1 Introduction

Much of the recent progress in the study of gamma-ray bursts (GRBs) results from the detection of bursts with good location accuracy by BeppoSAX that enabled the detection of counterparts at other wavelengths. The subsequent redshift determination of bursts have established that these bursts are at cosmological distances (Costa et al. 1997; van Paradijs et al. 1997). GRBs seem to be connected to massive stars and become powerful probes of the star formation history of the universe (Lamb & Reichart 2000; Hanlon et al. 2000; Berger et al. 2001). However not many redshifts are known and there is still much work to be done to determine the mechanisms that produce these enigmatic events.

The most plausible GRB progenitors are expected to be a newly formed black hole (BH) surrounded by a temporary accretion disk (Rees 1999; Mészáros 2001; Castro-Tirado 2001; van Putten 2001). The most popular models include the merger of a neutron star (NS) and a NS (Eichler et al. 1989; Ruffert & Janka 1999), NS and a BH (Paczynski 1991), BH white dwarf merger (Fryer et al. 1999) and models of failed supernovae or collapsars (MacFadyen & Woosley 1999; Paczynski 1998). An important exception is the model in which the GRB energy is provided by a newly formed neutron star (Usov 1992; Thompson 1994). Various explanations have been put forward for the complicated structure of the light curves. These range from internal shocks, caused by variations in the velocity of the outflow (Rees & Mészáros 1994; Piran 1999), to external shocks, caused by interactions with an external medium (Mészáros & Rees 1993; Dermer & Mitman 1999). In the internal shock model the instabilities in the wind leads to shocks which convert a fraction of the bulk kinetic energy to internal energy remote from the central engine. A turbulent magnetic field then accelerates electrons which radiate by synchrotron emission and inverse Compton scattering, generating the GRB. Many of the observed features in bursts can be reproduced in the internal shock models of GRBs (Sari & Piran 1997; Kobayashi et al. 1997; Daigne & Mochkovitch 1998; Panaitescu et al. 1999; Downes et al. 2001).

A variety of analytical techniques has been applied to the temporal and spectral profiles of GRBs which place constraints on the observed distributions which models must satisfy. The impressive results from these studies include (1) hard to soft evolution (Golenetskii et al. 1983; Borgonovo & Ryde 2001); (2) the duration-hardness anticorrelation (Kouveliotou et al. 1993); (3) the temporal asymmetry of pulses in GRBs (Nemiroff et al. 1993; Link & Epstein 1996); (4) a bimodal duration distribution of GRBs consistent with two lognormal distributions (Kouveliotou et al. 1993; McBreen et al. 1994); (5) the discovery of two different types of pulses in GRBs (Pendleton et al. 1997); (6) a correlation between $E_{\rm peak}$and intensity (Mallozzi et al. 1995); (7) energy dependence of the pulse duration (Norris et al. 1996); (8) a relationship between the pulse peak energy, $E_{\rm peak}$, and the photon fluence (Liang & Kargatis 1996; Crider et al. 1999); (9) lognormal pulse shapes and time intervals between pulses in long (McBreen et al. 1994; Hurley et al. 1998) and short GRBs (McBreen et al. 2001); (10) spectra well fit with a Band function (Band et al. 1993); (11) spectral hardening before a count rate increase (Bhat et al. 1994); (12) an X-ray excess in GRB spectra (Strohmayer et al. 1998); (13) a correlation between complexity and brightness (Stern et al. 1999) and (14) the unique properties of the pulses and power law relationships between the pulse properties and durations of GRBs (McBreen et al. 2002).

While GRBs display hard to soft spectral evolution, there is remarkable constancy of the pulses in GRBs throughout the burst (Ramirez-Ruiz & Fenimore 2000; Quilligan et al. 1999). The temporal and spectral properties of a few GRBs with known redshift have yielded two important results to suggest that GRB properties may be related to their luminosities. Ramiriz-Ruiz and Fenimore (1999) have shown that more rapidly variable bursts have higher absolute luminosities. Norris et al. (2000) have found an anticorrelation between the time delay in the arrival times of hard and soft photons in pulses and the luminosity of the GRB.

The light curves of GRBs are irregular and complex. Statistical studies are necessary to characterise their properties and hence to identify the physical properties of the emission mechanism. The statistical methods used for temporal studies can be broadly divided into four categories: (1) fits to individual pulses in the GRB using a number of pulse shape parameters (Norris et al. 1996; Lee et al. 2000b; Lee et al. 2000a); (2) a non-parametric approach to pulse shapes in GRBs (McBreen et al. 1994; Hurley et al. 1998; Young et al. 1995; Quilligan et al. 1999); (3) the average statistical properties of GRBs using a peak-aligned profile (Stern & Svensson 1996); and (4) the average power spectral density of GRBs (Belli 1992; Beloborodov et al. 2000; Chang & Yi 2000). One of the first studies (McBreen et al. 1994) revealed that lognormal distributions can adequately describe the properties of GRBs. Subsequent studies (Li & Fenimore 1996; Hurley et al. 1998; Quilligan et al. 1999) have confirmed the applicability of lognormal distributions in accounting for the wide range in the observed properties of pulses in GRBs. This result is not surprising because lognormal distributions arise from the product of probabilities of a combination of independent events and such conditions apply to the pulse generation process in GRBs.

In a different approach (Beloborodov et al. 2000) used Fourier analysis to study the power spectral density of long GRBs. This approach revealed that the diversity of GRBs is due to random realisations of the same process which is self-similar over a range of time scales (Stern & Svensson 1996). The slope of the PSD was -5/3 suggesting that GRBs are related to fully developed turbulence. The two different approaches are quite similar because the lognormal approach has been used to describe fully developed turbulence (Arneodo et al. 1999).

The work presented here expands on the earlier analysis (Quilligan et al. 2000) and provides new insight into the mechanism which generates GRBs. The aim is to provide a comprehensive description and understanding of the pulse properties in GRBs and combine it with other studies of the spectral properties. The wavelet analysis and the pulse selection algorithm are described in Sect. 2. The method for comparing the properties of the pulses before and after the strongest pulse in the GRB is also described in Sect. 2. The results are presented in Sect. 3, and discussed in Sect. 4. The conclusions are presented in Sect. 5.

Figure 1: Illustration of the background subtraction algorithm. The shaded region indicates the bursting phase of the GRB.