associating a par-ticular burst to a particular model category. In order toachieve the goal, multiple observational criteria are de-manded, but always with non-uniform instrumental se-lection effects. Ideally, with infinitely sensitive detectorsin all wavelengths, it may be possible to derive a setof quantitative observational criteria that can be usedto rigorously associate a particular GRB to a particularmodel category based on statistical properties. However,realistically this is essentially impossible since differentcriteria rely on completely different observational instru-ments with different observational bands and sensitivitieswhich are quite non-uniform. Also different criteria couldcarry different weights in judging the associated modelcategory of a particular burst. The weighting factors ofdifferent criteria are also difficult to quantify. Humaninsights rather than pure statistical analyses are needed.Another drawback of a physical classification scheme isthat it depends on the models, which are subject to fur-ther development as more data are accumulated. The classification criteria are therefore also subject to modi-fication based on data. This can be diminished by invok-ing model-independent criteria as much as possible. Forexample, the Type I/II GRB model classification schemediscussed in this paper only appeals to whether the modelinvokes a degenerate-star or a massive-star, regardless ofthe concrete progenitor systems or energy dissipation andradiation mechanisms (see § §
1) that demand more se-rious investigations of the observational criteria to judgethe physical origin of a particular GRB (i.e. the physicalmodel associated with this GRB).In the rest of the paper, we will discuss Type I/IIGRBs, which are defined as the GRBs that are asso-ciated with two distinct physical models. This is not anew classification scheme of GRBs to replace the exist-ing long/soft vs. short/hard classification scheme, but isa parallel classification of the models that the observedGRBs can be associated with based on multiple crite-ria data analyses. The two approaches are complemen-tary. As discussed above, T is energy-band-dependentand sensitivity-dependent, so that the membership of aparticular GRB to a particular duration category is notalways guaranteed. On the other hand, if adequate infor-mation is retrieved in an ideal observational campaign,the association membership of a particular GRB to aparticular physical model category is almost certain re-gardless of the detector energy band and sensitivity. Forexample, if a SN is detected to be associated with a GRB,one can safely associate this GRB to the Type II modelcategory regardless of its T detected by different detec-tors. TYPE I/II GRBS, THEIR OBSERVATIONAL CRITERIA,AND PHYSICS BEHIND
We reiterate here the definitions of the Type I/IIGRBs. Improving upon the descriptions presented inZhang et al. (2007b), we hereby more rigorously definethe following: • Type I GRBs (or compact star GRBs) are those Zhang et al.GRBs that are associated with the theoreticalmodels invoking destructive explosions in old-population, degenerate, compact stars. The like-liest model candidate is mergers of two compactstars. • Type II GRBs (or massive star GRBs) are thoseGRBs that are associated with the theoreticalmodels invoking destructive explosions in young-population massive stars. The likeliest model can-didate is core collapses of massive stars.Here we do not specify the progenitor systems ofeach model type. In reality, there could be mul-tiple possible progenitor systems within each modelcategory (see also Bloom et al. 2008). Within theType I model category, possible progenitor systems in-clude NS-NS mergers (Pacz´ynski 1986; Eichler et al.1989; Narayan et al. 1992; Rosswog et al. 2003), NS-BHmergers (Pacz´ynski 1991; Faber et al. 2006), and pos-sibly BH-WD or NS-WD mergers (Fryer et al. 1999;King et al. 2007)(c.f. Narayan et al. 2001), see Nakar(2007); Lee & Ramirez-Ruiz (2007) for reviews. On theother hand, within the Type II model category, one mayhave collapses of single stars (i.e. collapsars, Woosley1993; MacFadyen & Woosley 1999), or collapses of mas-sive stars in binary systems (Fryer et al. 2007).The definitions of Type I/II GRBs are based on thephysical models that GRBs can be associated with ratherthan their observational properties. The scheme is there-fore intended to be “operational”. The connections be-tween the physical model properties and the observa-tional criteria are not straightforward, and probably verydifficult for some GRBs.In the following, we review a list of observational cri-teria discussed in the literature that may be applied todifferentiate the two physically distinct model categoriesthat GRBs can be associated with (e.g. Donaghy et al.2006; Zhang et al. 2007b; Zhang 2006), and discuss thephysical justifications of each criterion. As justified be-low, some criteria (e.g. § § § § § § § § § Supernova Association
A positive detection of a supernova (SN) signature as-sociated with a GRB would undoubtedly establish theassociation of the burst with Type II. However, the sam-ple of the robust GRB-SN associations is currently small.Non-detections of a SN signature could be due to multi-ple reasons, e.g., the afterglow is too bright so that theSN light is buried beneath the afterglow level; the fol-low up observations were not “deep” enough or not at the right time window; or the lack of an underlying SNis genuine. Only the last case is helpful to judge thephysical model category of a burst, although the con-clusion is still not clear cut. A genuine SN-less GRB iscertainly consistent with the Type-I origin. However, ithas been discussed in the literature that some core col-lapse GRBs may not eject enough Ni to power a SN(Woosley 1993; Heger et al. 2003; Nagataki et al. 2003,2006; Tominaga et al. 2007), so that the lack of a genuineSN signature may not be evidence completely against theType II origin. On the other hand, we notice that thelarge uncertainties involved in SN explosion physics pre-vent the models from having a definite predictive powerregarding the SN signature. Looking back into the his-tory, the predictions of the SN signature accompanyingGRBs have followed a serpentine (and ironic) path. Thefirst core-collapse GRB model was dubbed “failed super-nova” (Woosley 1993), which predicts no SN signatureassociated with a GRB. Driven by the possible GRB980425/SN 1998bw association, the model was developedto allow a SN associated with a GRB within the “col-lapsar” scheme. According to MacFadyen & Woosley(1999), the model predicts that “collapsars will alwaysmake supernovae similar to SN 1998bw”. Indeed thestatement that “the data and models are consistent with,though not conclusive proof of, the hypothesis that ALLlong-soft GRBs are accompanied by SNe of Type Ic” wasmade right before the discovery of GRB 060614 and GRB060505 (Woosley & Bloom 2006). Would the discovery ofthe SN-less long GRBs (060614 and 060505) then beg fora dichotomy of core-collapse GRBs (one group with andanother group without the SN association)? Althoughthis is certainly plausible, a simpler picture would bethat all genuine SN-less GRBs have the Type I origin.In this paper, we take lacking a genuine SN as a supportto the Type I GRB, but do not take this criterion aloneto define a Type I GRB. On the other hand, since thereis no observational fact that demands the existence ofSN-less Type II GRBs , we do not automatically asso-ciate any genuine SN-less long GRB with the Type II(or Type II candidate) physical model categories unlessthere are other strong supports to the scenario (see § § Star Forming Rate of Host Galaxy
Type II GRBs are related to massive star deaths, sothey must reside in host galaxies with active star for-mation. So star forming rate (SFR), or more rigorously,specific star forming rate (SSFR, i.e. SFR per unit mass)of the host galaxy is a critical parameter to judge themembership of Type II GRBs.On the other hand, compact star mergers can occur inhost galaxies both with and without active star formation(Belczynski et al. 2006; Zheng & Ramirez-Ruiz 2007). Ifwe see a GRB residing in an elliptical or an early typegalaxy, we are more confident that no massive star isinvolved in the event, and that the burst should be as-sociated with Type I. Those Type I GRBs residing in In our opinion, GRB 060614 and GRB 060505 are notsolid Type II candidates. As will be discussed in § hysical origins of GRBs 7star-forming galaxies are more difficult to identify. Dueto the additional time delay required for the two com-pact objects to coalesce, a Type I GRB site is expectedto be more aged than the site with active star formation.As a result, at least some Type I GRBs should preferen-tially reside in the regions with relatively low SSFR inthe star forming host galaxy. On the other hand, thereare channels of fast mergers (Belczynski et al. 2006) thatlead to almost “prompt” mergers of compact stars. Insuch a case, Type I GRBs can reside in high SFR regionswithin star-forming galaxies. Position Offset with Respect to Host Galaxy
A related criterion is the offset of the GRB locationwith respect to the center of the host galaxy. The phys-ical motivation is that Type I GRBs invoke mergers ofbinaries including at least one NS, which likely receiveda “kick” at birth so that the binary system would mi-grate from its original birth location. By the time whenthe two compact stars coalesce, the system should havea large offset from the galaxy center or even be out-side of the host galaxy (Bloom et al. 1999). Indeed sev-eral Gold Sample Type I GRBs show such a property(Gehrels et al. 2005; Bloom et al. 2006; Fox et al. 2005;Berger et al. 2005; Barthelmy et al. 2005a; Troja et al.2008). On the other hand, Type II GRBs explode rightat the location where the progenitor stars are formedand therefore should be in the star forming regions in-side the host galaxy (Bloom et al. 2002). This is ingeneral consistent with the observations of long GRBs(Fruchter et al. 2006). Outliers do exist. For example,GRB 070125 is a long GRB whose birth location is in agalactic halo (Cenko et al. 2008b).Complications arise if a GRB is found not inside anygalaxy. It is difficult to judge whether a GRB is “kicked”out from a nearby host galaxy whose projected image isnear the location of the GRB, or it is associated witha more distant galaxy at high- z . This problem arisesfor a good fraction of short/hard GRBs detected in theSwift era. For example, GRB 060502B was suggestedby Bloom et al. (2007) to be associated with a nearbygalaxy at z = 0 .
287 (with a large angular offset), whileit is included by Berger et al. (2007) as one of the high- z missing-host short/hard GRBs. Duration
Theoretically, we do not know exactly which time scaledefines the GRB duration. In principle there are threetime scales that are relevant. The first one is the durationof the central engine activity t engine . This corresponds tothe accretion time scale of an accretion-powered centralengine model (usually invoking a black hole - torus sys-tem), or the spindown time scale of a spindown-poweredcentral engine model (usually invoking a rapidly rotat-ing millisecond magnetar or a maximally rotating blackhole whose spin energy is tapped via a magnetic torquethrough the Blandford-Znajek mechanism). The secondtime scale is the time scale t jet during which a relativisticjet is launched. In principle there could be epochs dur-ing which a jet is launched, but it is not relativistic ornot relativistic enough to power the observed gamma-rayemission. The third time scale is energy dissipation timescale t dis . Current Swift observations suggest that the GRB prompt emission is “internal” (Zhang et al. 2006).This requires that the relativistic jet dissipates energyinternally before being decelerated by the external cir-cumburst medium. The dissipation could be via internalshocks (Rees & M´esz´aros 1994) or magnetic reconnection(Usov 1992; Thompson 1994). In principle, one can havean active central engine without launching a relativisticjet, or have a relativistic jet without significant dissipa-tion. In general, the observed GRB duration T (whichalso depends on the energy band and the sensitivity limitof the detector) should satisfy T ≤ t dis ≤ t jet ≤ t engine . (1)In most studies, however, T ∼ t engine ∼ t jet ∼ t dis hasbeen assumed.If T is equal to or at least is proportional to t engine ,as is assumed by most central engine modelers, then theduration information may be tied to the progenitor prop-erties of GRBs. In particular, Type II GRB progeni-tors have a massive envelope, which can power a long-duration GRB through accretion. According to the col-lapsar scenario (MacFadyen & Woosley 1999), the dura-tion of the burst is defined by the envelope fallback timescale, which is typically 10s of seconds. The model there-fore suggests that Type II GRBs should typically havelong durations. On the other hand, NS-NS and NS-BHmergers typically have an accretion time scale ∼ T in both longand short GRBs (Zhang et al. 2006; Fan & Wei 2005;Lazzati & Perna 2007). The progenitor and central en-gine models must then be modified to invoke a muchlonger accretion time scale (King et al. 2005; Perna et al.2006; Proga & Zhang 2006), or a non-BH-torus centralengine (Dai et al. 2006; Staff et al. 2007). More im-portantly, several strong Type I GRB candidates (e.g.GRB 050724) are not short, but have softer, extendedemission (Villasenor et al. 2005; Barthelmy et al. 2005a;Norris & Bonnell 2006). The merger models thereforemust be modified to account for this extended emis-sion (Rosswog 2007). Type I GRBs no longer must be“short”.The discussion above only applies to the case whenthe line of sight pierces into the relativistic jet, i.e.the on-beam geometry. In this case, the observedtime scales reflect the time scales at the central engine(Kobayashi et al. 1997). In the case of an off-beam geom- Here we have assumed that T records the GRB internalemission only. This is true for most cases. Occasionally the ob-served prompt emission may also include the emission from the ex-ternal shocks. T should be removed from Eq.(1) for these cases. Zhang et al.etry, i.e. the jet with opening angle θ j is beaming towardsan angle θ v > θ j with respect to the line of sight, theobserved time scale no longer traces that of the centralengine. For a discrete pulse, if the pulse duration solelyreflects the duration of the emission powered by the cen-tral engine, i.e. the rising and falling of the lightcurvereflects the increase and decrease of the central engineluminosity (in constrast to those models that interpretthe decaying wing as the high-latitude emission), the ob-served duration off beam is related to the on-beam valuethrough the ratio of the Doppler factor (given the samecomoving value), i.e. t (off beam) t (on beam) = D ( θ = 0) D ( θ = θ v − θ j ) = 1 − β cos( θ v − θ j )1 − β . (2)where the Doppler factor is defined by D = 1Γ(1 − β cos θ ) , (3)and θ is the angle between the line of sight and the veloc-ity vector of the ejecta, which is taken as the closest ap-proach to the jet ( θ v − θ j ). For multiple emission episodes(i.e. multiple pulses in the light curve), the time intervalof the quiescent episodes do not vary with the viewingdirection. So Eq.(2) applies to the total duration of aGRB only if the prompt emission has one single pulse.Also since the observed flux is lower for a lower D , givena same detector sensitivity, the off-beam T tends to beshorter than that predicted by Eq.(2) due to the limitingflux threshold effect.The off-beam model predicts that the afterglow lightcurve should display a rising behavior initially before the1 / Γ beam enters the line of sight (Panaitescu & M´esz´aros1999; Granot et al. 2002). Broadband observations ofthe majority of GRB afterglows do not show such a sig-nature. So the off-beam geometry, if any, is rare.
Hardness
The connection between the hardness of spectrum andthe GRB progenitor is less direct. It is related to theunknown internal energy dissipation mechanism and ra-diation mechanism, which in turn depends also on thecomposition of the GRB ejecta. GRB spectra are usu-ally categorized as a smoothly-joined power-law, namely,the Band-function (Band et al. 1993). The hardness ofa GRB is likely related to the location of the E p , butthe flatness of the spectral index below E p may alsoplay a role. Theoretically, the spectral slope is moreclosely related to the particle acceleration mechanism(e.g. Sironi, & Spitkovsky 2009) and the “compactness”of the emission region (e.g. Pe’er et al. 2006). The spec-tral peak energy, E p , can be related to the GRB emis-sion model parameters more directly, although model-dependent (Zhang & M´esz´aros 2002a). We will mainlydiscuss the E p models more closely in the following.In general, E p is a function of the burst luminosity L ,the Lorentz factor Γ of the ejecta, and the radius R of theemission site from the central engine. In order to addresswhether a GRB is hard or soft, one needs to specify aparticular emission model. In the following we discussthree internal emission models currently discussed in theliterature. Internal shock model.
Within this model, thegamma-ray E p can be defined either by synchrotron ra-diation or synchrotron self-Compton (SSC). In generalone can write E p ∼ Γ ~ γ ke ( eB ′ /mc ), where k = (2 , B ′ ∝ L / R − Γ − for both the ordered and the randommagnetic field components (Zhang & M´esz´aros 2002a),one has E IS p ∝ γ ke L / R − (1 + z ) − ∝ γ ke L / Γ − δt − (1 + z ) − , (4)where L is the initial kinetic luminosity of the ejecta, δt is the variability time scale of the unsteady GRBejecta wind, and the internal shock radius is R ∼ Γ δt .Note that E p is negatively correlated with the bulkLorentz factor ( ∝ Γ − ), which is contrary to the intu-ition that high Γ bursts should be hard. Here γ e is thecharacteristic Lorentz factor of the electrons that con-tribute to the emission at E p . Under the fast cool-ing condition, which is generally satisfied for internalshocks, γ e corresponds to the minimum “injection” en-ergy of the electrons, which is related to the “relative”Lorentz factor between the two colliding shells Γ fs , i.e. γ e ∝ Γ fs ∼ (Γ f / Γ s + Γ s / Γ f ) /
2, where Γ f and Γ s are theLorentz factors of the fast and slow shells, respectively.If the Γ variation of a flow is proportional to the averageLorentz factor ¯Γ, i.e. ∆Γ ∝ ¯Γ or Γ f / Γ s ∼ const, then γ e essentially does not depend on ¯Γ, so that a higher E p should correspond to a lower Γ. On the other hand, itis possible that high-¯Γ flows may be more variable, e.g.Γ f / Γ s ∝ ¯Γ. If this is the case, then the negative de-pendence on Γ in Eq.(4) is canceled out (for k = 2) orreversed (for k = 4). In the traditional internal shockmodel, the variability time scale δt of the ejecta can bederived from the observation. Analyses of power densityspectra of GRB light curves (Beloborodov et al. 1998)suggest that the GRB temporal behavior may be self-similar, i.e. lacking a characteristic time scale. In thepast, the minimum variability time scale, which can beas small as milliseconds for both short and some long du-ration GRBs, has been adopted to estimate the internalshock radius. Alternatively, it is possible that the rapidvariability in GRB light curves may be caused by othermechanisms, such as relativistic turbulence inside theemission region (Narayan & Kumar 2009). Within thislatter scenario, the outflow variability time scale relevantto internal shocks can be much longer. Physically, Type IGRB outflows may directly carry the variability informa-tion from the inner central engine, i.e. the dynamic timescale of the innermost accretion torus around the blackhole, δt ∼ t dyn ∼ √ π ( GM bh /c ) ∼ M bh / M ⊙ )ms (where M bh is the mass of the black hole), or thespin period of the central magnetar or black hole, δt ∼ P engine ∼ E p for Type I and Type II GRBs basedon Eq.(4). On average, Type I GRBs have an isotropicgamma-ray luminosity L § § δt of Type I may be smallerthan that of Type II by 2-3 orders of magnitude. Thisgives E IS p (I) E IS p (II) ∼ (10 −
30) [ γ ke Γ − (1 + z ) − ](I)[ γ ke Γ − (1 + z ) − ](II) . (5)This suggests that in a large parameter space Type IGRBs can be harder than Type II GRBs. If γ e is similarfor both types, Type I GRBs can be harder than Type IIGRBs as long as their bulk Lorentz factors are not largerthan those of Type II by a factor more than (3 −
5) times.If γ e ∝ Γ, Type I are generally harder than Type II forboth the synchrotron model ( k = 2, regardless of thevalue of Γ), and the SSC model ( k = 4, the E p ratio ispositively dependent on Γ. Theoretically, Type I GRBsshould have higher Γ’s due to their less baryon loadingas compared with Type II GRBs. This favors a harderspectrum of Type I even more for the SSC model. Asystematically smaller redshift z for Type I GRBs (dueto the merger delay with respect to star formation) alsohelps to increase the hardness contrast between the twotypes. In reality, there are large dispersions in L , δt ,Γ, γ e and z in both types. On the other hand, the HRdistribution of the BATSE short/hard vs. long/soft di-chotomy also shows a large dispersion (Fig.2). In general,the statement that Type I GRBs are harder than TypeII GRBs can be made within the internal shock modelsin the statistical sense. For individual bursts, one can-not draw a firm conclusion regarding the hardness of aparticular burst due to the large uncertainties involvedin the parameters. Photosphere model.
The possibility that theobserved GRB emission has a dominant contribu-tion from the fireball photosphere (Thompson 1994;M´esz´aros & Rees 2000; M´esz´aros et al. 2002) has gainedincreasing attention recently (Rees & M´esz´aros 2005;Ryde 2005; Pe’er et al. 2007; Thompson et al. 2007;Ioka et al. 2007; Ghisellini et al. 2007; Ryde & Pe’er2008; Lazzati et al. 2009). In this model, E p is relatedto the observed photosphere temperature T ph . For a“naked” fireball, i.e., a fireball expanding into a vac-uum, the observed photosphere temperature (and hence E p ) depends on whether the photosphere radius R ph isbelow or above the fireball coasting radius R c . For alarge dimensionless entropy of the fireball η ≥ η c ∼ [ L R − , ] / (where R is the initial radius of the fire-ball. Throughout the text the convention Q n = Q/ n isadopted in cgs units.) , the fireball becomes transparentduring the acceleration phase (i.e. R ph < R c ). The ob- This critical entropy is derived (Zhang & M´esz´aros 2002a)within the discrete shell regime, rather than the continuous windregime (M´esz´aros & Rees 2000; M´esz´aros et al. 2002). This is usu-ally justified, since typically one has η > η c in this regime. served fireball temperature is essentially the temperatureat the central engine, i.e. T ph ∼ T , so that E ph, p ∼ kT (1 + z ) − ∼ L / R − / (1 + z ) − . (6)This is the regime discussed in most photosphere mod-els (Thompson 1994; M´esz´aros & Rees 2000; Ryde 2005).On the other hand, if the fireball becomes transparentbeyond the coasting radius ( R ph > R c ), the photospheretemperature drops with radius due to the decrease ofresidual internal energy during the expansion, so that T ph = T ( R c /R ph ) / (M´esz´aros & Rees 2000). Thedetailed parameter dependences are related to whetherthe opacity is defined by a discrete shell or a continu-ous outflow wind (M´esz´aros et al. 2002). For the former( η c < η < η c , where η c ∼ L R − , ] / ), one has(Zhang & M´esz´aros 2002a) E ph, p ∼ L − / R − / Γ(1 + z ) − . (7)For the latter ( η < η c ), one has E ph, p ∼ L − / R / Γ / (1 + z ) − . (8)If additional energy dissipation occurs at small radii, pairproduction can occur which enhances photon opacity andincreases the photosphere radius (M´esz´aros et al. 2002;Rees & M´esz´aros 2005). We note that the “naked” fire-ball scenario is more relevant to Type I GRBs.With the presence of a stellar envelope, the photo-sphere emission of a Type II GRB is likely modified.Due to continuous energy dissipation and heating insidethe envelope, the jet cannot reach the maximum Lorentzfactor but instead stores a significant energy in heat be-fore erupting out from the envelope. Effectively, theGRB fireball “central engine” is moved from the centralblack hole or magnetar to the location slightly below thestellar envelope (Thompson 2006; Thompson et al. 2007;Ghisellini et al. 2007). The jet at this radius R ∼ R ∗ has a moderate Lorentz factor Γ ∗ and a comoving tem-perature T ′∗ ∼ ( L/ π Γ ∗ R σ ) / , and an observer frametemperature T ∗ = Γ ∗ T ′∗ . As the jet erupts out from theenvelope, it will undergo rapid acceleration under its ownthermal pressure. If R ∗ is greater than photosphere ra-dius for a naked central engine, the fireball would becometransparent shortly after exiting the star due to the rapidfall of density. So the real photosphere radius is essen-tially R ph ∼ R ∗ , and R ph < R c is always guaranteed.The peak energy E p is defined by T ph = T ∗ . This leadsto a variation of Eq.(6) in the form of E ph, ′ p ∼ L / Γ / ∗ R − / ∗ (1 + z ) − . (9)Within the photosphere models, it is not obvious whyType I GRBs should be systematically harder than TypeII GRBs. The trend, if any, should be opposite. Thelogic is the following. First, given the same parametersof L , R and z , one typically has E ph, p > E ph, p > E ph, p (e.g. Eq.(24) of Zhang & M´esz´aros 2002a). Next, thestellar envelope effectively “raises” the photosphere forType II GRBs, so Eqs.(7) and (8) are usually not rele-vant. One therefore may only compare the case of Eq.(6)for the two types of GRB, since Eq.(9) can be related toEq.(6) through R = R ∗ / Γ ∗ . Equation (6) suggests that0 Zhang et al.Type I GRBs, typically with smaller L , should be softerthan Type II GRBs at the same redshift. A smaller z forType I GRBs may compensate their softness, but in gen-eral it is not straightforward to claim that Type I GRBsshould be systematically harder than Type II GRBs forthe photosphere model. Pairs may lower the photospheretemperatures of some high- L GRBs (especially for TypeII), which may help to account for the observed trend,but no handy analytical formula is available to performdirect comparisons.The recent Fermi-detected GRB 080916C (Abdo et al.2009) showed a series of featureless Band-function spec-tra. The expected photosphere emission component ismissing, suggesting a Poynting flux dominated flow atthe base of the central engine (Zhang & Pe’er 2009). Atleast for this burst, the observed E p is not the thermalpeak of the photosphere emission. Magnetic dissipation model.
Finally, if theGRB outflow is Poynting flux dominated (Usov1992; M´esz´aros & Rees 1997; Spruit et al. 2001;Lyutikov & Blandford 2003; Liang & Noguchi 2009),the characteristic frequency of emission would take a dif-ferent form and have different dependences on the ejectaparameters. The locations of the magnetic reconnectionregions are unknown. If dissipation occurs at small radii,the effect is to modify the photosphere emission throughcontinuous heating (Giannios 2008). This is effectivelya photosphere model, which has been discussed above.Alternatively, a Poynting-flux-dominated outflow canreach a global dissipation at a large radius where theMHD approximation is broken (Usov 1994; Spruit et al.2001; Zhang & M´esz´aros 2002a; Lyutikov & Blandford2003).Lacking a macroscopic reconnection model, E p in thereconnection model is difficult to calculate. Under differ-ent assumptions, the expression of E p may take differentforms. For example, in a random electric/magnetic fieldin the magnetic reconnection region, electron accelera-tion may be balanced by radiation cooling. The typicalelectron Lorentz factor is therefore γ e ∝ B − / . Thesynchrotron peak energy may be then expressed in theform of (Zhang & M´esz´aros 2002a) E magp ∝ Γ(1 + z ) − , (10)which depends on Γ and z only. Type I GRBs can thenbe harder than Type II GRBs, again because Type IGRBs tend to have a cleaner environment, and hence,less baryon loading, than Type II GRBs.Similar to the duration discussion ( § E p is smaller by a factorof the Doppler factor ratio (Eq.[2]). This effect has beendiscussed by, e.g. Yamazaki et al. (2004b). Spectral Lag
Soft GRB emission usually arrives later than hardemission in some GRBs. This “spectral lag” is evident forlong-duration GRBs (Norris et al. 2000; Gehrels et al.2006; Liang et al. 2006), but is typically negligible forshort-duration GRBs (Norris & Bonnell 2006; Yi et al.2006). Usually, the lag may be visualized as the timedifferences of the peaks of the “same” pulse in differentenergy bands. Statistically it can be derived through a cross-correlation analysis of the pulse profiles in differentenergy bands (Norris et al. 2000). Technically, what isusually measured is the lag time ∆ t between two BATSE(or Swift BAT) bands E and E + ∆ E . Mathematically,this corresponds to | R E +∆ EE ( dt/dE ) dE | . It is thereforeimportant to study dt/dE (or dE/dt ) in theoretical mod-els.Theoretically, the leading model of the spectral lag isthe “kinetic” effect, i.e. the delay is due to the fact thatthe observer is looking at the increasing latitudes withrespect to the line of sight with time (e.g. Salmonson2000; Ioka & Nakamura 2001; Norris & Bonnell 2006;Shen et al. 2005; Lu et al. 2006). One can derive thespectral lag within this model as follows. Since the cool-ing time scale in the GRB emission region is very short,one may assume that the decay of GRB pulses is dom-inated by this high-latitude “curvature” effect. The co-moving emissivity is assumed to be uniform everywhereacross the conical jet. Softer emission comes from higherlatitudes (due to their smaller Doppler factor) and there-fore is delayed by a time t ∼ (1 + z )( R GRB /c )(1 − cos θ )with respect to the emission from the line of sight, where θ is the angle from the line of sight. The observed pho-ton energy is related to the comoving one via E = D E ′ ,where D is the Doppler factor [Eq.(3)]. One thereforehas dEdt = cE ′ R GRB (1 + z ) d D d ( − cos θ )= − cE ′ β (1 + z ) R GRB
Γ(1 − β cos θ ) . (11)The negative sign denotes “lag”, i.e. increasing E (harder) corresponds to a decreasing arrival time t (ear-lier). When θ → dEdt = − cE ′ Γ (1 + z ) R GRB = − E ′ (1 + z ) τ Γ = −
21 + z Eτ , (12)where τ = R GRB c (13)is the angular spreading time, which could be relatedto the observed half width (in the decaying wing) of theGRB pulse . Notice that R GRB is a value one cannot di-rectly measure, therefore in the above expression it needsto be combined with Γ to derive τ , leaving only onepower in the Γ-dependence in Eq.(12). Another com-ment for this expression is that dE/dt is E -dependent,i.e. for the same GRB pulse, the lag between E and( E + ∆ E ) should be different from that between E and ( E + ∆ E ). This can be understood with Eq.(11)by noticing that different E corresponds to different D ,and hence, different θ . For θ > dE/dt takes a differ-ent form than Eq.(12), which is valid for the hardest (onaxis) pulse. In principle, τ is the upper limit of the observed half widthin the decaying wing, since part of the tail may be buried beneaththe next rising pulse. hysical origins of GRBs 11One can immediately draw the following inference fromEq.(12). Since dE/dt ∼ E/τ , one can get the lag ∆ t ∼ τ if one takes ∆ E ∼ E . This is to say, the lag time iscomparable to the pulse width itself. So spectral lags donot carry direct information of the progenitor. On theother hand, since pulse width can be related to variabil-ity time scale, which may be related to the physical types( § τ are typi-cally much smaller than those of Type II GRBs, whosevariability time scales are longer due to the additionalmodulation of the stellar envelope. One therefore mayexpect that Type I GRBs have shorter lags than TypeII GRBs. This is consistent with the fact that short du-ration GRBs (preferentially Type I) have negligible lags,while long duration GRBs (preferentially Type II) havelong lags.Another commonly discussed argument is that TypeI GRBs may have larger Γ’s than Type II GRBs (dueto a “cleaner” environment with less baryon loading),and that this might be the origin of short lags (e.g.Norris & Bonnell 2006). According to Eq.(12), one canargue (cid:12)(cid:12)(cid:12)(cid:12) dtdE (cid:12)(cid:12)(cid:12)(cid:12) ∝ . (14)if different bursts have similar τ and E ′ (see alsoShen et al. 2005). However, the two assumptions (same τ and E ′ ) lack physical justifications. In particular, E ′ depends on the dissipation mechanism and the proper-ties (e.g. B field strength) in the dissipation region,which depends on the burst parameters such as L , δt ,etc. Although the central engine variability time scales( τ ) may be arguably similar within the Type I or TypeII category, respectively, they are considerably differentbetween the two types. We therefore conclude that theLorentz factor argument is not robust. Type I GRBs canhave larger Γ’s, but it is not the main reason for theirshort spectral lags.A major issue of such a kinetic (high-latitude cur-vature effect) model is that the peak flux of thepulse drops rapidly with angle (Fenimore et al. 1996;Kumar & Panaitescu 2000), so that the flux is expectedto be too low in softer bands to interpret the observedflux. None of the previous kinetic modelers (Salmonson2000; Ioka & Nakamura 2001; Shen et al. 2005; Lu et al.2006) have seriously confronted the flux predictions withthe data (although the timing data have been well inter-preted by the models). One way to increase the high-latitude flux is to invoke a non-power-law instantaneousspectrum at the end of internal emission (e.g. at theshock crossing time in the internal shock model), e.g.a power law with exponential cutoff (Zhang et al. 2009)or a Band function (Qin 2008). The curvature effectof these models predicts that the spectral peak sweepsacross different energy bands, making the flux not dropas rapidly as in the case of a power law spectrum. In-deed, GRB 060218 can be modeled by an evolving cutoff Notice that this is different from Norris & Bonnell (2006) whoargued ∆ t ∝ Γ − / based on the expression of the angular spread-ing time rather than based on the differential property dE/dt asdiscussed in this paper. power law (Campana et al. 2006), and GRB 050814 canbe modeled by the curvature effect model invoking a cut-off power law spectrum (Zhang et al. 2009). However,the light curve for a given band is always a decay func-tion unless the spectral index before E p is much flatterthan -1. This is not supported by the spectral data ofmost GRBs. One is then obliged to abandon the hypoth-esis of a uniform jet. A structured jet with a less energyand/or a lower Lorentz factor at large angles from the jetaxis and with the line of sight piercing into the wing ofthe structured jet (Zhang & M´esz´aros 2002b; Rossi et al.2002; Zhang et al. 2004) can be invoked to account forthe observed spectral lag data.In reality, there might be additional mechanisms thatare related to the observed spectral lags of GRBs, butthe kinetic effect must exist, and may play the dominantrole to define spectral lags in most GRBs. Statistical Correlations
Observationally, some empirical correlations amongseveral observed quantities have been claimed (see e.g.Zhang 2007 for a summary). Most of these correlationswere discovered for long/soft GRBs. Here we discuss twoof them that are potentially related to Type I/II diver-sity.
Amati (Yonetoku) relation.
Statistically, more en-ergetic long GRBs are harder. This is usually expressedin terms of E p (1 + z ) ∝ E / γ,iso (Amati et al. 2002) and E p (1 + z ) ∝ L / γ,iso (Yonetoku et al. 2004). The dis-persions of the correlations are large, and outliers doexist (e.g. the nearby GRB 980425/SN 1998bw is anoutlier of the Amati-relation). It has been argued thatthe observed correlations are solely due to some selec-tion effects (Nakar & Piran 2005; Band & Preece 2005;Butler et al. 2007). However, the fact that the correla-tions are valid for most z -known GRBs which cover fivedecades in isotropic energy (Sakamoto et al. 2006) sug-gest that there is likely underlying physics that drivessuch correlations.Inspecting the expressions of E p in various GRBprompt emission models discussed in § E p is indeed generally a function of L , it is usually alsoa function of other parameters, in particular, the bulkLorentz factor Γ which is usually not directly measured.In order to interpret the Amati/Yonetoku relations, oneneeds to introduce a rough dependence between Γ and L .We now again discuss the three prompt emission modelsand investigate how the correlations may be interpretedwithin each model. • For the internal shock models, the Am-ati/Yonetoku relations require that γ ke r − isroughly constant. If γ e is roughly constant, thenthe internal shock radius should be similar fordifferent bursts. This suggests that Γ is essentiallyindependent of L (since the variability time scalemay be similar among Type II GRBs), a require-ment not immediately evident based on physicalarguments. Alternatively, if γ e ∝ Γ, the relationcan be naturally satisfied for the synchrotronmodel ( k = 2). This suggests that high-¯Γ GRBsare more variable. In other words, while the2 Zhang et al.maximum Lorentz factor of the outflows Γ M canvary from burst to burst, the minimum Lorentzfactors Γ m for different bursts are similar to eachother, so that γ e ∝ (Γ M / Γ m ) ∝ ¯Γ. • Within the photosphere model, the most relevantregime for Type II GRBs is the one with a stel-lar envelope (Eq.[9]). An interpretation of theAmati/Yonetoku relation can be made (Thompson2006; Thompson et al. 2007) by introducing an-other assumption that the total energy of dif-ferent GRB jets is quasi-universal, a conclusionreached in the pre-Swift era (Frail et al. 2001;Bloom et al. 2003). Recent Swift observationssuggest that the “achromatic” behavior, the de-manded characteristic of a jet break, is not com-monly seen (Liang et al. 2008). This raises the is-sue of interpreting some afterglow temporal breaksas jet breaks. Furthermore, the inferred totalenergies (after beaming correction) are found toa have larger scatter than the pre-Swift sam-ple (Liang et al. 2008; Kocevski & Butler 2008;Racusin et al. 2009). In any case, if one be-lieves E γ = E γ,iso θ j ∼ const, using the argu-ment that baryon sheath near the breakout ra-dius leads to Γ ∗ ∼ θ − j ∝ E / γ,iso (Thompson 2006;Thompson et al. 2007), one can translate Eq.(9)into E p ∝ L / γ,iso ∝ E / γ,iso by taking the triv-ial proportionality L ∝ L γ,iso ∝ E γ,iso . Thefirst proportionality is based on the fact thatthe GRB efficiency is not a function of L γ,iso (Lloyd-Ronning & Zhang 2004); while the secondproportionality is based on the fact that the dis-persion of T is not large and that T is not cor-related to L γ,iso . In view of the fact that GRB080916C disfavors the photosphere origin of E p (Zhang & Pe’er 2009), we regard this interpreta-tion as no longer attractive. • The magnetic dissipation model lacks a robust pre-diction for E p . In any case, similar to the othertwo models, the Amati/Yonetoku relation can besatisfied if one assigns a particular Γ − L correla-tion. For example, the specific model described inEq.(10) requires Γ ∝ L / .When the optical afterglow light curve temporal break( t opt ) is included, a tighter correlation involving E p and E γ,iso is obtained (Ghirlanda et al. 2004; Liang & Zhang2005) for some long duration GRBs. However, the phys-ical connections between the prompt emission properties( E p and E γ,iso ) and the afterglow properties ( t opt ) or theglobal collimation degree of the jet are not straightfor-wardly expected. Furthermore, optical afterglow tempo-ral break data of Type I GRBs are still poor to draw anyconclusion. We therefore do not discuss these relationsin this paper. Luminosity-lag relation.
Norris et al. (2000) dis-covered a relation between the gamma-ray peak luminos-ity L pγ,iso and the spectral lag ∆ t between the BATSEChannel 1 (25-50 keV) and Channel 3 (100-300 keV),i.e. L pγ,iso ∝ (∆ t ) − . . The relation was refined byGehrels et al. (2006) who corrected the observed spec- tral lag to that between two common bands in the cos-mic proper rest frame of GRBs. This correction takestwo steps. First, the observed spectral lag ∆ t betweenthe bands from E to ( E + ∆ E ) can be expressed as∆ t = ∆ t rest ( E rest )(1 + z ), where ∆ t rest ( E rest ) is thespectral lag between E rest to ( E rest + ∆ E rest ) in thecosmic proper rest frame. Second, what one cares aboutis the intrinsic spectral lag between a common rest frameenergy interval, e.g. from E to ( E + ∆ E ). One needs anadditional relation between ∆ t rest ( E ) and ∆ t rest ( E rest ).There is no universal relation for this, but there is anempirical relation between pulse width and energy, i.e.the pulses become narrower with energy with w ∝ E − a with a ∼ (0 . − .
4) (Fenimore et al. 1995; Norris et al.2005; Liang et al. 2006; Zhang & Qin 2008).
Assumingthat the spectral lag is proportional to the pulse width (see e.g. Norris et al. 2005), one may derive ∆ t rest ( E ) =∆ t rest ( E rest )( E/E rest ) − a = ∆ t rest ( E rest )(1 + z ) a . Thisfinally gives ∆ t rest ( E ) = ∆ t ( E )(1 + z ) a − . (15)In Gehrels et al. (2006), a ∼ / L pγ,iso ∝ [∆ t (1 + z ) a − ] − δ ∝ (cid:20) ∆ t (1 + z ) / (cid:21) − δ (16)is found for a sample of long GRBs, with δ ∼
1. Outliersdo exist for long GRBs, and short GRBs are noticeablyoff the track of the correlation.Is there an underlying physical mechanism that jus-tifies the observed L pγ,iso ∝ (∆ t rest ) − δ correlation? Itis not obvious based on the theoretical arguments above.According to Eq.(12), the intrinsic lag is related to the in-trinsic variability time scale of the burst. So a L − lag neg-ative relation may be related to another, probably moreintrinsic L − V positive relation, where V is the variabil-ity parameter. Technically, there are different definitionsof the variability parameter (Fenimore & Ramirez-Ruiz2000; Reichart et al. 2001; Guidorzi et al. 2006), but inany case, a more variable light curve (high V ) wouldhave shorter variability time scales (corresponding to τ ),and hence, shorter spectral lags (∆ t ). Observationally,indeed a positive L − V relation is observed, althoughwith a large scatter (Fenimore & Ramirez-Ruiz 2000;Reichart et al. 2001; Guidorzi et al. 2006). The interpre-tation of this correlation within the internal shock modelinvokes several assumptions: (1) The smallest variabil-ity time scale is defined by the collisions above the pairphotosphere; (2) The true jet energy is quasi-universal(Frail et al. 2001); (3) Narrower jets have higher Γ’s(Kobayashi et al. 2002; M´esz´aros et al. 2002) . Thisis a relevant interpretation to the observed L pγ,iso ∝ (∆ t rest ) − δ relation. However, in view of the assump-tions invoked in the reasoning (the above three as well asthe assumption that the w − E correlation is similar to∆ t − E correlation as invoked earlier), we expect that thecorrelation should not be very tight, and may not followthe same simple power law. This is consistent with the The third assumption may be in conflict with the explanationof the Amati/Yonetoku relation within the standard internal shockmodel as discussed in § L (and hence, on θ ). hysical origins of GRBs 13data (see § L pγ,iso ∝ (∆ t rest ) − δ correlation invokes varying Doppler factors among dif-ferent bursts (Salmonson 2000; Ioka & Nakamura 2001).These models assume a universal comoving propertiesof ALL GRBs, and invoke the off-beam geometry to in-terpret longer durations and spectral lags. As alreadydiscussed, the comoving properties of GRBs depend onmany parameters. The off-beam model is not supportedby early afterglow observations. We therefore regardthese early models invoking pure geometrical effects asno longer favorable in view of the recent observationalprogress. Energetics and Beaming
Type II GRBs are generally expected to be more en-ergetic than Type I GRBs. In the standard BH-toruscentral engine model, the total energy of the burst ispositively correlated with the total available fuel in thetorus. Massive stars are much more abundant in mass,which can reach ∼ M ⊙ of fuel in total. On the otherhand, a NS-NS merger system has a total energy budgetof ∼ . M ⊙ . After the prompt collapse, the availablefuel in the torus is of order ∼ . M ⊙ . A BH-NS mergersystem has even less fuel to begin with ( ∼ . M ⊙ ). Itwould reach a similar total energy budget in accretion asthe NS-NS system. In these models, Type I GRBs areexpected to be 10-100 times less energetic than Type IIGRBs. Alternatively, GRBs may be powered by the spinenergy of the central object (a rapidly spinning BH orNS). For the case of a NS central engine, Type I GRBsmay reach similar energies as Type II GRBs. For thecase of a BH engine whose spin energy is extracted via amagnetic torque (Blandford & Znajek 1977; Li 2002), aType II GRB is again expected to be ∼
10 times moreenergetic than a Type I GRB if it is powered by a NS-NS merger, again because of the more massive BH in theType II GRB. A BH-NS merger Type I GRB, on theother hand, may reach the same energetics as Type IIGRBs if the initial BH in the binary system is massiveenough and has a large enough angular momentum.In order to relate this theoretically motivated total en-ergy budget to the observed energy, one needs to in-troduce the beaming factor. The standard GRB jetmodels invoke a conical jet with uniform energy dis-tribution (M´esz´aros et al. 1998; Rhoads 1999; Sari et al.1999). More complicated (maybe more realistic) jet mod-els invoke distributions of jet energy with angle from thejet axis (M´esz´aros et al. 1998; Zhang & M´esz´aros 2002b;Rossi et al. 2002; Zhang et al. 2004). Theoretically, itis difficult to model how jets are launched from thecentral engine. On the other hand, one can speculateabout the collimation angle of jets from two types ofGRBs from the theoretical point of view: Type II GRBsshould tend to have narrower jets than Type I GRBs due to the additional collimation of the stellar enve-lope (Zhang et al. 2003). Type I GRB jets tend to bebroader (Aloy et al. 2005). Observationally this predic-tion has not been tested statistically. Observations ofsome individual bursts seem to support this picture. Forexample, the Type I Gold Sample burst GRB 050724was found to have a beaming angle wider than ∼ o (Grupe et al. 2006; Malesani et al. 2007). Type II GRBson the other hand, have a typical beaming angle of ∼ o (Frail et al. 2001; Bloom et al. 2003; Liang et al. 2008;Kocevski & Butler 2008; Racusin et al. 2009). Oppositecases are also observed in some GRBs. For example, theshort GRB 051221 (a Type I candidate) has a narrowjet with θ j ∼ o − o (Burrows et al. 2006). This is con-trary to the theoretical expectation if it is indeed a TypeI GRB. On the other hand, the Type II GRB 060729(Grupe et al. 2007, 2009a) may have a large opening an-gle since its X-ray afterglow keeps decaying without abreak for hundreds of days.The observed “isotropic” energy is the total energy di-vided by the beaming factor (2 · πθ j / π = θ j / ∼ (20 / ∼
15 difference in thebeaming factor, the isotropic energy of a typical Type IGRB should be a factor ∼ − Afterglow Properties
Broadband afterglow emission has been interpreted asthe external forward shock emission as the fireball is de-celerated by the circumburst medium. An ideal observa-tional campaign can lead to diagnostics of the circum-burst medium properties (Panaitescu & Kumar 2002;Yost et al. 2003), which can shed light on the progenitorsystem of the GRB (e.g. Fan et al. 2005; Greiner et al.2009a; Xu et al. 2009). In particular, if a stratifiedstellar-wind-type medium ( n ∝ R − ) (Dai & Lu 1998;Chevalier & Li 2000) is identified, the burst can be iden-tified as a Type II GRB. The case of a constant densitymedium is, however, less informative. Although Type IGRBs are expected to reside in such a medium, someGold-Sample Type II GRBs have been found to reside ina constant medium as well (Panaitescu & Kumar 2002;Yost et al. 2003). The mechanism of forming such amedium before the death of the massive star is unknown.In any case, one needs more information to establish theassociation of a burst with a physical model categoryif it goes off in a constant density medium. For exam-ple, the afterglow luminosity of Type I GRBs should besystematically lower than that of Type II GRBs due tothe expectation of both a lower medium density in themerger environment (relevant for ν < ν c ) and a system-atically lower blastwave energy (Panaitescu et al. 2001;Fan et al. 2005; Kann et al. 2008). A Type I GRB can beeven “naked” (i.e. no detectable afterglow) if the ambientmedium density is low enough. Such GRBs are indeed4 Zhang et al.observed (e.g. GRB 051210, La Parola et al. 2006).A related issue is the GRB radiative efficiency. Ob-servations and theoretical modeling suggest that the ef-ficiency is similar for both Type I and Type II GRBs(Zhang et al. 2007a; Berger 2007; Gehrels et al. 2008),so that it cannot be regarded as a useful criterion to tellthe model category that is associated with a particularGRB. Redshift Distribution
Statistically, redshift distributions of Type I and TypeII GRBs should be different. Type II GRBs generallytrace the star-forming history of the universe . Type IGRBs are expected to be “delayed” with respect to starformation due to the long merger time scale asociatedwith the shrinking of the binary orbits due to gravita-tional radiation (Belczynski et al. 2006). On average, itis expected that the mean redshift of Type I GRBs islower than that of Type II GRBs. Luminosity Function
The luminosity function of long duration GRBs iscategorized by a broken power law with a break ∼ erg s − (Guetta et al. 2005; Liang et al. 2007;Virgili et al. 2009a). Below the break the power law in-dex is > −
1, while above the break the power law index is < −
2. Low luminosity GRBs may form a distinct bumpat
L < erg s − (Liang et al. 2007; Virgili et al.2009a; Dai 2009). As argued below, most long GRBsare Type II GRBs, so this luminosity function may beregarded as that of Type II GRBs. There is however nodirect theoretical reason for such a luminosity function.For Type I GRBs, the luminosity function has not beenstudied in detail due to the limited sample with redshiftmeasurements so far (but see Virgili et al. 2009b). Theluminosity function of the BATSE short/hard GRB sam-ple was studied (Guetta & Piran 2006), but as discussedbelow, it is not justified that this population is identi-cal to the Type I population. This issue will be furtherdiscussed in § § Gravitation Wave Signals
Probably the most definite criterion to differentiateType I GRBs from Type II GRBs is through detect-ing their gravitational wave (GW) signals. Althoughthe GW signature of a Type II GRB is highly uncer-tain (e.g. Kobayashi & M´esz´aros 2003), the wave formsof NS-NS and NS-BH mergers are well predicted (e.g.Dalal et al. 2006). Detections of these signals would un-ambiguously associate some GRBs to the Type I modelcategory. However, this criterion can only be appliedin the future when the GW detectors reach the desiredsensitivities. TYPE I AND TYPE II SAMPLES AND THEIRSTATISTICAL PROPERTIES
Sample selection
The above consideration suggests that theoreticallythere is no handy, distinct criterion that can be used to Metallicity may play additional role to select Type II GRBs(e.g. Wolf & Podsiadlowski 2007; Nuzaet al. 2007; Li 2008), butthe issue is inconclusive. immediately determine the physical model category thata burst is associated with. In this section, we attemptto explore the topic further from the observational pointof view. The current standard approach is to use threecriteria, “duration”, “hardness”, and (when available)“spectral lag”, to categorize bursts as “long” (implic-itly assumed to be associated with “Type II”) or “short”(implicitly assumed to be associated with “Type I”), anduse these samples to explore the statistical properties ofother observational properties (e.g. Nakar 2007; Berger2009). In other words, it is often implicitly assumed thatLong / soft / long lag = Type IIShort / hard / short lag = Type I . (17)The problem with such an approach is that these crite-ria may not be always reliable. A notable example wasGRB 060614, which is a long GRB but is very likely as-sociated with Type I (Gehrels et al. 2006; Zhang et al.2007b). Another complication is related to GRB 080913,GRB 090423, and some other intrinsically short GRBs(e.g. Levan et al. 2007). These GRBs can be detectedas short/hard GRBs if their redshifts were low enough,but their physical properties are more close to those ofType II GRBs. Some short/hard GRBs (e.g. 060121, deUgarte Postigo et al. 2006) are very energetic, which arenot easy to be accommodated within the Type I progen-itor models.In this paper, we adopt an alternative approach. In-stead of sticking to the observed gamma-ray properties,we adopt the observational criteria that are directly re-lated to the progenitor systems to select the samples, andthen go back to investigate the other properties (includ-ing duration, hardness, spectral lag, etc) of the samples.
The advantage of this approach is that we can start withthose GRBs whose progenitor systems are more confi-dently inferred. We can then use them to verify whetherthe ansatz Eq.(17) is justified.We define the following three samples based on thecriteria detailed below.
Type II Gold Sample.
This sample is defined suchthat at least one of the following two criteria are satisi-fied.1. There is a spectrally confirmed SN association withthe GRB;2. The specific star forming rate (SSFR) is very high(to be specific, the SSFR satisfies log SSFR > − . > .
63 Gyr − in the sample of Savaglio etal. 2009); the GRB location does not have a largeoffset from the center; and there is no stringentupper limit on the existence of a SN associated withthe GRB.Notice that the GRB properties (duration, hardness andlag) are not the considerations to define the sample.Since not many GRBs have host SSFR information pub-lished, this sample is by no means complete, and thereshould be many more Type II GRBs that are not in-cluded. The purpose of selecting this sample is to usethe most stringent criteria to investigate how the bestType II GRB candidates look like. As a result, we donot include the GRBs that have a claimed SN bumpin the optical light curve but no confirmed SN spec-hysical origins of GRBs 15troscopic signature. The threshold of SSFR is arbi-trary. This limiting value was chosen because Table 11 ofSavaglio et al. (2009) has a mix of long and short GRBsfor log SSFR(Gpc − ) < − .
3, which is the regime whereconfusion arises. The lower bound log SSFR > − . > . .This sample should be expanded significantly later whenthe host galaxy information of the Swift GRBs is re-leased. Right now the Type II Gold Sample includes33 GRBs (Table 1 Top Panel). This is already a largeenough sample to study the statistical properties of TypeII GRBs. Type I Gold Sample.
The Gold Sample of TypeI GRBs is defined by at least one of the following twocriteria.1. The host galaxy is elliptical or early type;2. The GRB location has a relatively low local SSFR,or a large offset from the center of the host galaxy;and deep searches reveal stringent upper limits onthe existence of an underlying SN.Again the GRB properties (duration, hardness, lag) arenot considered. Some arguments (Belczynski et al. 2006;Zheng & Ramirez-Ruiz 2007) have suggested that a frac-tion of Type I GRBs may be located in star forming re-gions of star forming galaxies. Our criteria do not selectthose, since we do not demand completeness of sample se-lection. After systematically checking the archival data,we only identify 5 bursts in the Type I Gold Sample:GRBs 050509B, 050709, 050724, 060614 , and 061006(Table 1 Middle Panel). The details of individual GRBsare presented in the Appendix. Other SGRB Sample.
Most short/hard GRBs inthe Swift era satisfy neither of the two criteria of theType I Gold Sample. Some of them do not have theirhost galaxies convincingly identified. Others have hostgalaxies with active star formation. These GRBs areusually regarded as Type I candidates simply becausethey are “short/hard”. There could be a good fractionof Type I GRBs in this sample, but we are not sure thatthey can ALL be associated with Type I. Since we define Besides those included in the Savaglio et al. (2009) sample(which covers from GRB 970228 to GRB 061126), we only in-clude GRB 080520 and GRB 060602A based on the SFR criterion.They have a high SFR (though SSFR is not measured) typicalfor other Type II Gold sample GRB host galaxies. For example,GRB 080520 has ∼ M ⊙ yr − (Malesani et al. 2008), which iscomparable to the highest in the Savaglio et al. (2009) sample. In the literature GRB 060614 is usually taken as a contro-versial candidate for Type I. This was mainly because of its longduration. We do not consider duration as a criterion when select-ing the Gold Sample. This burst satisfies the criterion the Gold Samples not based on the GRB properties, weleave these bursts in a separate sample, without speci-fying whether they are associated with Type I or TypeII. There are 20 bursts in this sample (Table 1 BottomPanel). The details of individual GRBs are presented inthe Appendix.
Duration-Hardness Distribution
Figure 2 presents the traditional T -hardness ratio(HR) plot of GRBs. Superimposed on the BATSE data(orange small dots) are the three samples defined above:Type II Gold Sample (blue), Type I Gold Sample (red),and other SGRB sample (green). The HR is defined asthe fluence ratio between (50-100) keV and (25-50) keV.For BATSE bursts, this corresponds to the fluence ratiobetween channel 2 and channel 1. For other detectors(HETE-2, Swift/BAT, Konus/Wind, INTEGRAL) withdifferent detector energy bands, we perform spectral fitsand use the fitted model to derive the HR. Besides theobserved points (open symbols), we also plot the cor-responding “rest-frame” points (filled symbols) for eachburst. The HR is then defined as the flux ratio betweenthe rest-frame (50-100) keV band and (25-50) keV bands,which is again derived from spectral fitting. For a powerlaw fit, the rest frame HR is the same as the observedone. For a curved spectrum (e.g. a Band function or anexponential cutoff power law), the two can be different.The T values are energy- and detector-dependent. Wedo not make efforts to convert all T to the BATSE-band, since this requires time-dependent spectral anal-yses and extrapolations, and for many bursts the dataquality is not sufficient to perform such an analysis. In-stead we simply plot T measured by different detectors(e.g. Swift and HETE). The correction to the BATSE-band T is usually not significant for most long GRBs,but could be significant to those GRBs with soft ex-tended emission. Traditionally, the “rest frame” T arenot used to defined long vs. short for a particular GRB.We present them here just to show how the intrinsic dis-tribution may differ from the observed one. To derive therest-frame T rest , we simply divide the observed value by(1 + z ). More rigorously one needs to again take into ac-count the light curve evolution with energy. This againrequires a time-dependent spectral analysis. Since mostbursts do not have such detailed information, and sincethe correction would not be significant for most bursts,we neglect this correction for the sake of simplicity anduniformity. For short GRBs with extended emission, weuse circles to denote the short spikes only (excluding theextended emission), while using squares to denote the fullemission with extended emission included. These two lo-cations for the same burst with and without extendedemission are connected by lines. Since the mean HR isderived, the HRs including extended emission are usuallysmaller than those without, as the extended emission istypically softer than the initial short spikes.From Fig.2 one can make the following interesting ob-servations. First, the Type II GRBs are generally long,and they well represent the long/soft population of theBATSE GRBs in the T -HR plane. However, some TypeII GRBs have a duration close to the 2-second separationline, and their intrinsic duration can be shorter than 2 s(e.g. GRB 040924 with T = 2 . ± .
24 s at z = 0 . T = 2 . ± .
67 at z = 1 . four out of fiveType I Gold Sample GRBs are not strictly “short” . Ex-cept GRB 050509B, all the others have extended emissionaside from the initial “short/hard” spike. The spike it-self is longer than 2 s for GRB 050724 and GRB 060614. All 5 Type-I Gold Sample bursts have a moderate HR.None has an extremely hard spectrum.
Thirdly, theOther SGRB Sample fills in the short/hard region in the T − HR diagram more uniformly, suggesting that it rep-resents the BATSE short/hard sample well. Some burstsin the sample also have extended emission.
Empirical correlations
Figure 3a displays the E p − E γ,iso (Amati) relation ofthe three samples. The spectral parameters are collectedfrom the published papers or GCN circular reports (seeTable 1 for references). For those GRBs with extendedemission (including Type I Gold Sample GRBs 050724,060614, and 061006), we only consider the short hardspikes. For all the bursts, the isotropic gamma-ray en-ergy ( E γ,iso ) is calculated in the GRB rest-frame 1 − keV band through extrapolation based on the spectralparameters. We can see that most GRBs in the Type IIGold Sample indeed follow the E p ∝ E / γ,iso (Amati) rela-tion. However, there are three noticeable outliers: GRB980425, GRB 031203, and GRB 050826. The first twoare nearby low-luminosity (LL) GRBs, which have beenargued to be from a distinct population (e.g. Liang et al.2007; Virgili et al. 2009a; Dai 2009). Another nearbyLL GRB 060218 is a soft burst (Campana et al. 2006)and satisfies the Amati-relation well. GRB 050826 with T ∼
35 s is an intermediate Type II GRB betweenthe more “classical” Type II and the nearby LL-GRBs(Kann et al. 2007), and deviates from the relation. Wealso pay special attention to the two intrinsically shortType II GRBs. Although GRB 040924 is right on theAmati-relation track, GRB 080520 seems to be slightlyoff the track. The Type I Gold Sample and the OtherSGRB Sample are populated above the conventionalAmati-relation track. Since many short/hard GRBs have E p outside the BAT band, their E p error bars are large.The values in our analyses are adopted from Butler et al.(2007). In any case, it seems that they follow a sepa-rate track with a shallower slope than the Amati-relation.Excluding GRBs 080913, 090423 and 060121 (which arelikely Type II, see § σ limits of the slope as (0.15-0.53) (see Fig.3a). GRB080913 is marginally within the 3 σ regions for the Type IIAmati-relation, but is also consistent with this new trackdefined by Type I and other short/hard GRBs within 3 σ .GRB 090423 aligns with the Type II Amati-relation moreclosely (see also Lin et al. 2009).A likely reason that the Type I and the Other SGRBSamples deviate from the Amati relation of Type IIGRBs is simply because they have shorter durationsso that they have smaller E γ,iso values than the TypeII GRBs with a similar E p . To test this, we plot the E p − L pγ,iso relation (Yonetoku relation) in Fig.3b. Wecan see that the distinction between Type II and TypeI GRBs becomes less significant, although the corre-lation now has a much larger scatter. Noticing the E p ( + z ) / k e V E iso / erg Fig. 3.— (a) The E p − E γ,iso diagram of the three samples ofGRB discussed in the paper: Type II Gold Sample (blue), Type IGold Sample (red), and other short/hard GRBs (green). Two pos-sible redshifts z = 4 . , . E p − E γ,iso correlations for both Type II andType I/Other SGRB samples are plotted (solid lines) with the 3 σ boundary (dashed line) marked. (b) The E p − L pγ,iso diagram. Thesame convention has been used. large error bars of the Type I and Other SGRB Sam-ples, one may conclude that there is no distinct differ-ence among the three samples as far as the Yonetokurelation is concerned. A similar conclusion was drawnby Ghirlanda et al. (2009) in an anaylsis of the BATSEGRBs.Figure 4a displays the luminosity-spectral lag dia-gram of GRBs with the three samples plotted. Agroup of Gold Sample Type II GRBs indeed define a L pγ,iso ∝ (∆ t rest ) − δ correlation track (Norris et al. 2000;Gehrels et al. 2006), although several low-luminosity,long-lag GRBs lie below the extrapolation of the track(see also Gehrels et al. 2006; Liang et al. 2006). GoldSample Type I GRBs are clustered at the lower left cor-hysical origins of GRBs 17ner. This is as expected: short durations define shortlags, and smaller energy budgets define lower luminosi-ties. About half of the “Other SGRBs” are clusteredclose to the Type I Gold Sample, suggesting that theymay be associated with Type I as well. Some others fill inthe gap between the Type I and Type II Gold Samples.In particular, GRB 060121 lies right on the track for bothputative redshifts 1.7 and 4.6 (de Ugarte Postigo et al.2006). GRB 070714B is also close to the track. TheSN-less GRB 060505 clusters with other nearby low-luminosity Type II GRBs. Finally, the two high- z GRBs080913 (notice that only the upper limit of spectral lagis derived) and 090423 are consistent with satisfying the L pγ,iso − lag correlation of Type II, but are also consistentwith the zero-lag trend of Type I/Other SGRB.As discussed in § § T / (1 + z ) − lag / (1 + z ) / diagram of the threesamples of bursts. Again points of the same burst withand without extended emission are connected by lines.We investigate a possible correlation between durationand spectral lag. Since the spectral lags are defined forthe short/hard spikes only for those GRBs with extendedemission, we use T excluding the extended emission forthose bursts. A positive correlation between T and lagwith slope 0 . ± .
14 is obtained, with the Spearman’srank correlation coefficient r = 0 . P < − . This is consistent withour naive expectation, suggesting that spectral lags areclosely related to durations, and may not carry additionalinformation in defining the categories of GRBs. Luminosity and Redshift Distributions
Figure 5(a) and (b) display the observed 2-dimensionalluminosity-redshift ( L pγ,iso − z ) and energy-redshift( E γ,iso − z ) distributions of the three samples. GRBsin the Type I Gold Sample are all at z < .
5. Includ-ing the Other SGRB Sample, the upper boundary of z reaches ∼ z ∼
1. In terms of luminosity distribution, theType II GRBs on average are ∼ L pγ,iso ∼ . × erg s − (for the Type I Gold GRB 061006). Including the OtherSGRB Sample, several short GRBs (070714B, proba-bly 060313, and especially the latest GRB 090510) canreach L pγ,iso ∼ erg s − . GRB 060121 even reaches L pγ,iso ∼ − erg s − for the two fiducial redshifts Fig. 4.— (a) The L pγ,iso − lag diagram. Same convention asFig.3 is adopted. GRB 080913 and GRB 090423 satisfy both thecorrelation defined by Type II GRBs and the “zero lag” trend de-fined by Type I and Other SGRB Samples. Two possible redshifts z = 4 . , . − T (intrinsic) diagram of the three samples. The same GRBswith/without extended emission is connected by dotted lines. Thespectral lags of these GRBs are for the short/hard spikes only. Apositive correlation between duration and spectral lag is derived(dashed line). See text for details. in discussion. This luminosity is high even for Type IIGRBs. GRB 080913 has L pγ,iso ∼ . × erg s − .GRB 090423 has L pγ,iso ∼ . × erg s − (Nava et al.2009). Both are moderate to high luminosities for TypeII GRBs, and are very high when compared with theType I and Other SGRB Samples (except for GRB060121). In the E γ,iso − z diagram, the separation be-tween Type II and Type I is more distinct, with mostSGRB sample bursts lying below the Type II distribu-tion. But GRB 080913 and GRB 090423 become moder-ate in the Type II Sample due to their intrinsically shortdurations. The clearer separation between Type II andType I/Other SGRB Samples is mainly due to the short8 Zhang et al. Fig. 5.— (a) The L pγ,iso − z diagram, and (b) the E γ,iso − z diagram of the three samples. The same convention as Fig.3 isadopted. duration of the SGRB sample, which makes them lessenergetic. However, GRB 060121 is still as energetic asthe average Type II GRBs. Afterglow Properties
Figures 6 and 7 present the intrinsic afterglow lightcurves in the X-ray and optical bands for the three sam-ples. Figure 6 presents the rest-frame 2 keV specific lu-minosity light curves. Since many Type II Gold Sam-ple GRBs are pre-Swift, we do not have many TypeII X-ray light curves. The ones that are plotted in-clude two low luminosity GRBs (060218 and 050826) andtwo intermediate-to-high luminosity GRBs (080520 and050525A). These do not fully represent the Type II GRBX-ray afterglow properties. In order to compensate forthis weakness of sample selection, we also overplot theX-ray light curves of a group of early Swift long GRBsin the sample of Nousek et al. (2006). Since we alreadydemonstrated that the Type II Gold Sample representsthe BATSE long GRBs well, we assume that the Nousek
Fig. 6.—
The rest frame 2 keV X-ray afterglow luminosity lightcurves of GRB 080913, GRB 090423, and the three samples. Allbursts are placed at z = 1. The color scheme is the same as inthe other figures. Since most Type II Gold Sample bursts are pre-Swift ones and have no X-ray light curves, we also add the z -knownlong GRBs in the sample of Nousek et al. (2006) (grey), which aregenerally believed to be Type II GRBs. GRB 080913 and GRB090423 (cyan) both have bright X-ray afterglows typical of TypeII GRBs. GRB 090423
Type II GRB Afterglows Type I GRB Afterglows Other Short-Hard GRB Afterglows Afterglows of GRB 080913 and GRB 090423 C o rr ec t e d R c m a gn i t ud e ass u m i ng z = t (days after burst in the observer frame assuming z = 1) GRB 080913
Fig. 7.—
The rest frame optical light curves of GRB 080913,GRB 090423, and the three samples. The color scheme is the sameas in the other figures. Similar to Kann et al. (2007, 2008), theyare plotted at a common redshift of z = 1. As with the X-raylight curves (Fig. 6), the optical afterglows of the Type II GoldSample GRBs are clearly more luminous than those of the TypeI Gold Sample and the Other Short-Hard Sample. The latter twopopulations are in good agreement with each other. GRB 060121is the single short-hard GRB which is optically highly luminous.GRB 080913 and GRB 090423 both have bright optical afterglowstypical of Type II GRBs. Sample represents the Type II GRB X-ray afterglowswell. We can see that these bursts occupy the upperportion of the light curve space in Fig.6. By contrast,the Type I Gold Sample occupy the lower portion, andthe Other SGRB Sample populate in between with muchhysical origins of GRBs 19overlap with both Gold Samples. Low luminosity TypeII GRBs have luminosities comparable to Type I GoldSample GRBs.Figure 7 presents the optical light curves with cor-rected R c -magnitude by moving all GRBs to z = 1(Kann et al. 2007, 2008). One big difference betweenthese optical light curves and the X-ray light curves(Fig. 6) is that most Type II GRBs are represented,exceptions being those GRBs that had negligible opti-cal afterglows but strong supernovae signatures (GRBs980425, 031203, and XRF 060218), dark GRBs, wherethe optical emission was probably totally supressed byline-of-sight extinction in the host galaxy (GRBs 990506,000210, 020819B, 051022), and some with very sparse op-tical data (XRF 020903, GRBs 030528, 050826, 060602A,080520). Most data have been taken from Kann et al.(2007, 2008), where the methods of creating the intrin-sic light curves are also presented. Similar to the X-raylight curves, the Type II GRB afterglows form a muchmore luminous group than the Type I GRB afterglows(Kann et al. 2008). The light curves of Type I GoldGRBs and those of most Other SGRBs overlap, indicat-ing that they are likely drawn from the same population.The most prominent exception is again GRB 060121 withan optically luminous afterglow (see Kann et al. 2008, formore details), which is comparable to the afterglows ofType II GRBs.For both X-ray and optical afterglows, GRB 080913and GRB 090423 have a luminosity comparable to orhigher than the average luminosity of the Type II GRBafterglows (Greiner et al. 2009a; Salvaterra et al. 2009;Tanvir et al. 2009). NATURE OF SHORT/HARD GRBS
Based on the theoretical considerations and the statis-tical analyses presented above, in this section we attemptto address the question whether the ansatz Eq.(17) isvalid, i.e. whether Type II GRBs are simply associatedwith “long/soft/long lag” GRBs while Type I GRBs aresimply associated with “short/hard/short lag” GRBs. Inparticular, we will address the nature of the Other SGRBSample. It is likely that some (maybe many) GRBs inthe Other SGRB Sample are associated with Type I. Thequestion is whether they are ALL associated with TypeI.
Are all short/hard GRBs associated with Type I?
The most straightforward possibility is to accept thatall short/hard GRBs are associated with Type I GRBs.Inspecting the Other SGRB Sample, one may raisethe following arguments in support of this suggestion:(1) They indeed occupy the short/hard domain of theBATSE T -HR diagram, which is in distinct contrast toType II GRBs that predominantly occupy the long/softdomain; (2) Most of them deviate from the E p − E γ,iso relation and the L pγ,iso − lag relation for Type II GRBs;(3) The redshift and luminosity distributions of the ob-served sample are different from those of Type II, al-though with much overlap; (4) The afterglow luminosi-ties are systematically lower than those of the Type IImajority, although with some overlap. However, as dis-cussed below, there are reasons to be suspicious of thisstraightforward conclusion. Are some short/hard GRBs associated with TypeII?
The fact that some Type II Gold Sample GRBs are in-trinsically short naturally raises the possibility that theobserved short/hard GRBs are contaminated by TypeII GRBs. A small contamination is expected given theoverlapping log-normal distributions of T for the twopopulations. A more intriguing possibility is that thecontamination is not the simple extension of the T dis-tributions, but accounts for a good fraction of the ob-served short/hard GRBs.Conservatively speaking none of the 4 arguments dis-cussed in § < / L short GRBs in star-forming galaxies may instead be Type II GRBs. For ex-ample, GRB 060121 (de Ugarte Postigo et al. 2006) has E γ,iso = 2 . × erg and L γ,p,iso = 3 . × erg s − for z = 4 . E γ,iso = 4 . × erg and L γ,p,iso =2 . × erg s − for z = 1 .
7. These energy values aretypical for Type II GRBs, and the luminosity values evenbelong to the bright end of the Type II distribution. Itsoptical afterglow luminosity is also typical for Type IIand much brighter than those of the Type I Gold sample.Given the possible redshifts, this burst lies right on theAmati-relation and the luminosity-spectral lag relationsof most Type II GRBs (see Figs.[3] and [4]). GRB 060313(Roming et al. 2006), whose z ≤ .
1, can have E γ,iso ∼ . × erg s − for z = 1. Some afterglow light curvefeatures (e.g. the very shallow decay of the UVOT,Roming et al. 2005, light curve with flickering features)are hard to accommodate within the merger scenarios.GRB 061201 also shows a very flat early light curve(Stratta et al. 2007) in both X-ray and optical bands,0 Zhang et al.with the first clear X-ray “plateau” appearing in a shortGRB. Some models (e.g. Kumar et al. 2008) attribute X-ray plateaus to the signature of massive star accretion.Within such a scenario, GRB 061201 is then a TypeII candidate. GRB 060121 also shows strong tempo-ral variability in the afterglow (de Ugarte Postigo et al.2006), similar to GRB 060313. Even for the not veryenergetic short/hard GRB 051221A, its identity as aType I GRB is not unquestionable. Its host galaxyhas log(SSFR)= 0 . E γ ∼ × ergs. This is smaller than but not far offfrom the E γ distribution of Type II GRBs (Frail et al.2001; Bloom et al. 2003; Liang et al. 2008; Racusin et al.2009), and it is also much higher than some other TypeI GRBs (e.g. GRB 050509B with E γ,iso ∼ . × ergs, Gehrels et al. 2005). Although a low den-sity n ∼ − − − cm − was inferred from afterglowmodeling (Soderberg et al. 2006; Burrows et al. 2006), itstill belongs to the reasonable n -range of other TypeII GRBs (Panaitescu & Kumar 2001, 2002; Yost et al.2003). The recent short/hard GRB 090510 detectedby both Swift and Fermi (GBM/LAT) (Hoversten et al2009; Ohno et al. 2009; Guiriec et al. 2009; Rau et al.2009) is also located in a star forming host galaxy,and has an inferred total (collimation-corrected) jetgamma-ray and kinetic energies (assuming n ∼ − ) E γ /E k ∼ erg. It is again not far-off fromthe E γ /E K distributions of Type II GRBs (Frail et al.2001; Bloom et al. 2003; Liang et al. 2008; Racusin et al.2009), and a Type II origin is possible. Finally,Nysewander et al. (2009) pointed out that the optical-to-X-ray flux ratios of short GRBs are quite similar to thoseof long GRBs, suggesting a similar circumburst mediumdensity for the two populations. This is consistent withmost short GRBs being associated with Type II.Another strong argument for the Type-II associationof some (even many) short GRBs is related to luminos-ity function analyses. Following the similar methodol-ogy of modeling L − z distribution of Type II GRBsin Virgili et al. (2009a), Virgili et al. (2009b) have stud-ied the required luminosity function of Type I GRBs inorder to reproduce the observed L − z distribution forboth Type I and Other SGRB samples. The results sug-gest that the underlying luminosity function (defined as N ( L ) dL ∝ L − q ) must be very shallow (e.g. q ∼ .
5) inorder to reproduce the L − z distribution data. This shal-low luminosity function is different from Type II GRBsand other astrophysical objects. A more severe problemis that it cannot reproduce the observed log N − log P distribution of BATSE short/hard GRBs. This appar-ent conflict disfavors the hypothesis that all short/hardGRBs are associated with Type I.Theoretically, the duration of a GRB is defined byEq.(1). We now discuss the three relevant time scalesin turn and address how a short GRB can in principle beassociated with Type II.Firstly, recent studies of the collapsar model suggestthat the engine time scale t engine may not be always long.According to the standard collapsar model (Woosley 1993; MacFadyen & Woosley 1999; Proga et al. 2003), t engine can last as long as the fallback material from thecollapsar envelope is available to fuel the accretion diskor torus. However, one should bear in mind that therotating torus may form only when the specific angu-lar momentum of the accreting gas is higher than theso-called critical specific angular momentum value, i.e. l crit = 2 R g c , where R g is the gravitational radius. Notethat l crit is proportional to the mass of the BH. Duringthe collapsar evolution the mass accretion rate is veryhigh, therefore the BH mass and consequently the crit-ical angular momentum increase very fast. As a result,the specific angular momentum of the rotating material,which was initially sufficient for the torus formation (i.e.,when the BH was just formed), may become insufficientat a later stage of the collapsar evolution when the BHmass increases. Janiuk & Proga (2008) showed that thesimple, often cited, estimates of the total mass avail-able for torus formation and consequently the duration ofa GRB (MacFadyen & Woosley 1999; Proga et al. 2003)are only upper limits. They revised these estimates bytaking into account the long term effect so that as theBH accretes the minimum specific angular momentumneeded for torus formation increases. These new esti-mates predict a significant (an order of magnitude) re-duction of the total energy and overall duration of thecentral engine t engine because only a fraction of the ro-tating stellar envelope can form a torus.If a Type II GRB is powered by the black hole spin(Blandford & Znajek 1977) rather than accretion, t engine of a Type II GRB can be also short, since accretion of ma-terials with a very low specific angular momentum wouldslow down the BH and consequently suppress the jet pro-duction. The interplay among the BH mass, BH spinparameter, and the critical specific angular momentumof accreting gas needed for the torus to form have beendiscussed by Janiuk et al. (2008). They studied severaldifferent cases and reached the conclusion that depend-ing on the parameter settings, t engine can be as short asa second.Secondly, the time scale during which a relativistic jetis launched ( t jet ) may be in principle shorter than thecentral engine activity time scale ( t engine ). There is noworking baryon-loading model for GRBs, and it is notclear how a clean, high entropy outflow is launched. Forexample, if the engine power has several episodes andthe power in the earlier episodes is not high enough,the earlier jet may be choked or be launched but witha heavy baryon loading. The ejecta may therefore be-come a “dirty” fireball. The GRB episode is then onlyrelated to the late “clean” fireball phase when baryonloading is reduced.Thirdly, energy dissipation is needed to convertother forms (kinetic and magnetic) of energy to ra-diation (Rees & M´esz´aros 1992; M´esz´aros et al. 1993;Rees & M´esz´aros 1994; Thompson 1994). For a baryonicfireball, a steady outflow may not generate significantinternal, non-thermal emission without internal shocks.The energy dissipation time scale ( t dis ) can be smallerthan t jet . This gives an additional room to reduce theduration of Type II GRBs.Finally, some other possibilities of producing shortGRBs from collapsars have been proposed in the pre-Swift era. For example, Zhang et al. (2003) proposedhysical origins of GRBs 21that a short/hard pulse of gamma-ray emission may beassociated with eruption of the fireball from the stellarenvelope. Yamazaki et al. (2004a) envisioned a geomet-ric model to unify long and short GRBs based on a line-of-sight effect. The original pictures proposed in thesepapers are no longer supported by the current data, butsome ideas may be borrowed to associate short GRBswith Type II model category. Is there a “Type III” model category?
The current data do not demand the existence of athird type of GRB models to be associated with cos-mological GRBs , i.e. those neither associated withmassive star deaths nor compact star mergers. How-ever, the possibility is not ruled out by the data, ei-ther. Some “hostless” short GRBs (Berger 2009), somelong GRBs without X-ray afterglows (Vetere et al. 2008),and the SN-less long-duration, low-energy GRB 060505(Fynbo et al. 2006; Ofek et al. 2007; Th¨one et al. 2008;McBreen et al. 2008; Kann et al. 2008) are oddballs thatmay hold the clues to identify possible new model cate-gories of GRBs. NATURE OF GRB 080913 AND GRB 090423
We now discuss the possible origin of GRB 080913 at z = 6 . z = 8 .
3. We mainly focus onGRB 080913. The case of GRB 090423 is amazingly sim-ilar to GRB 080913, and the conclusion for GRB 080913can be directly applied to GRB 090423 as well.
Prompt properties and empirical correlations
As discussed in § T , bothbursts are “long” and therefore may be associated withType II according to the ansatz Eq.(17). However, theassociation of a particular GRB to a particular physicalmodel type should not have a z -dependence. The identi-cal burst, if it have occured at z <
1, would be recognizedas a short/hard GRB, and hence, a Type I candidate ac-cording to the ansatz Eq.(17). So it is not straightfor-ward to determine the physical model category a GRBshould be associated with based on the observed T -HRdata.We inspect the compliance of GRB 080913 and GRB090423 with the empirical correlations. First, they areconsistent with the E p − E γ,iso Amati-relation (Fig.3),although GRB 080913 is near the 3 σ upper boundary.This has been regarded as one argument in support of theType II origin of GRB 080913 by Greiner et al. (2009a).On the other hand, GRB 080913 is also consistent withthe new track defined by Type I and short/hard GRBswithin 3 σ . This suggests that the possibility that it isa Type I GRB (or at least similar to other short/hardGRBs) is not ruled out based on this criterion. The com-pliance of GRB 090423 with the Amati-relation is morerobust. Second, inspecting the L pγ,iso − lag correlation, itseems that both GRB 080913 and GRB 090423 are con-sistent with being Type II GRBs - this was another argu- Again “cosmological GRBs” do not include SGR giant flaresthat are believed to account for a small fraction of short/hardGRBs. ment by Greiner et al. (2009a). However, both GRBs arealso consistent with the “zero-lag” trend of short GRBs.In conclusion, based on statistical properties, bothGRBs can be taken as good Type II candidates. How-ever, the criterion based on empirical correlations is notrobust enough to claim the case, and supports from othercriteria (see below) are needed to draw firmer conclu-sions.
Afterglow properties
The rest-frame broadband (X-ray and optical) after-glow luminosities of GRB 080913 are moderate, brack-eted between those of Type II and Type I Gold Sampels(Fig.6 and Fig.7). Although the early luminosities arerelatively low, a distinct energy injection episode raisesthe afterglow luminosity level of this burst to those ofType II at later epochs. Greiner et al. (2009a) have mod-eled the afterglow and suggested that the light curves areconsistent with the deceleration of a relativistic jet by adense circumburst medium with constant density. Thedata are consistent with the existence of an achromaticplateau in X-ray and several optical/IR bands, which canbe interpreted within the framework of a continuouslyfed forward shock. Alternatively, the X-ray rebrighten-ing around 10 s may be due to an X-ray flare, whosesofter emission may also account for the rebrightening inthe IR/optical bands.Improving upon Greiner et al. (2009a), we have per-formed a more detailed numerical modeling of the broad-band afterglow data. The optical emission can be wellmodeled by standard synchrotron radiation from the for-ward shock, while the X-ray emission is likely dominatedby the synchrotron self-Compton emission (SSC). Thefollowing parameters can fit the optical data well (al-though we do not apply a parameter search to judgewhether this is the best fit): the initial isotropic kineticenergy of the fireball E K,iso ∼ . × erg, the am-bient density n ∼ − . the electron equiparti-tion parameter ǫ e ∼ .
04, the magnetic field equipar-tition parameter ǫ B ∼ − , and the electron spectralindex p ∼ .
2. If the late rebrightening is interpretedas an energy injection from the central engine with atime-dependent luminosity L = L ( t/t ) q , the data areconsistent with t ∼ . × s, L ∼ . × erg s − , q ∼ t < t , and q ≤ − t > t . In any case,a high-density constant medium is needed. This is con-sistent with the expectation at high- z (Gou et al. 2004)as well as the fitted density of GRB 050904 at z = 6 . θ j > .
22 rad, which corre-sponds to a geometrically-corrected total gamma-ray en-ergy E γ > . × ergs, and a geometrically-correctedtotal kinetic energy E K > . × ergs. This valueis consistent with those of Type II GRBs (Frail et al.2001; Bloom et al. 2003; Liang et al. 2008; Racusin et al.2009). This is probably the strongest argument in favorof associating the burst with Type II.GRB 090423 has even brighter X-ray and optical af-terglow luminosities than GRB 080913. Although wedid not perform detailed afterglow modeling, the after-glow parameters favor those of Type II GRBs, similar toGRB 080913.2 Zhang et al. Short Type II or high- z Type I?
Since the discovery of GRB 080913, there hasbeen a debate about its progenitor. As discussedabove, data analyses and theoretical modeling sug-gest that GRB 080913 is very likely a Type II GRB(Greiner et al. 2009a), although a Type I association(Perez-Ramirez et al. 2008; Belczynski et al. 2008) isnot ruled out. The evidence in support of the TypeII origin of GRB 080913 includes: large values ofthe geometrically-corrected gamma-ray ( E γ ) and kinetic( E K ) energies, moderately bright intrinsic afterglow lu-minosities, a required high density of the circumburstmedium, and the marginal compliance of the E p − E γ,iso relation of Type II GRBs.On the other hand, if GRB 080913 were a high- z Type I GRB, as suggested by its intrinsically short du-ration, it would have to be an energetic merger event,likely due to a BH-NS merger with a rapidly rotat-ing massive BH. The energy tapping mechanism wouldhave to be the Blandford & Znajek (1977) mechanism(Perez-Ramirez et al. 2008). For this possibility, onerequires that during the short age of the Universe at z = 6 .
7, i.e. τ ∼ . × yr for the concor-dance universe, a BH-NS system is formed and merged.Belczynski et al. (2008) have modeled this possibility indetail, and claimed that the event rates for massive starcore collapses that give rise to Type II GRBs and for com-pact star mergers (both NS-NS and BH-NS) are compa-rable at z = 6 .
7. They concluded that both scenarios arepossible. However, there are several factors that wouldchange this conclusion. First, Belczynski et al. (2008)assumed that all the mergers give rise to GRBs. In real-ity it may be that only a fraction of mergers give rise toGRBs. This fraction factor may be calibrated throughconfronting the observed number ratio of Type I andType II GRBs with the model predictions. In the cur-rent population synthesis models, this factor is not takeninto account (K. Belczynski, 2008, personal communica-tion). Secondly, GRB 080913 would be a high-luminosityType I GRB if it is associated with that category. Con-sidering the power law luminosity function inferred forType I GRBs (Virgili et al. 2009b), detecting one high- L event would demand many more low- L events, whichwould require a significant increase of the required eventrate of compact star mergers that is inconsistent withthe results of population synthesis. Finally, as we ar-gued above, the large value of the geometrically-correctedgamma-ray and afterglow energies do not favor a NS-NSmerger model. Only BH-NS mergers with a highly spin-ning BH should be counted. This would greatly reducethe theoretically predicted event rate that satisfies theconstraint.The detection of GRB 090423, another intrinsicallyshort/hard, high- z , high- L GRB, strongly supports aType II association of both GRB 080913 and GRB090423. As argued above, the probability of detectinga high- L Type I event at high- z is much smaller thanthat of detecting a moderate- L Type II event. With oneevent, one may still argue for a chance coincidence. Withthe detection of GRB 090423, the chance probability ofdetecting two high- L merger events at high- z is greatlyreduced, and one can more firmly associate both GRBswith Type II. With two intrinsically short high- z Type II GRBs de-tected, one must ask why these events tend to existat high- z . One possibility would be that it is simplya threshold selection effect. Both events have moder-ate gamma-ray luminosities, and were detected not farabove the threshold. It is possible that there exists othersofter pulses that are below the sensitivity threshold ofSwift/BAT (J. S. Bloom, 2009, private communication).On the other hand, such softer emission would be easilydetected by Swift/XRT if it was indeed there. Both GRB080913 and GRB 090423 have X-ray flares. However, ex-trapolating them into the gamma-ray band using a sim-ple spectral model suggests that they would appear aslow-level extended emission of short GRBs (Fig.1). Onemay still argue for missing soft emission before the XRTslew. This is not ruled out, but the XRT slew time cor-responds to a rest frame time 99.5/7.7=12.9 s for GRB080913 and 72.5/9.3=7.8 s for GRB 090423. The intrin-sic T ’s have to be in any case smaller than these valuesfor these bursts.A more intriguing possibility would be that this is dueto a physical origin and reflects the intrinsic property ofthe high- z massive stars. These high- z stars may not bespinning as rapidly as their low- z sisters, so that only asmaller mass is left after the prompt collapse. More high- z GRB data are needed to test whether such a scenariois demanded by the data. HOW TO ASSOCIATE A BURST WITH A PHYSICALMODEL CATEGORY?
The extensive discussion presented above suggests thatit is not always easy to associate a particular GRB toa particular physical model category based on observa-tional criteria. The multiple observational criteria dis-cussed in this paper are summarized in Table 2. This isan extension of Figure 2 of Zhang (2006). New criteriaare added based on the discussion in this paper. A newcolumn lays out the issues of each criterion. The criteriaare sorted by relevant observations. The first six rows(duration, spectrum, spectral lag, E γ,iso , E p − E γ,iso re-lation, and L pγ,iso -lag relation, are based on the gamma-ray properties only. The next five rows (supernova as-sociation, circumburst medium type, E K,iso , jet openingangle, and the geometrically corrected energies E γ and E K ), are based on follow-up broadband observations andafterglow modeling. The next three rows (host galaxytype, specific star forming rate of the host galaxy, andoffset of the GRB from the host galaxy) are based onobservations of the host galaxies. The next two rows(redshift distribution and luminosity function) are statis-tical properties. The final row is the gravitational wavecriterion. In general, most of these criteria are not “con-clusive”, i.e., one cannot draw a firm conclusion basedon a single criterion. Nonetheless, there are several cri-teria which, if satisfied, would unambiguously associatea GRB to a certain physical model category. These aremarked in bold in Table 2. In particular, if a GRB isfound in an elliptical or an early type galaxy, or if theSSFR of its host galaxy is very low, one would be ableto associate it with Type I. On the other hand, a SNassociation or the identification of a wind-type mediumin a GRB would establish its association with Type II.Unfortunately, the above four criteria are usually notsatisfied for most GRBs. One is then obliged to use mul-hysical origins of GRBs 23tiple criteria since there are overlapping predicted prop-erties between the two physical model types for each in-dividual criterion. In Fig.8 we cautiously propose anoperational procedure to discern the physical origin of aGRB based on the available data.Several features are worth commenting on in Fig.8. (1)The criteria to define the physical model category a burstis associated with are less stringent compared with thoseused to define the Gold Samples in § §
5, we have gained confidence on additionalcriteria so that more bursts can be analyzed. (2) Thereare five outcomes in the flowchart. Besides the solid TypeI/II identifications, we also define Type I/II “candidates”and the “unknown” category. The Type I/II candidatesrefer to those with evidence of associating a burst to aparticular physical model category, but the evidence isnot strong enough to make a firm claim. The unknowncategory includes the oddball GRBs that do not obvi-ously fit into any criteria discussed in this paper, or theobservational data are not adequate for us to make thejudgement. They may be associated with Type I, TypeII or a completely new type of models. (3) Some qualita-tive rather than quantitative criteria have been used (e.g.high/low SSFR, large offset, large/small E γ , E K ). Thereason is that it is very difficult to adopt quantitativecriteria at the current stage, since the distributions ofthese quantities predicted by both physical model typesand displayed in the statistical analyses of the Type I/IIGold Samples are continuous, without sharp transitions.The “high/low” and “large/small” definitions are basedon the statistical properties, and therefore in the relativesense. If confusion occurs (e.g. the quantity is near theboundary and not easy to judge whether it is high/low,large/small, one can follow the “?” sign to go downthe flowchart. The flowchart is reasonably operational,i.e. essentially every GRB with reasonable afterglowfollow up observations can find a destiny in the chart.For example, the SN-less long-duration GRB 060614(Gehrels et al. 2006; Gal-Yam et al. 2006; Fynbo et al.2006; Della Valle et al. 2006a) is associated with Type I(based on low SSFR), and the other SN-less GRB 060505(Fynbo et al. 2006; Ofek et al. 2007; Th¨one et al. 2008;McBreen et al. 2008) can be associated with a Type Icandidate based on its small energetics, or an “unknown”burst if one argues that the L pγ,iso − lag relation is satis-fied for this burst (McBreen et al. 2008). GRB 080913and GRB 090423 (the main topic of this paper) find theirhomes as Type II candidates based on the E p − E γ,iso correlation. GRB 060121 (a high- z short GRB) satisfy-ing the E p − E γ,iso is also found to be associated withthe “Type II candidate” outcome in the flowchart. (4)It is possible that the procedure and the criteria may befurther revised as more data are accumulated. The cur-rent procedure only reflects the best knowledge for thetime being.In the flowchart, there are five thick arrows that bridgethe short-duration and long-duration GRBs. This sug-gests that the duration information sometimes is mislead-ing. Some long duration GRBs can be associated withType I (e.g. GRB 060614 and probably GRB 080503,Peyley et al. 2008), and some short duration GRBs can be associated with Type II (e.g. GRB 060121, GRB080913 and GRB 090423). We also present two dashedarrows in the flowchart. These two tracks (a short GRBassociated with a SN and a long GRB with an ellipti-cal/early type host galaxy) are in principle possible, butsuch bursts have never been observed so far . The or-der of the criteria in Fig.8 is based on the “definiteness”of the criteria, with the higher-level ones carrying moreweight than the lower-level ones. Notice that “hardness”is generally not regarded as a definitive criterion in theflowchart (except for the relative hardness of the shortspike and the extended emission). SUMMARY
Prompted by the interesting question whether the z = 6 . z = 8 . z GRBs associated with the Type I physical model cate-gory (Perez-Ramirez et al. 2008), we performed a morethorough investigation on the two physically distinct cat-egories of GRB models and their predicted observationalcharacteristics. We further developed the “Type I/II”concept proposed in Zhang et al. (2007b) in the followingdirections. (1) We have reviewed and expanded the pos-sible multiple observational criteria, and discussed theirphysical origins from the theoretical point of view. Bydoing so, we are able to differentiate those criteria thatare more closely related to the progenitor types and thosethat are more directly related to radiation physics. Inparticular, we argue that SN association, host galaxyproperties (type and SSFR), and the offset of the GRBlocation in the host galaxy are more directly related tothe progenitor types. The gamma-ray properties, suchas duration, hardness, spectral lag, empirical correla-tions, are more related to jet dissipation and radiationprocesses in the emission region, and can only be re-lated to progenitors indirectly. Afterglow and statisti-cal properties can be used to diagnose GRB progenitor,but theoretical modeling is needed. Gravitational wavesignals may be the best criterion to directly probe theprogenitor system, but they are too faint for the cur-rent detectors to detect. (2) We use several key observa-tional criteria that are directly related to GRB progeni-tors to define the Gold Samples for Type I and Type II,respectively. These criteria do not involve GRB gamma-ray emission properties such as duration, hardness, spec-tral lag, etc. We then use these samples to investigatetheir statistical properties, especially their distributionin the duration-hardness space. We found that the TypeII Gold Sample represent the BATSE long/soft popula-tion well. The Type I Gold Sample, on the other hand,is not very representative of the short/hard population.The Type I Gold Sample GRBs are typically “long” andnot particularly “hard”. (3) Although some short/hardGRBs detected in the Swift era may share a similar ori-gin as the Type I Gold Sample, we suggest that some(maybe most) high- L short GRBs may be instead asso-ciated with Type II, namely, of a massive star origin . The GRB field is full of surprises. If some short/hard GRBsare indeed associated with Type II as argued in this paper, onemay someday discover a SN associated with a short/hard GRB.We encourage continuous SN searches for all nearby GRBs, bothlong and short. z indeed suggest that a TypeI association of these bursts is essentially impossible.The proposed procedure to associate a particular GRBto a particular physical model category is subject to fur-ther test with new observational data. More detailedanalyses may allow more quantative criteria to discernthe physical origin of GRBs. Based on past experience,the chances are high that new observations will bringsurprises that continuously call for modifications of thecriteria, which would further our understanding of thephysical origins of cosmological GRBs. We thank the referee, Jon Hakkila, for insightfulcomments that significantly improved the presentationof the paper. This work is partially supported byNASA (through grants NAG05GB67G, NNX08AN24G,and NNX08AE57A at UNLV, and NNX08AL40G atPSU), the National Natural Science Foundation (AwardID 0908362 for BZ), the National Natural Science Foun-dation of China (grant 10873002 for EWL, and grants10503012, 10621303, 10633040 for XFW), and the Na-tional Basic Research Program of China (”973” Program2009CB824800 for both EWL and XFW), and the re-search foundation of Guangxi University (Grant M30520for EWL). 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GRB z log SSFR SN? T T w/ EE HR a lag b E p E γ,iso L p,iso name redshift Gyr − sec sec S (50 − keV ) S (25 − keV ) sec keV 10 erg 10 erg/sType II Gold970228 0.695 0.082 ? ∼
80 n/a 1.07 0 c ±
38 1 . ± . . +5 . − . ∼ . . +0 . ,b − . ±
23 0 . ± .
13 14 . +0 . − . . ± . . +0 . − . ±
30 21 ± ± . ± . ± ±
24 (6 . ± . × − . +7 . − . × − d ±
43 0 . ± .
09 16 . +3 . − . ± . +0 . − . ±
51 7 . ± . +32 − ± . +0 . − . ±
62 229 ±
37 3517 +210 − ± . ± .
02 283 ±
57 94 ± +54 − ∼
30 n/a 0.98 0.045 ± ±
11 0 . ± .
13 73 . +5 . − . ∼
68 n/a 1.25 ... 183 ±
18 22 . ± . ± ∼
15 n/a 1.19 ... 408 ±
14 14 . ± . +80 − ∼
30 n/a ? ... 134 ±
10 9 . ± . . +4 . − . ∼
500 n/a 2.14 ... 579 ±
116 67 ±
14 558 +128 − ∼
25 n/a 0.37 ... 101 ± . . ± . ± ∼
30 n/a 0.78 ... 217 ±
26 7 . ± . . ± . ∼
270 n/a 1.87 ... 59 ± . ± . . . − . ∼
60 n/a 3.23 ... 364 ±
73 10 ± . +7 . − . ± . ± .
04 142 ±
13 66 ±
16 450 +94 − ∼ . ±
15 0 . ± .
17 ...020903 0.25 0.555 Y ∼
13 n/a 0.66 ... 3 ± ± × − ...021211 1.006 -0.841 Y ∼ . ± .
04 46 ± . ± .
13 155 +33 − ∼ . . ± . ±
13 47 ± ± ∼ . . +0 . − . ± . ± . . ± . ∼ . . ± . ± . ± . . +3 . − . ∼
40 n/a 0.65 0.24 ± ∼ ∼ .
01 0 . +0 . − . ± . ± .
04 67 ± . ± .
09 191 ± ± ±
13 3 ± . +1 . − . ± . +0 . − . . ± . . ± .
57 111 . ± . ± +790 − ± . +0 . − . ∼
200 n/a 1.52 ... 418 ±
143 53 ± +48 − ∼ +356 − . ± . ± . × − . ± . × − ± +570 − . ± .
06 6 . +2 . − . ...080520 1.545 ? ? 2.82 ± ∼
30 0 . ± .
019 ...Type I Gold050509B 0.2248 -0.853 N 0.040 ± ± . +611 − . +4 . − × − . +0 . − . ± ± j ± .
002 83 +18 − (2 . ± . × − . +0 . − . ± . ± .
12 1.26/1.12 − . ± . +400 − +11 − × − . +0 . − . ∼ . ± . . ± .
009 302 +214 − . ± .
04 1 . +0 . − . ∼ . . ± .
04 1.52/1.18 ... 640 +144 − . ± .
12 24 . +1 . − . Other Short-Hard Bursts000607 0.14 ? ? ∼ .
008 n/a 2.18 ... ... ... ...050813 ∼ ± − . ± .
014 210 +710 − (1 . +2 . − . ) × − . ± . g > ± − . ± .
024 410 +650 − > . ± .
032 ... Z h a n g e t a l. TABLE 1 — Continued
GRB z log SSFR SN? T T w/ EE HR a lag b E p E γ,iso L p,iso name redshift Gyr − sec sec S (50 − keV ) S (25 − keV ) sec keV 10 erg 10 erg/s051221A 0.5464 0.804 ? 1.4 ± ± .
004 402 +72 − . +0 . − . . ± . ± ∼
120 1.55/0.57 h ± i +134 − . +3 . − . /22 . +17 . − . ± / ± ≤ . ± ± × − +306 − ≤ . +0 . − . ...060502B 0 .
287 ? ? 0.09 ± − ± × − +720 − +5 − × − . ± . . ± ± ∼
223 (3 . ± . × − ∼ . k .
131 ? ? 0.5 ± . ± .
008 620 +1070 − . ± .
021 47 . +6 . − . . ± . +3 . − . × − +458 − . +0 . − . ...061210 0 . ≃ ± +760 − . +0 . − . . ± . . ± ± j +810 − . +0 . − . . ± . ± +746 − . ± .
01 24 . ± . ∼ ∼
100 1.82/1.56 0 . ± .
007 1120 +780 − . +0 . − . . ± . ± ∼
68 0 . ± .
001 1 . +0 . − . ± ∼
100 2.02/0.96 (0 . ± × − ,l ∼ . ± .
08 3 . ± . ∼ ±
40 1.0 -0.013 ± m ... ... ...080913 6.7 ? ? 8 ± ± .
42 121 +232 − ± .
81 1200 +1622 − . ± . . +0 . − . +6 − ± ∼ h y s i c a l o r i g i n s o f G R B s TABLE 1 — Continued
GRB z log SSFR SN? T T w/ EE HR a lag b E p E γ,iso L p,iso name redshift Gyr − sec sec S (50 − keV ) S (25 − keV ) sec keV 10 erg 10 erg/s Note . — Values of Ep and Eγ,iso are taken from Amati et al. (2008) and
Lp,iso are caculated in this work unless otherwise stated below. Futher references are:
GRB970228 - z :Tinney et al.(1998); SSFR:Savaglio et al. (2009); T c : Frontera et al. (1998); lag:Bernardini et al. (2007); GRB970508 - z :Metzger et al. (1997);SSFR:Savaglio et al. (2009); T
90: Paciesas et al. (1999); spectrum:Djorgovski et al. (1997); lag: Norris et al. (2000).
GRB971214 - z :Kulkarni et al. (1998);SSFR:Savaglio et al. (2009); T
90: Paciesas et al. (1999); spectrum: Dal Fiume et al. (2000); lag: Norris et al. (2000)
GRB980425 - z :Tinney et al. (1998);SSFR:Savaglio et al. (2009); T
90: Galama et al. (1998); spectrum: Yamazaki et al. (2004); lag: Zhang (2008).
GRB980613 - z :Djorgovski et al. (1999);SSFR:Savaglio et al.(2009); T
90: Smith et al. (1998); spectrum: Soffitta et al. (2001); ;lag: Norris et al. (2000).
GRB980703 - z :Djorgovski et al. (1998);SSFR:Savaglio et al. (2009); T
90: Paciesas et al. (1999); spectrum:Ghirlanda et al. (2004); lag: Norris et al. (2000).
GRB990123 - z :Andersen et al. (1999);SSFR:Savaglio et al. (2009); T
90: Paciesas et al. (1999); spectrum: Ghirlanda et al. (2004); lag: Norris et al. (2000).
GRB990506 - z :Bloom et al. (2003);SSFR:Savaglio et al. (2009); T
90: Paciesas et al. (1999); spectrum: Ghirlanda et al. (2004); lag:Schaefer (2007).
GRB990712 - z :Vreeswijk et al. (2001);SSFR:Savaglio et al.(2009); T
90: Heise et al. (1999); spectrum: Frontera et al. (2001); lag:Hakkila and Giblin (2006).
GRB991208 - z :Dodonov et al. (1999);SSFR:Savaglio et al. (2009); T
90: Hurley et al. (2000b); spectrum:Hurley et al. (2000b).
GRB000210 - z :Piro et al. (2002);SSFR:Savaglio et al. (2009); T
90: Piro et al. (2002); spectrum: Piro et al. (2002).
GRB000418 - z :Bloom et al. (2003);SSFR:Savaglio et al. (2009); T GRB000911 - z :Price et al. (2002);SSFR:Savaglio et al. (2009); T
90: Price et al. (2002); spectrum: Price et al. (2002).
GRB000926 - z :Castro et al. (2000);SSFR:Savaglio et al. (2009); T GRB011121 - z :Greiner et al. (2003a);SSFR:Savaglio et al. (2009); T
90: Greiner et al. (2003a); spectrum: Greiner et al. (2003a).
GRB011211 - z :Holland et al. (2002);SSFR:Savaglio et al. (2009); T
90: Holland et al. (2002); spectrum: Piro et al. (2005).
GRB020405 - z :Masetti et al. (2002);SSFR:Savaglio et al. (2009); T
90: Price et al. (2003); spec-trum: Price et al. (2003).
GRB020813 - z :Barth et al. (2003);SSFR:Savaglio et al. (2009); T GRB0208019B - z :Jakobsson et al. (2005);SSFR:Savaglio et al.(2009); T GRB020903 - z :Soderberg et al. (2004);SSFR:Savaglio et al. (2009); T GRB021211 - z :Vreeswijk et al. (2003);SSFR:Savaglio et al.(2009); T GRB030328 - z :Martini et al. (2003);SSFR:Savaglio et al. (2009); T GRB030329 - z :Greiner et al. (2003b);SSFR:Savaglio et al. (2009); T GRB030528 - z :Rau et al. (2005);SSFR:Savaglio et al. (2009); T GRB031203 - z :Prochaska et al. (2004);SSFR:Savaglio et al. (2009); T Ep , Eiso :Ghisellini et al. (2006).
GRB040924 - z :Prochaska et al.(2004);SSFR:Savaglio et al. (2009); T GRB041006 - z :Stanek et al. (2005);SSFR:Savaglio et al. (2009); T e . GRB050525A - z :Della Valle et al. (2006b);SSFR:Savaglio et al. (2009); T f ; Lag:Gehrels et al. (2006); Ep , Eiso :Golenetskii et al. (2005a)
GRB050826 - z :Halpern and Mirabal(2006);SSFR:Savaglio et al. (2009); T f . GRB051022 - z :Doty et al. (2005);SSFR:Savaglio et al. (2009); T GRB060218 - z :Soderberg et al.(2006b);SSFR:Savaglio et al. (2009); T f ; lag:Gehrels et al. (2006). GRB060602A - z :Jakobsson et al. (2007);SSFR:n/a; T f . GRB050820 - z :Jakobsson et al.(2008);SSFR:n/a; T f ; Ep , Eiso :Sakamoto et al. (2008).
GRB050509B - z :Gehrels et al. (2005);SSFR:Savaglio et al. (2009); T f ; lag:Gehrels et al.(2006); Ep , Eiso :Butler et al. (2007).
GRB050709 - z :Fox et al. (2005);SSFR:Savaglio et al. (2009); T Ep , Eiso :Butler et al.(2007).
GRB050724 - z :Barthelmy et al. (2005a);SSFR:Savaglio et al. (2009); T f ;lag:Gehrels et al. (2006); Ep , Eiso :Butler et al. (2007).
GRB060614 - z :Della Valle et al.(2006a);SSFR:Savaglio et al. (2009); T Ep , Eiso :Golenetskii et al. (2006b).
GRB061006 - z :Berger et al. (2007);SSFR:Savaglio et al.(2009); T f ; Ep , Eiso :Butler et al. (2007).
GRB000607 - z :Nakar et al. (2006); T GRB050813 - z :Prochaska et al. (2006); T HR :Sato et al. (2005);lag:Ferrero et al (2007),Gehrels et al. (2006); Ep , Eiso :Butler et al. (2007).
GRB051210 - z :Berger et al. (2007); T Ep , Eiso :Butler et al. (2007).
GRB051221A - z :Soderberg et al. (2006a);SSFR:Savaglio et al. (2009); T Ep , Eiso :Golenetskii et al. (2005b).
GRB060121 - z :Levan et al.(2006),de Ugarte Postigo et al. (2006); T Ep , Eiso :Butler et al. (2007).
GRB060313 - z , T Ep, Eiso :Golenetskii et al.(2006a).
GRB060502B - z :Bloom et al. (2007);, T Ep, Eiso :Butler et al. (2007).
GRB060505 - z :Ofek et al. (2007);SSFR:Savaglio et al. (2009); T Ep , Eiso :Hullinger et al. (2006); Lp :McBreen et al. (2008). GRB060801 - z :Cucchiara et al. (2006); T Ep , Eiso :Butler et al. (2007).
GRB061201 - z :Stratta et al. (2007); T Ep , Eiso :Butler et al. (2007).
GRB061210 - z :Berger (2007); T Ep , Eiso :Butler et al. (2007).
GRB061217 - z :Berger (2007); T Ep , Eiso :Butler et al. (2007).
GRB070429B - z :Cenko et al.(2008a); T Ep , Eiso :Butler et al. (2007)
GRB070714B - z :Cenko et al. (2008a); T f ; lag:Cenko et al. (2008a); Ep , Eiso :Butler et al. (2007).
GRB070724A - z :Cucchiara et al. (2007);; T f ; Ep , Eiso : estimated with Γ − Ep relation. GRB071227 - z :Berger (2009); T f ,Sato et al. (2007); lag:Sakamoto et al. (2007); Ep , Eiso :Golenetskii et al. (2007).
GRB080503 - T GRB080913 - z , T Ep :Palshin et al.(2008), Eiso :this work.
GRB090423 - z , T Eiso :Tanvir et al. (2009);spectrum:this work;lag:Krimm et al. (2009); Lp :Nava et al. (2009); Ep :Salvaterra et al. (2009). a HR=S(50-100keV)/S(25-50keV) b Lag between 25-50keV and 50-100 keV. c absence of lag between 2-26keV and 40-700 keV d BATSE data are not completed or recoreded (Norris et al. (2000)) e http://space.mit.edu/HETE/Bursts/GRB041006/ f http://grb.physics.unlv.edu g We adopted z=1.4 for this burst. h only EE i lag between 6-40keV and 80-400 keV j lag between 25-50keV and 100-350 keV k got from Eγ,isot l Lag between 25-50keV and 100-350 keV l Lag between 15-25keV and 50-100 keV
TABLE 2Observational criteria for physically classifying GRBs.
Criterion Type I Type II IssuesDuration Usually short, but can Long without short/hard spike, No clear separation line.have extended emission. can be shorter than 1s in rest frame.Spectrum Usually hard (soft tail) Usually soft Large dispersion, overlappingSpectral Lag Usually short Usually long, can be short. Related to variability time scale
Eγ,iso
Low (on average) High (on average) Wide distribution in both, overlapping Ep − Eγ,iso
Usually off the track. Usually on the track. Some Type II off the track.
Lpγ,iso − lag Usually off the track. Usually on the track. Some Type II off the track.SN association No. Yes.
Some Type II may be genuinely SNless.Medium type Low- n ISM.
Wind or High- n ISM. Large scatter of n distribution. EK,iso
Low (on average) High (on average) Large dispersion, overlappingJet angle Wide (on average) Narrow (on average) Difficult to identify jet breaks Eγ and EK Low (on average) High (on average) Type I BH-NS BZ model ∼ Type II.Host galaxy type
Elliptical, early and late Late Deep spectroscopy needed.SSFR
Low or high High (exception GRB 070125) overlappingOffset Outskirt or outside Well inside How to claim association if outside? z -distribution Low average z High average z overlapping L -function Unknown Broken power law, 2-component overlappingGW signals Precisely modeled Unknown No data yet Fig. 8.—
A recommended procedure to judge the association of a particular GRB to a particular physical model category. Multipleobservational criteria have been applied. Question marks stand for no information being available to judge the validity of the criterion.The two dotted arrows stand for the possibilities that are in principle possible but have never been observed. Five thick arrows bridge thelong-duration and short-duration GRBs, suggesting that the there can be long duration Type I and short duration Type II GRBs.APPENDIX
DETAILS OF THE TYPE I GOLD SAMPLE • GRB 050509B: No optical afterglow is detected. The host galaxy is very likely a bright cD elliptical galaxy in anearby galaxy cluster at z = 0 . ± . • GRB 050709: The host galaxy is identified with the optical afterglow, and is a star forming galaxy at z =0 . ± . • GRB 050724: The host is an early type galaxy at z = 0 . ± . • GRB 060614: The host galaxy has a low SSFR (Gal-Yam et al. 2006; Savaglio et al. 2009). Very stringentupper limits for any associated SN fainter than any known SN achieved (Gal-Yam et al. 2006; Fynbo et al. 2006;Della Valle et al. 2006a). Satisfies criterion • GRB 061006: A faint host galaxy is detected at z = 0 . ± . DETAILS OF OTHER SHORT/HARD GRB SAMPLE • GRB 000607: This was a IPN-localized GRB. A putative host galaxy at z = 0 .
14 was proposed (Gal-Yam et al.2008). • GRB 050813: No optical afterglow detected. The X-ray error circle is associated with a galaxy cluster at z ≃ .
72 (Prochaska et al. 2006). Moderately deep SN limit (relevant to this low- z interpretation) was reportedby (Ferrero et al 2007). • GRB 051210: A Swift GRB with X-ray afterglow (La Parola et al. 2006). A galaxy appeared outside the errorbox, but is likely the host. No lines are observed. It is argued that z > . • GRB 051221A: Host galaxy is a star forming galaxy at z = 0 . • GRB 060121: HETE-2 GRB with a faint optical afterglow, leading to the discovery of an extremely fainthost galaxy. The redshift of the afterglow can be estimated as either 4.6 or 1.7 (de Ugarte Postigo et al. 2006;Berger et al. 2007). • GRB 060313: Bright short/hard GRB with bright afterglow (Roming et al. 2006). A faint host galaxy is iden-tified whose redshift is unknwon (Berger et al. 2007). Spectral analysis of the UVOT data suggests z ≤ . • GRB 060502B: No optical afterglow is detected. The XRT position is close to a nearby early type galaxy at z = 0 .
287 (Bloom et al. 2007). The chance probability for the association is 0.03. There is another faint objectin the field of view, which could be the host galaxy at a high redshift (Berger et al. 2007). • GRB 060801: No optical afterglow is detected. Two possible sources may be considered as the host. One has aredshift z = 1 .
131 (which is slightly outside the XRT error box using the UVOT-aligned XRT position). Anothersource is within the error box, but is likely even farther away (Berger et al. 2007). • GRB 061201: Optical afterglow was detected by UVOT. No host galaxy was identified. Candidates includegalaxy cluster Abell 995 ( z = 0 . z = 0 . z (Stratta et al. 2007). • GRB 061210: A Swift GRB with delayed X-ray afterglow detection. No optical afterglow detected. The hostgalaxy is likely a star forming galaxy at z = 0 . ± .
001 (Berger et al. 2007). • GRB 061217: A faint Swift burst without optical afterglow detection. Within the XRT error circle, there is astar forming galaxy at z = 0 . • GRB 070429B: A Swift GRB with delayed X-ray afterglow detection. The host galaxy is likely a faint galaxy at z = 0 . ± . • GRB 070707: Detected by INTEGRAL and have X-ray and optical afterglow detected. A very faint host galaxycandidate was reported with no redshift information (Piranomonte et al 2008). • GRB 070714B: A Swift GRB with optical afterglow. A secure host galaxy at z = 0 . ± . • GRB 070724A: A Swift GRB with X-ray afterglow. A potential host galaxy is detected, which is a star forminggalaxy at z = 0 .
457 (Cucchiara et al. 2007). • GRB 070729: A Swift GRB with faint X-ray afterglow. A putative red host galaxy is identified (Berger & Murray2007). No redshift is known. • GRB 070809: A Swift GRB with X-ray and optical afterglow. A nearby, edge-on spiral galaxy may be the host,with z = 0 . • GRB 071227: A Swift GRB with X-ray and optical afterglows. A host galaxy is identified as an edge on spiralgalaxy. The redshift is z = 0 . • GRB 080123: A Swift GRB with X-ray afterglow. No host galaxy detection is reported. • GRB 080503: A Swift GRB with short initial spike and very bright extended emission. X-ray and opticalafterglows are detected. There is no galaxy directly at the GRB position. There are faint galaxies nearby, butone cannot make firm statements regarding their association with the GRB (Perley et al. 2009).After this work is finished, two more interesting short/hard GRBs were detected, whose observational propertiesstrengthen the main theme of this paper. We include them here as follows. • GRB 090426: This is rest-frame 0.35 s short/hard GRB at z = 2 . • GRB 090510: This is bright short/hard GRB detected by both Swift and Fermi (GBM/LAT) (Hoversten et al2009; Ohno et al. 2009; Guiriec et al. 2009) with bright X-ray and optical afterglows (Grupe et al. 2009b;Kuin et al. 2009; Olivares et al. 2009). With a redshift z ∼ . t ∼ ∼ − .