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Prompted by various analyses of long (Type II) GRB rates and their relationship to the cosmic star-formation history, metallicity and luminosity function evolution, we systematically analyze these effects with a Monte Carlo code. We test various cosmic star-formation history models including analytical and empirical models as well as those derived from cosmological simulations. We also explore expressions for metallicity enhancement of the GRB rate with redshift, as presented in the literature, and discuss improvements to these analytic expressions from the point of view of galactic evolution. These are also compared to cosmological simulations on metal enrichment. Additionally we explore possible evolutionary effects of the GRB rate and luminosity function with redshift. The simulated results are tested with the observed Swift sample including the L, z, and peak flux (log N-log P) distributions. The observational data imply that an increase in the GRB rate is necessary to account for the observations at high redshift, although the form of this enhancement is unclear. A rate increase due to lower metallicity at higher redshift may not be the singular cause and is subject to a variety of uncertainties. Alternatively, evolution of the GRB luminosity function break with redshift shows promise as a possible alternative., Comment: MNRAS Accepted. Minor changes to text. 12 pages, 5 figures, 4 tables

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 "prompt mergers"), it is difficult to reconcile the models with all the data. The data are instead statistically consistent with the following two possible scenarios. First, that short/hard GRBs are a superposition of compact-star-merger origin (Type I) GRBs and a population of GRBs that track the star formation history, which are probably related to the deaths of massive stars (Type II GRBs). Sec- ond, the entire short/hard GRB population is consistent with a typical delay of 2 Gyr with respect to the star formation history with modest scatter. This may point towards a different Type I progenitor than the traditional compact star merger models., Comment: ApJ, accepted. Addition models and statistical tests added, main conclusion expanded but largely unchanged

(Abridged) 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. 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 review the observational criteria and their physical motivations. 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, and 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. We suggest that GRB 080913 and GRB 090423 are more likely Type II events. We re-emphasize the importance of invoking multiple observational criteria, and cautiously propose an operational procedure to infer the physical origin of a given GRB with available multiple observational criteria, with various caveats laid out., Comment: 32 pages, ApJ, in press. The strengths and weaknesses of physical classification and its relation to phenomenological classification are fully discussed in a newly added section 3. Discussions on GRBs 090423, 090426, and 090510 are included