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2 Analysis of the light curves of gamma ray bursts

A large sample of the brightest BATSE GRBs was used with the data combined from the four energy channels (Fishman & Meegan 1995). The analysis procedures are described in detail elsewhere (Quilligan et al. 2002; McBreen et al. 2001, 2002a). The full sample consisted of 100 GRBs with duration T90 < 2 s where T90measures the burst integrated count from 5% to 95% of the total, 319 GRBs with T90 > 2 s and a further fainter sample of 79 GRBs with T90 > 100 s to include very long bursts. The cumulative light curves of most GRBs could be approximated by a linear function implying constant output over most of the duration of the burst (McBreen et al. 2002a). Two significant minorities were visually identified that are better described by nonlinear changes in the cumulative count. In category A the running count increased towards the tallest pulse in the burst resulting in a nonlinear increase in the cumulative profile. In category B the running count decreased after the tallest pulse in the burst causing the cumulative profile to increase at a much slower rate as time progressed. In category A the normalised cumulative profile was fit by the function

\begin{displaymath}{R}(t_{i})={I}_{{\rm min}} + c (
t_{{i}} - t_{{0}})^{\beta}
\end{displaymath} (1)

where R(ti) is the cumulative count at time ti and  $I_{{\rm min}}$ is the minimum count at t0. In category B the function used was

\begin{displaymath}{D}(t_{{i}})={I}_{{\rm max}} - c (
t_{{\rm max}} - t_{{i}})^{\beta}
\end{displaymath} (2)

where D(ti) is the cumulative count at time ti, $t_{{\rm max}}$ is the time at the end of the fitted section of the burst and  $I_{{\rm max}}$ is the value of the count at  $t_{{\rm max}}$. $I_{{\rm max}}$usually has a value close to unity. The profiles were fit using the Levenberg-Marquardt nonlinear minimisation algorithm. The fitted sections include at least 5 pulses $\geq$$5 \sigma$ from the running profile, 20$\%$ of the GRB duration and 30$\%$ of the cumulative total. In the two categories there were 19 and 11 GRBs that satisfied the selection criteria. An increase in number occurs when the selection criteria are relaxed.

The median number of pulses N in GRBs with T90 > 2 s is only 6 (Quilligan et al. 2002) and the requirement on N restricts the GRBs to about half of the total. The number of pulses is important because they may originate from explosions in the central engine and discriminate against GRBs, where the emission is not well resolved into pulses because of the washing out of time structure in the jet before the gamma-ray photosphere, and interactions with the external medium including the effects of early afterglow (Dermer & Mitman 1999). The changes in the cumulative count presented here are quite different from the smooth power law decays in GRBs of the FRED (i.e. Fast Rise Exponential Decay) type (Giblin et al. 2002) and the smooth decays in a sample of pulses within GRBs (Ryde & Svensson 2001).

Most GRBs with T90 < 2 s can also be approximated by a linear fit to the cumulative light curve (McBreen et al. 2002a). The GRBs have a median value of N = 2.5 (McBreen et al. 2001) and no short GRBs were found to meet the criteria used for long GRBs.


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