Swift BAT has detected $200 long-duration GRBs, with redshift measurements for $50 of them. We derive the luminosity function (È HL ) and the local event rate ( HL 0 ) of the conventional high-luminosity (HL) GRBs by using the z-known Swift GRBs. Our results are generally consistent with that derived from the CGRO BATSE data. However, the fact that Swift detected a low-luminosity (LL) GRB, GRB 060218, at z ¼ 0:033 within $2 years of operation, together with the previous detection of the nearby GRB 980425, suggests a much higher local rate for these LL-GRBs. We explore the possibility that LL-GRBs are a distinct GRB population from the HL-GRBs. We find that LL 0 is $325 þ352 À177 Gpc À3 yr À1 , which is much higher than HL 0 (1:12 þ0:43 À0:20 Gpc À3 yr À1 ). This rate is $0.7% of the local Type Ib/c SNe. Our results, together with the finding that less than 10% of Type Ib/c SNe are associated with off-beam GRBs, suggest that LL-GRBs have a beaming factor typically less than 14, or a jet angle typically wider than 31 . The high local GRB rate, small beaming factor, and low-luminosity make the LL-GRBs distinct from the HL-GRBs. Although the current data could not fully rule out the possibility that both HL-and LL-GRBs are the same population, our results suggest that LL-GRBs are likely a unique GRB population and that the observed low-redshift GRB sample is dominated by the LL-GRBs.

The two high-redshift gamma-ray bursts, GRB 080913 at z = 6.7 and GRB 090423 at z = 8.3, recently detected by Swift appear as intrinsically short, hard GRBs. They could have been recognized by BATSE as short/hard GRBs should they have occurred at z ≤ 1. In order to address their physical origin, we perform a more thorough investigation on two physically distinct types (Type I/II) of cosmological GRBs and their observational characteristics. We reiterate the definitions of Type I/II GRBs and then review the following observational criteria and their physical motivations: supernova association, specific star forming rate of the host galaxy, location offset, duration, hardness, spectral lag, statistical correlations, energetics and collimation, afterglow properties, redshift distribution, luminosity function, and gravitational wave signature. Contrary to the traditional approach of assigning the physical category based on the gamma-ray properties (duration, hardness, and spectral lag), we take an alternative approach to define the Type I and Type II Gold Samples using several criteria that are more directly related to the GRB progenitors (supernova association, host galaxy type, and specific star forming rate). We then study the properties of the two Gold Samples and compare them with the traditional long/soft and short/hard samples. We find that the Type II Gold Sample reasonably tracks the long/soft population, although it includes several intrinsically short (shorter than 1s in the rest frame) GRBs. The Type I Gold Sample only has 5 GRBs, 4 of which are not strictly short but have extended emission. Other short/hard GRBs detected in the Swift era represent the BATSE short/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 multiple observational 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 of GRBs, and re-emphasize the importance of invoking multiple observational criteria. We cautiously propose an operational procedure to infer the physical origin of a given GRB with available multiple observational criteria, with various caveats laid out.

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The intriguing observations of the Swift/Burst Alert Telescope (BAT) X-ray flash (XRF) 060218 and the BATSE-BeppoSAX gamma-ray burst GRB 980425, both with much lower luminosity and redshift compared to other observed bursts, naturally lead to the question of how these low-luminosity (LL) bursts are related to high-luminosity (HL) bursts. Incorporating the constraints from both the flux-limited samples observed with Compton Gamma-ray Observatory (CGRO)/BATSE and Swift/BAT and the redshift-known gamma-ray burst (GRB) sample, we investigate the luminosity function for both LL and HL GRBs through simulations. Our multiple criteria, including the log N − log P distributions from the flux-limited GRB sample, the redshift and luminosity distributions of the redshift-known sample and the detection ratio of HL and LL GRBs with Swift/BAT, provide a set of stringent constraints to the luminosity function. Assuming that the GRB rate follows the star formation rate (SFR), our simulations show that a simple power law (PL) or a broken power-law model of luminosity function fails to reproduce the observations and a new component is required. This component can be modelled with a broken power, which is characterized by a sharp increase in the burst number at around L < 10 47 erg s −1 . The lack of detection of moderate-luminosity GRBs at redshift ∼0.3 indicates that this feature is not due to the observational biases. The inferred local rate, ρ 0 , of LL GRBs from our model is ∼200 Gpc −3 yr −1 at ∼10 47 erg s −1 , much larger than that of HL GRBs. These results imply that LL GRBs could be a separate GRB population from HL GRBs. The recent discovery of a local X-ray transient 080109/SN 2008D would strengthen our conclusion if the observed non-thermal emission has a similar origin as the prompt emission of most GRBs and XRFs.

The origin and progenitors of short-hard gamma-ray bursts remain a puzzle and a highly debated topic. Recent Swift observations suggest that these GRBs may be related to catastrophic explosions in degenerate compact stars, denoted as "Type I" GRBs. The most popular models include the merger of two compact stellar objects (NS-NS or NS-BH). We utilize a Monte Carlo approach to determine whether a merger progenitor model can self-consistently account for all the observations of short-hard GRBs, including a sample with redshift measurements in the Swift era (z-known sample) and the CGRO/BATSE sample. We apply various merger time delay distributions invoked in compact star merger models to derive the redshift distributions of these Type I GRBs, and then constrain the unknown luminosity function of Type I GRBs using the observed luminosity-redshift (L − z) distributions of the z-known sample. The best luminosity function model, together with the adopted merger delay model, are then applied to confront the peak flux distribution (log N − log P distribution) of the BATSE and Swift samples. We find that for all the merger models invoking a range of merger delay time scales (including those invoking a large fraction of