SHORT VERSUS LONG AND COLLAPSARS VERSUS NON-COLLAPSARS: A QUANTITATIVE CLASSIFICATION OF GAMMA-RAY BURSTS

Kouveliotou et al. (1993) have shown that gamma-ray bursts (GRBs) can be divided into two groups according to their observed duration. Long bursts (LGRBs) with observed durations T₉₀ > 2 s and short ones (SGRBs) with T₉₀ < 2 s. They have also found that SGRBs are harder on average than LGRBs, supporting further the possibility that the two populations arise from different physical sources. Later on afterglow observations enabled the localizations of GRBs and identifications of their hosts. These observations further supported the different sources hypothesis. Hosts of LGRBs have a large star formation rate while SGRB hosts include both star-forming and non-star-forming galaxies. The position distribution of LGRBs within their host, toward the center and within high star-forming regions (Fruchter et al. 2006), differs from the position distribution of SGRBs within their hosts, which is more diffuse and with no apparent association with star formation (Barthelmy et al. 2005; Fox et al. 2005; Gehrels et al. 2005; Nakar 2007; Berger 2009).

These observations have led to the realization that GRBs have two different progenitors and they are generated by at least two different mechanisms. Recently we have shown that low-luminosity GRBs are generated by a third mechanism, most likely shock break out. This is different from either Collapsars or regular non-Collapsar short GRBs (Bromberg et al. 2011a). As such, they compose a third physical group. This third group, of low-luminosity GRBs contains very few bursts and its existence is not relevant to the discussion here. We stress that this division is based on different physical mechanisms and this third group of low-luminosity GRBs should not be confused with the phenomenologically suggested "intermediate group" (see, e.g., Řípa et al. 2012 and references therein) for which there is no physical basis. The association of LGRBs with star-forming regions and in several cases with Type Ic SNe suggests that they involve stellar collapse. The Collapsar model (Paczynski 1998; MacFadyen & Woosley 1999) suggests that a central engine within the collapsing star (powered most likely by an accretion disk onto a newly formed compact object or by a magnetar) powers a jet that penetrates the stellar envelope and produces the observed gamma-rays once it is outside the star. SGRBs are typically weaker and are observed at lower distances. They are more numerous (locally), but being harder to detect there are less observed SGRBs than LGRBs. Those SGRBs with identified locations are associated with a wide range of stellar population ages. Their properties are consistent with those expected from binary neutron star mergers (Eichler et al. 1989), although the exact origin is still uncertain (see Nakar 2007 for a recent review). Since the origin of this group is still uncertain we will denote them simply as non-Collapsars.

It is commonly implicitly assumed that there is a one-to-one correspondence between the observed groups of LGRBs and SGRBs and the astrophysical groups of Collapsars and non-Collapsars. However, a quick inspection of the duration distribution (Figure 1) suggests that this is not the case and there is a significant overlap between the two groups of long and short GRBs: There are SGRBs of Collapsar origin and vice versa. Apart from a slight difference in the average hardness, all other high-energy emission properties of LGRBs and SGRBs are remarkably similar. This makes it difficult to identify the origin of any individual burst (Nakar 2007) and lacking a better criteria, the original division according to T₉₀≶2 s is widely used. However, this criteria was established for a specific detector (BATSE) with a specific observational window. SGRBs are typically harder than LGRBs and as such they are more difficult to detect by softer detectors like Swift/BAT than by BATSE. Indeed, Swift's short/long detection rate is 1/10 versus BATSE's 1/3 (when the criterion T₉₀≶2 is used). This suggests that Swift's division line between the two groups might be at a shorter duration, as indeed is seen in a visual inspection of Swift's duration distribution (see Figure 1).

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Zhang et al. (2009) suggested to classify individual GRBs using various subsets of properties, e.g., spectral lag, peak energy, etc. These subsets of properties are selected phenomenologically, and are not based on any physical model. The main problem of those classification criteria, which are based on the high-energy emission alone, is that there is a significant overlap, which cannot be quantified, between Collapsars and non-Collapsars in all of them. As a result, the quality of the classification of any of these phenomenological methods cannot be quantified and it is therefore impossible to estimate the fraction of misclassified GRBs. This poses a major problem in using such a method especially since the sample of GRBs with "good data" (afterglow detection, good localization, redshift measurements, etc.), is small and very sensitive to misclassification. Other attempts used a statistical approach and tried to evaluate the overlap between the two populations by fitting the distribution of GRBs with two underlying distributions—in this case two lognormal distributions (Horváth 2002; Levesque et al. 2010). The quality of such classification schemes depends entirely on similarity of the true distribution of the two populations to the arbitrarily chosen fitted distribution. Such approach can be trusted only if we know, for example based on physical arguments, what is the underling distribution of at least one of the two populations. Recently, in Bromberg et al. (2011b) we have shown, based on generic physical properties of the Collapsar model, that at short durations the Collapsar distribution is flat. Namely the number of Collapsars per unit duration at short durations is independent of the duration. Building on this result we estimate here the probability that a GRB with a given duration is a Collapsar or not. Not surprisingly, this probability depends on the detector and we calculate it for the three major GRB detectors: BATSE, Swift, and Fermi GBM. An improved version of this method is obtained by adding a hardness dependence. We present a refined probability distribution that is based on both the duration and the hardness. Needless to say our method is statistical in nature. We cannot determine whether a specific burst is a Collapsar or not, but we can give a probability estimate for this question.

We begin, in Section 2, with a discussion of the Collapsars' duration distribution and an analysis of the observed duration distribution of GRBs. In Section 3, we calculate the probability that an observed GRB is a non-Collapsar. Our results imply that short-duration Collapsars have been wrongly classified as non-Collapsars, mostly in Swift sample, and this has lead to potential misinterpretation of some of the observed data. In Section 4, we discuss the consistency of our findings with some of the recent studies and the implications on the inferred properties of non-Collapsars. We summarize our results and their implications in Section 5. We provide a table of the probabilities for each one of the observed Swift bursts with T₉₀ < 2 s to be a non-Collapsar in the Appendix.

Within the Collapsar model a GRB can only be produced after the jet has emerged from the surface of the collapsing star. We (Bromberg et al. 2011b) have recently shown that this leaves a distinctive mark on the observed duration distribution: It is flat at durations shorter than the typical breakout time of the jet from the star (about a few dozen seconds modulo the redshift). In a nutshell, this result arises from a simple fact. The burst duration is the difference between two quantities: the engine operating time and the jet breakout time. Under quite general conditions the resulting distribution is flat at durations that are shorter than the typical jet breakout time. Indeed, when we plot in Figure 2 the quantity dN_GRB/dT₉₀ instead of the traditionally shown dN_GRB/dlog T₉₀ (e.g., Figure 1; Kouveliotou et al. 1993), this flat distribution is evident. The plateau appears over about an order of magnitude in duration around a few seconds, in the GRB duration distributions of BATSE, Swift, and Fermi GBM, as depicted in Figure 2. The duration is characterized by T₉₀ during which 90% of the fluence is accumulated.

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At the short end the distribution is rising toward shorter durations. This "bump" in the duration distribution is inconsistent with a Collapsar origin for most of the short-duration GRBs. This simple conclusion is consistent with other evidence that a second, non-Collapsar, population of short-duration GRBs exists with a different origin than the longer ones. (e.g., Kouveliotou et al. 1993; Barthelmy et al. 2005; Fox et al. 2005; Gehrels et al. 2005; Nakar 2007).

Therefore, within this model all we need to do in order to quantify the non-Collapsars' duration distribution is to determine the height of the Collapsars' plateau at short durations. To do so we fit the overall observed duration distribution to a model that includes Collapsars and non-Collapsars. The Collapsar distribution is characterized, of course, by a plateau at short durations (see Equation (1) below). In order to determine its height, we must include in the global fit also the long end of the duration distribution. We have tried fitting the data with various ad hoc functional forms. All of these fits provide results that are consistent within the uncertainty, implying that the results are insensitive to exact function that we fit at long durations. Below we present the results for just one model in which the long duration part is chosen to be a power law with an exponential cutoff.

Before turning to this fit we stress the difference between our approach and numerous previous attempts (e.g., Horváth 2002; Levesque et al. 2010) to fit the observed GRB duration distribution. These works use various functional forms assuming either two (long and short) or three (long, intermediate, and short) burst populations (usually a lognormal distribution is chosen for each population). So far, all of these attempts are phenomenological and have no physical basis for the shapes of the distributions used. From this point of view, there is no reason to a priori prefer one model over the others. In contrast, our approach is based on a physical model for the short-duration Collapsar distribution (Bromberg et al. 2011b).

In the following we describe a fit of the observed data to a Collapsar distribution described by a plateau at short durations (T₉₀ ⩽ T_B) and a product of a power law and an exponential cutoff at long durations. The non-Collapsar distribution is lognormal. Together we have

$$\begin{eqnarray} \frac{{\it dN}_{{\rm GRB}}}{dT_{90}} &=& A_{{\rm NC}}\frac{1}{T_{90}\sigma \sqrt{2\pi }}e^{-\frac{(\ln T_{90}-\mu)^2}{2\sigma ^2}} \nonumber\\ && + A_C \left\lbrace \begin{array}{@{}lc}1 & T_{90}\le T_B \\ \ms \left(\frac{T_{90}}{T_B}\right)^\alpha e^{-\beta (T_{90}-T_B)} & T_{90}>T_B, \end{array} \right. \end{eqnarray} \tag{ 1 }$$

where the first term corresponds to non-Collapsars and the second one to Collapsars.

We consider the data sets of BATSE,³ Swift,⁴ and Fermi GBM.⁵ As we are not interested in the details of the distribution at long durations, we limit the data to the duration regime of 0–200 s, which is sufficient to obtain an accurate estimate of the plateau height. Changing this range to 0–1000 s has no significant effect on our results. The data are binned into equally spaced logarithmic bins (note however that while doing so we keep the function dN/dT₉₀ and not dN/dlog T₉₀). Bins with less than five events are merged with their neighbors to get more reliable statistical errors. We fit each sample with a distribution function according to Equation (1). After normalization we are left with six free parameters (A_C/A_NC, T_B, μ, σ, α, β). The resulting χ² per degrees of freedom (DOF) are 0.9 (with 31 DOF), 1.3 (with 22 DOF), and 1.1 (with 23 DOF) for the BATSE, Swift, and Fermi GBM, respectively. The corresponding parameters are given in Table 1. Figure 2 depicts the resulting distribution functions and the data we use. We find plateaus that extend up to T_B ∼ 20 s in the BATSE and Fermi GBM duration distributions, and up to T_B ∼ 10 s in Swift. This is consistent with our expectations from the Collapsar model (Bromberg et al. 2011b).

The probability that a GRB with a given T₉₀ is a non-Collapsar is given by the fraction of non-Collapsars within the observed GRBs at a given duration:

$$\begin{equation} f(T_{90})=A_{{\rm NC}}\frac{1}{T_{90}\sigma \sqrt{2\pi }}e^{-\frac{(\ln T_{90}-\mu)^2}{2\sigma ^2}}\left(\frac{{\it dN}_{{\rm GRB}}}{dT_{90}}\right)^{-1}, \end{equation} \tag{ 2 }$$

where dN_GRB/dT₉₀ is given by Equation (1). To estimate the errors in f_NC we simulate, for each one of the samples, distributions of T₉₀ drawn randomly from the best-fit distribution function dN_GRB/dT₉₀. We then bin the simulated data sets and repeat the process of parameter fitting using Equation (1) to obtain f_NC. We repeat this processes 1000 times and look for the ranges of f_NC that encompasses 68% of the cases. Figure 3 depicts f_NC(T₉₀) for the BATSE, Swift, and Fermi GBM samples. The solid lines depict f_NC, calculated from the observed data, and the blue region describes the 1σ error estimate. Table 2 lists the T₉₀ values that correspond to some selected probabilities for the three detectors.

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These results clearly show that the choice of T₉₀ = 2 s as a threshold to identify non-Collapsars is suitable for BATSE, and possibly also for Fermi GBM. A BATSE (Fermi GBM) burst with T₉₀ = 2 s has a probability >70% (≳ 40%) to be a non-Collapsar. However, the probability of a similar Swift burst to be a non-Collapsar is only 0.16 ± 0.14. It is clearly most likely a Collapsar. The level of false identification, for a given duration threshold, T_th can be seen in Figure 4, which depicts the integrated fraction of Collapsars (out of the total number of GRBs) with duration T₉₀ ⩽ T_th. The total number of Collapsars with duration T₉₀ < 2 s in the Swift sample is estimated to be 19 ± 5 out of 53 GRBs. Thus, an arbitrary Swift sample selected with the T_th = 2 s criterion contains about 40% Collapsars that have been misclassified as non-Collapsars. This should be compared with about 10% and 15% of misclassified Collapsars in the corresponding BATSE and Fermi samples (see Figure 4) with the same T_th. The criterion T_th = 2 s for selecting non-Collapsars in Swift is therefore very bad for most studies of non-Collapsars.

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Any single criteria that should distinguish according to the durations between Collapsars and non-Collapsars should be detector dependent. A longer T_th increases the size of the SGRBs sample (which are supposedly non-Collapsars) but it increases at the same time the number of misidentified Collapsars in the sample. A shorter threshold yields smaller but cleaner samples. The specific choice of T_th should be considered for each study, balancing the need of a large sample with the importance of purity. A reasonable choice that should be adequate to many studies is choosing the threshold probability as f_NC = 0.5. This reconciles these conflicting requirements and allows us to classify both Collapsars and non-Collapsars with a single criterion. Adopting this probability we find that the corresponding T₉₀ threshold values are T_th = 0.8 ± 0.3 s for Swift, T_th = 1.7^+0.4_−0.6 s for Fermi GBM, and T_th = 3.1 ± 0.5 s for BATSE. The total number of misclassified Collapsars in samples selected according to these criteria constitute about 20% of the Swift samples and ∼14% of the BATSE and Fermi GBM samples (Figure 4).

3.1. The Non-Collapsar Probability as a Function of Duration and Hardness

As already mentioned short GRBs are harder on average than long ones (Kouveliotou et al. 1993). Following these observations there is a rich literature on the division of bursts on the hardness-duration plane (e.g., Řípa et al. 2012 and references therein). It is natural to expect that the ratio of non-Collapsars to Collapsars and the probability function, f_NC, should increase with the GRB hardness. Therefore, the combination of duration and hardness provides a stronger way to distinguish between non-Collapsars and Collapsars. To examine the duration-hardness probability we divide the samples into three hardness subgroups: soft, intermediate, and hard, and perform the same analysis on each subgroups. We fit a duration distribution function and calculate the probability function, f_NC, and its 1σ variance. We consider two hardness thresholds: The soft and intermediate subgroups are separated by the average hardness of Collapsars, which we estimate using GRBs with T₉₀ > 20 s, where the contribution of non-Collapsars in all samples is negligible. The intermediate and hard subgroups are separated by the average hardness of non-Collapsars, which is estimated using GRBs with T₉₀ < 0.5 s (see Figure 5). The spectral hardness of different satellite samples is quantified differently for each detector, depending on the available information for each database. For BATSE we use the hardness ratio parameter, HR₃₂, defined as the ratio between the photon counts in energy channel 3 (100–300 keV) and energy channel 2 (50–100 keV). In Swift and Fermi GBM samples, we use the power-law index (PL) of the observed spectrum obtained by fitting a single power law in the energy range 15–150 keV (Swift) or 10–2000 keV (Fermi). Note that in the Swift sample, only ∼87% of the GRBs have a spectral fit to a single power law. The spectrum of the other 13% is fitted with a power law + exponential cutoff, and we omit these bursts from this analysis.

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If the distribution functions of Collapsars and non-Collapsars do not depend strongly on the spectral hardness, then varying the hardness threshold would only change the relative ratio of Collapsars to non-Collapsars, while the overall shape of the duration distribution functions of the two populations would remain unchanged. To examine this, we fit each hardness subgroup with the same distribution function as in the full sample of the corresponding detector. We only rescale A_NC and A_C according to the number of non-Collapsars and Collapsars in the subgroup relative to their number in the full sample. We evaluate the ratio of non-Collapsars by dividing the number of GRBs with T₉₀ < 0.5 s in the subgroup with their number in the full sample. The ratio of Collapsars is evaluated in a similar way using GRBs with T₉₀ > 20 s. We find good fits in all hardness subgroups with χ²/DOF of ∼0.8–1.8. This good fit indicates a weak dependency of the duration distributions of Collapsars and non-Collapsars on the hardness.

Figure 6 depicts the observed duration distributions of the three hardness subgroups of each detector. The harder subgroups have more prominent "bumps" at short durations together with relatively lower plateaus that become visible only at longer durations. This is the expected behavior if the fraction of non-Collapsars increases with the GRB hardness. The dN/dT₉₀ distributions and their χ²/DOF values are shown in Figure 6. The resulting probability functions of each subgroup are shown in Figures 7–9. In Table 3 we list the T₉₀ values that correspond to specific values of f_NC in each subgroup. In the hard BATSE subgroup non-Collapsars dominate the distributions up to T₉₀ = 7.8^+1.4_−1.0 s, while in the hard Swift and Fermi GBM samples non-Collapsars dominate up to T₉₀ = 2.8^+1.5_−1.0 and T₉₀ = 5.4^+3.9_−2.0 s, respectively. The transition between Collapsars and non-Collapsars in the intermediate subgroups roughly follow the same values as in the complete samples: T₉₀ = 2.9 ± 0.4, T₉₀ = 0.6^+0.2_−0.3, and T₉₀ = 1.6^+0.8_−0.6 s for BATSE, Swift, and Fermi GBM, respectively. In the soft subgroups non-Collapsars dominate only up to T₉₀ = 1.1^+0.2_−0.3 s in BATSE, T₉₀ = 0.3^+0.4_−0.2 s in Swift, and up to T₉₀ = 0.6^+0.6_−0.3 s in Fermi GBM.

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Table 3. The T₉₀ (s) at Different f_NC in the Three Hardness Subgroups for Each Satellite

		${{\rm Hardness}{$\!\!f_{{\rm NC}}$}}$		0.9	0.8	0.7	0.6	0.5	0.4	0.3
		Hard
		(HR32 > 5.5)		2.8+0.6−0.3	4.2+0.8−0.5	5.4+1.0−0.6	6.6+1.2−0.8	7.8+1.4−1.0	9.1+1.7−1.2	10.8+2.1−1.4
BATSE		Intermediate
		(5.5 >HR32 > 2.6)		0.6+0.1−0.2	1.3+0.2−0.2	1.8+0.2−0.3	2.3+0.3−0.4	2.9+0.4−0.4	3.6+0.4−0.5	4.4+0.5−0.6
		Soft
		(2.6 >HR32)		⋅⋅⋅	0.2+0.2−0.2	0.5+0.2−0.3	0.8+0.2−0.3	1.1+0.2−0.3	1.5+0.3−0.4	2.0+0.3−0.5
		Hard
		(PL > −1.13)		0.9+0.6−0.4	1.4+0.9−0.5	1.9+1.1−0.6	2.3+1.3−0.8	2.8+1.5−1.0	3.4+1.9−1.1	4.2+2.2−1.4
Swift		Intermediate
		(−1.13 > PL > −1.65)		0+0.09	0.16+0.09−0.16	0.3+0.1−0.2	0.4+0.2−0.2	0.6+0.2−0.3	0.7+0.2−0.4	1.0+0.3−0.5
		Soft
		(−1.65 > PL)		0+0.05	0+0.18	0.09+0.22−0.09	0.16+0.28−0.16	0.3+0.4−0.2	0.4+0.4−0.2	0.5+0.5−0.3
		Hard
		(PL > −1.34)		1.5+1.0−0.5	2.5+1.6−0.8	3.4+2.2−1.1	4.3+3.0−1.5	5.4+3.9−2.0	6.6+5.1−2.5	8.2+7.1−3.3
FermiGBM		Intermediate
		(−1.32 > PL > −1.52)		0.3+0.2−0.2	0.6+0.3−0.2	0.9+0.5−0.3	1.2+0.6−0.5	1.6+0.8−0.6	2.0+1.0−0.8	2.6+1.4−1.0
		Soft
		(−1.52 > PL)		0.06+0.14−0.06	0.17+0.25−0.17	0.3+0.4−0.2	0.4+0.5−0.2	0.6+0.6−0.3	0.8+0.7−0.4	1.1+0.9−0.5

Notes. The bold font highlights the T90 values that correspond to a probability of 50% to be a non-Collapsar.

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The probability functions we obtained here can be used to classify the GRBs detected by BATSE, Swift, and Fermi GBM according to their duration and hardness. For GRBs that cannot be assigned to one of those hardness subgroups (e.g., the 13% of Swift GRBs whose spectra are fitted with a power law + exponential cutoff) the classification can be done using the overall probability function of the complete Swift sample. For GRBs that have been detected by HETE and INTEGRAL we recall that the spectral window observed by HETE is 8–500 keV, which is closer to the Swift/BAT while INTEGRAL, on the other hand, observes at a spectral range of 15 keV–10 MeV, which is closer to BATSE's range. As a first approximation, one can use the corresponding f_NC values of these detectors.

In the Appendix, we collect all Swift GRBs with T₉₀ < 2 observed to date. The table includes also GRBs with a hard short spike plus a soft extended emission and a number of other GRBs with duration >2 s that are sometimes considered as possible non-Collapsars. For each GRB we calculate the probability to be a non-Collapsar from the duration and power-law index, f_NC(T₉₀, PL). For those GRBs with a spectral fit of a power law + exponential cutoff, we calculate the probability to be a non-Collapsar from the duration alone, f_NC(T₉₀). Important GRBs are emphasized with bold text. The table also includes a few important GRBs detected by HETE or INTEGRAL. For these GRBs, we estimate f_NC(T₉₀) using the probability functions of Swift and BATSE, respectively. This table can be used to evaluate the contamination by Collapsars in present samples of SGRBs and to select low-contamination samples in future studies.

The commonly used criterion to distinguish Collapsars from non-Collapsars is the duration (T₉₀≷2 s). This criterion is applied to GRBs that are detected by all gamma-ray satellites including Swift that supplies the largest number of well-localized short-duration GRBs. As we have shown earlier, Swift GRBs with T₉₀ > 0.8 s have high probability to be Collapsars. This could have led to a "Collapsar contamination" in current Swift samples of SGRBs that are based on the 2 s criterion, and might have affected the results of studies based on these samples. Interestingly, such studies (e.g., Berger 2009, 2011) have shown that the environments of SGRBs are different than the environments of LGRBs. LGRBs are associated with intensive star formation, arise in low-metallically irregular star-forming galaxies (see, however, Levesque et al. 2010b, 2010c; Savaglio et al. 2012 for examples of high-metallicity LGRB hosts), and are concentrated toward star-forming regions in their galaxies, whereas SGRBs are associated with a broad distribution of galaxy types, arise in hosts with a broad range of star formation rates (SFRs) and metallicities, and show a larger scatter in the distance distribution from their hosts' centers. One may wonder how these results are consistent with our claim that the 2 s classification is not valid for the Swift sample.

Table 4 lists the GRBs and the host galaxy characteristics used in the Berger (2009, 2011) sample. It also includes the probability that the associated SGRB are non-Collapsars (based the combination of duration and power-law index). In addition to eight "classically selected" SGRBs (T₉₀ < 2 s), this sample includes also four GRBs with T₉₀ > 2 s. These GRBs are characterized by a short hard initial spike followed by a long tail of softer emission. They are often considered as non-Collapsars since their initial spikes resemble a classical SGRB (see Nakar 2007). However, since the overall duration is not well defined, our classification scheme cannot attribute a non-Collapsar probability to these bursts.

Even though our probabilistic approach is incapable of determining whether a specific burst is a Collapsar or not, a clear picture emerges from Table 4. Four out of eight classifiable bursts are non-Collapsars at very high probabilities. Two bursts are almost certainly Collapsars while the last two are marginal: The probability of each one of those two to be a Collapsar is larger than 60%, however the probability that both are Collapsars is less than 50%. These fractions are consistent with what is expected, according to our analysis, from a Swift sample with a 2 s criteria for which ∼60% of the bursts should be non-Collapsars and the rest Collapsars.

Within the sub-sample of four non-Collapsars, we observe a large spread in SFRs, in specific SFRs, and in galactic luminosities. Distances from the center of the host have typically large observational error, but at least one is quite far from the center (∼44⁺¹²₋₂₃ kpc). There is not enough data to determine the metallicity. These results show a large spread in the observed quantities, in a large contrast with the rather narrowly distributed host properties of LGRBs (Collapsars). This is similar to the conclusion of Berger (2009, 2011). It demonstrates that also when a less contaminated, but smaller, sample is examined non-Collapsars hosts have a different distribution than Collapsar hosts and consequently that the two populations have different progenitors. On the other hand, as expected, the properties of the hosts of the two Collapsar candidates are fully consistent with those of typical LGRB hosts. Finally, the properties of the hosts of the two bursts with marginal classification are also consistent with being either Collapsar or non-Collapsar hosts.

The conclusion that the properties of the non-Collapsars' hosts are widely distributed whereas those of the Collapsars' hosts are narrowly distributed implies that our classification is consistent with the results of Berger (2009, 2011) even though the latter are based of a significantly contaminated sample. A wide distribution contaminated by a narrowly distributed population retains it basic feature of a wide distribution, and this is what happens here. The non-Collapsars within the Berger (2009, 2011) SGRB sample are numerous enough to result in a wide distribution that is significantly different from the one of Collapsars. However, while our conclusions are in line with the basic results of Berger (2009, 2011), the details of the distribution, such as the ratio of high-SFR to low-SFR hosts or the distribution of distances from center, are influenced by the contamination and a quantitative study of the distribution of the host properties should take this factor into account.

The possible effects of contaminating Collapsars on studies of properties of SGRBs vary from one study to another. Different samples have different contaminations and different properties are influenced differently. The probabilities given in the Appendix can be used to evaluate the likelihood that different bursts are non-Collapsars or Collapsars and, with these probabilities, to estimate the quality of a specific sample and the significance of results based on this sample. In general, one should proceed with care before simply adopting the results of a study of an SGRB sample as reflecting the properties of non-Collapsars. In this context it is interesting to mention a few GRBs that play a major role in the current view of non-Collapsar properties. GRB 060121 and GRB 090426 are two SGRBs with a secure host at redshift ⩾2 that have led to the suggestion of a high-redshift non-Collapsar population. GRB 100424A has a redshift of z = 1.288. All other SGRBs with secure redshift are at z ⩽ 1. We find that the probabilities that these bursts are non-Collapsars are 0.17^+0.14_−0.15, 0.10^+0.15_−0.06, and 0.08^+0.12_−0.04 for GRBs 060121, 090426, and 100424A, respectively. Surely, one cannot establish a new population of high-redshift non-Collapsars based on these events. Another pivotal burst is 051221A; the only SGRB to date with a clear simultaneous optical/X-ray break in its afterglow, which is used to measure its beaming (Soderberg et al. 2006; Burrows et al. 2006). We find that the probability that GRB 051221A is a non-Collapsar is 0.18^+0.08_−0.11. This highlights our ignorance of the collimation (if there is any) of non-Collapsar outflows. It also highlights the fact that no firm conclusion can be drawn on non-Collapsars based on a single burst that is classified using its high-energy emission properties alone.

GRBs are widely classified as long and short, according to their duration T₉₀≶2 s, based on the general belief that this observational classification is associated with a physical one and that the two populations have different origins: Long GRBs are Collapsars and short ones are non-Collapsars (possibly arising from neutron star mergers, but at present, this association is still uncertain). This classification scheme is known to be imperfect due to the large overlap in the duration distribution between the two populations. It is also used for all detectors, although it is known that any classification scheme depends on the detector (e.g., Nakar 2007). The problem with this method is that, first it is impossible to know how trustworthy are results that are based on a single classified event. Second, the level of contamination in any studied sample is unknown. The main reason for this flawed practice is simply the lack of a reliable and quantifiable classification scheme. This is what we provide in this paper. Based on a physically motivated model, we have shown in an earlier study (Bromberg et al. 2011b) that at short durations the Collapsar distribution is flat, up to a typical duration of ∼20 s. This enables us to recover the non-Collapsar distribution from the overall duration distribution and to assign probability that a burst with a given duration and hardness is a non-Collapsar.

We carry out this analysis for three major GRB satellites, BATSE, Fermi, and Swift. We first find the probability that a burst is a non-Collapsar based on its duration alone, f_NC(T₉₀). We find that it depends strongly on the observing satellite and in particular on its spectral window. For a given duration the probability that a BATSE burst is a non-Collapsar is larger than the probability that a Swift burst is a non-Collapsar. A useful threshold duration that separates Collapsars from non-Collapsars is that where f_NC(T₉₀) = 0.5. We find that it is T₉₀ = 3.1 ± 0.5 s in BATSE, T₉₀ = 1.7^+0.4_−0.6 s in Fermi GBM, and T₉₀ = 0.8 ± 0.3 s in Swift.

As short GRBs are harder on average than long ones (Kouveliotou et al. 1993), it is natural to expect that GRBs with a hard spectrum have a higher probability to be non-Collapsars than softer ones. Thus, a better classification can be achieved by considering the hardness, in addition to the duration. We separate the sample of each satellite to three sub-samples based on the bursts hardness and repeat the analysis. Not surprisingly there are fewer non-Collapsars in the soft subgroups and more in the harder ones. Interestingly, the duration distributions of both Collapsars and non-Collapsars depend only weakly on the hardness and only the relative normalization between the two groups varies as we consider subgroups of different hardness. As there are more non-Collapsars in the hard subgroups, non-Collapsars dominate in these subgroups even at relatively long durations. For example, in the hard BATSE subgroup the probability, f_NC, that a burst is a non-Collapsar remains >0.5 up to durations T₉₀ ≃ 8 s. In the hard Fermi GBM and Swift subgroups f_NC > 0.5 up to ≃ 5 and ≃ 3 s, respectively. A soft GRB, on the other hand, is more likely to be a Collapsar. In this case, f_NC > 0.5 up to T₉₀ ≃ 1 s for BATSE's soft subgroup, up to T₉₀ ≃ 0.6 s in Fermi GBM, and only up to T₉₀ ≃ 0.3 in Swift's subgroups. These values should replace the average values as dividing durations between Collapsars and non-Collapsars, whenever hardness information is available. In particular, for Swift, 2.8^+1.5_−1.0, 0.6^+0.2_−0.3, and 0.3^+0.4_−0.2 s should replace the value of 0.8 ± 0.3 s for the hard, intermediate, and soft subgroups, respectively. Our results well agree with the overall behavior seen when comparing different satellites. Swift's window is much softer than BATSE's and Fermi's and the transition in Swift's overall sample between non-Collapsars and Collapsars occurs at shorter durations relative to the other satellites. This is a general pattern seen in both the overall sample and in the hardness subgroups.

We find that the transition between Collapsars and non-Collapsars is not sharp and that there is a large overlapping region where both Collapsars and non-Collapsars co-exist. There are short-duration Collapsars with durations shorter than 1 s as well as non-Collapsars at observed durations as long as 10 s. As such at the region of 2–10 s there is a mixture of soft Collapsars and hard non-Collapsars, which may give a false impression of the existence of an intermediate group there (e.g., Řípa et al. 2012). The traditional method to divide bursts to "long" and "short" according to a sharp observed duration criteria: T₉₀≶2, introduces both "false positive" and "false negatives" when we interpret duration as a proxy for a different physical origin. The choice of the division criteria should depend on the detector's observing windows but it should also depend on our tolerance for contamination by "falsely" classified bursts. When interested in Collapsars, the solution is trivial. Choosing a conservative large duration will eliminate a few short-duration Collapsars but will result in a sample containing practically only Collapsars. The small number of short-duration bursts makes it difficult to adopt a similar conservative policy for them and the classification criterion should be chosen carefully in each study. Finally, our results show clearly that no high-significance result concerning non-Collapsars can be derived based on a single burst, which is classified according to its high-energy properties alone.

Next we examine the implication of the currently used criterion T₉₀≶2 on the different satellite samples. It is conservative for BATSE, where only 10% of bursts that are shorter than 2 s are Collapsars. One can consider a BATSE (T₉₀ ⩽ 2 s) sample as reasonably free of false positives. The corresponding fraction of "false positives" for Fermi is higher (20%) but still acceptable for many purposes. However, this criteria is not good for Swift. About 40% of Swift bursts with T₉₀ < 2 s, which have been traditionally classified and studied as SGRBs, are Collapsars. Thus, the standard and commonly used sample of Swift GRBs with T₉₀≶2 s, which is the source of the only sample of well-localized short GRBs, is heavily contaminated with Collapsars. This must have influenced the results of non-Collapsars' studies that are based on Swift GRBs. Interestingly, this Collapsar contamination did not qualitatively affect the main conclusion concerning non-Collapsar hosts (Berger 2009, 2011), namely, the observation that these hosts have a wide distributions of SFRs, luminosities, and metallicities and that the conclusion that the positions of non-Collapsars has a wide spread within the host galaxy. Such distributions are significantly different than those of the Collapsar's host. However, quantitative features of these distributions must have been distorted.

While the complete implications of our results on studies of non-Collapsars are beyond the scope of this work, there are three important points that stand out. (1) There is no convincing evidence for high-redshift non-Collapsars. All the bursts with secure redshift that are non-Collapsars at high probability are at z < 1. (2) There is no convincing evidence for beaming in non-Collapsars. GRB 051221A is the only SGRB that shows a multi-wavelength afterglow break, which is interpreted as a jet break, and is considered as the strongest evidence for beaming in non-Collapsars. However, our results show that the probability that this burst is indeed a non-Collapsar is only 0.18^+0.08_−0.11. Apparently, non-Collapsars may or may not be beamed, as far as we currently know. (3) The duration of a non-negligible fraction of the non-Collapsars is 10 s and even longer. This implies (under most GRB models) that the central engine of these events works continuously in the mode that produces the initial hard GRB emission for that long. This fact should be accommodated by any model of non-Collapsar central engine.

We thank the anonymous referee for helpful comments. This research is supported by an ERC advanced research grant, by the Israeli Center for Excellence for High Energy AstroPhysics (T.P.), by ERC and ISF grants, and Packard, Guggenheim, and Radcliffe fellowships (R.S.), and by an ERC starting grant and ISF grant no. 174/08 (E.N.)

The probability of Swift GRBs and some additional interesting LGRBs to be non-Collapsars is provided in Table 5.