Astron. Astrophys. 323, 312-316 (1997)

1. Introduction

Since the discovery of -ray bursts more than 20 years ago, their origin and emission mechanisms remain mysterious, a major reason for this is that the -ray burst events are all transient and so far no quiescent counterpart of a -ray burst has been observed. These limitations prevent us from measuring the source distance. Before 1991 it was widely believed that the GRBs originate from our Galaxy (Higdon & Lingenfelter 1990). However, the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory (CGRO) discovered that the distribution of GRBs is isotropic but radially non-uniform (Meegan et al. 1992; Fishman et al. 1994). This suggests that GRBs are either cosmological (e.g. Mao & Paczynski 1992; Piran 1992; Dermer 1992; Fenimore & Bloom 1995) or originated in an extended halo of our Galaxy (e.g. Brainerd 1992; Li & Dermer 1992; Podsiadlowski et al. 1995; Wei & Lu 1996). Although it is now very difficult to determine whether GRBs are within an extended halo of our Galaxy or at cosmological distances, we hope to look for some evidences from analyzing the statistical properties of GRB sources.

If GRB sources are at cosmological distances, then the expansion of the universe would have some effects on the statistics of GRBs. First, the burst temporal structure will be stretched by a factor , so on average, the temporal structure of dimmest bursts (presumably distant) should be longer than that of bright bursts (presumably nearer) by a factor . This time dilation phenomenon has been discovered in BATSE GRBs catalog (Norris 1994 ; Norris et al. 1994; Davis et al. 1994). Various tests that measure time dilation between dimmest and bright bursts have been made and a time dilation factor of about 2 has been found. Second, the number of GRBs would be decreased with distance due to redshift, causing the value of to be smaller than 0.5 (the value expected from nearby homogeneous sources), where for a given source, V is the volume of the smallest sphere containing the source, and is the maximum volumn accessible to the detector. , here is the maximum count rate and is the minimum count rate required to trigger the instrument. The value of decreases monotonously with redshift z (Mao & Paczynski 1992), so we can determine the redshift z from the observed value of . These two methods can estimate the distance scale of GRBs independently, therefore if the distance obtained from these two methods are consistent, it would be strong evidence in favor of the cosmological origin of GRBs.

Fenimore & Bloom(1995) have calculated the redshift z according to the observed time dilation and distribution (where N is the number of bursts with peak intensity larger than P). They found that the redshifts obtained from these two methods are quite different: from the observed time dilation factor of about 2, they obtained a redshift of , while is needed to be consistent with the observed distribution. They tend to favor the explanation that a large fraction of the observed time dilation is intrinsic to the bursts rather than the result of the expansion of the universe.

In this paper, we use a method similar to that of Fenimore & Bloom(1995) to calculate the distance scale of bursts according to the observed time dilation and statistics, by assuming a power-law spectrum of bursts. We found that the distance thus calculated is very sensitive to the spectral index , when , the distance obtained from these two independent methods are consistent. In the next section, we calculate the maximum redshift of bursts using statistics. In Sect. 3, the redshifts of bursts have been estimated according to the observed time dilation. Finally a short discussion and conclusion are given in Sect. 4.

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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