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3 Results on the light curves of GRBs

The 19/11 GRBs that satisfied the selection for categories A/B are listed in Table 1. The running and cumulative light curves and fits to the nonlinear sections of the bursts are given in Figs. 1 and 2 for three bursts in each category. The cumulative light curve smoothes the spiky nature of the running light curve. In category A the highest peak flux frequently occurs near the end of the nonlinear increase and subsequently the bursts stops abruptly (Fig. 1a) or continues at a much reduced rate (Fig. 1c) due to decrease in accretion. In category B there is a decrease in the running light curve that is an approximate mirror image of bursts in category A (Fig. 2) and the nonlinear slowdown in the cumulative light curve results from the drop in amplitude of the pulses in the running profiles.

The GRBs in Table 1 have large numbers of pulses. The errors due to the BATSE counting statistics can be neglected because they are very small compared with the large fluctuations caused by the pulses in the running light curves. Equations (1) and (2) were fit to the cumulative light curve to obtain the best fit to the data (Figs. 1 and 2). The values of $\beta $ are in the range 1.8 to 2.3 (Table 1). The range in $\beta $ was estimated by varying $\beta $ from 1.5 to 2.5 and visually estimating the range where there was agreement between the fitted functions and the cumulative light curves. The values are listed in Table 1 and typically are in the range $\pm$0.2. The fluctuations between the fitted curve and the cumulative data are due to the pulses and the time intervals between them in the running light curve. These residuals are inherent to the pulsed nature of GRBs. The value of c (Table 1) is given for the parabolic value $\beta = 2$ for all bursts to enable comparison of the normalised cumulative profiles. The errors on the hardness ratios (Table 1) are all less than 7% with the exception of the soft GRB 6903 where it is 50%.


  \begin{figure}
\includegraphics[width=8.8cm,clip]{aaef111f1.ps}
\end{figure} Figure 1: The running (dashed) and cumulative (solid) light curves of the BATSE bursts with trigger numbers  a) 3105, b) 3860 and c) 6963 with count per 64 ms and cumulative count scales on the left and right vertical axes. The inserts give the cumulative count (solid) and the fit of the function (dashed) for the relevent section. The start and end times are listed in Table 1 and t1 is shifted to zero for the inserts. The vertical axes in the inserts are the normalised cumulative count.


  \begin{figure}
\includegraphics[width=8.8cm,clip]{aaef111f2.ps}
\end{figure} Figure 2: The running (dashed) and cumulative (solid) light curves of the BATSE bursts with trigger numbers a) 678, b) 4039 and c) 6694 with the same notation as Fig. 1.


   
Table 1: The GRBs that satisfied the criteria for category A (first 19 rows) and category B (second 11 rows). The columns refer to BATSE trigger number, the number of pulses $N \geq 5~\sigma$, the number of those pulses  $N^{\prime }$ included in the fitted region between times t1 and t2 with a minimum value of 7 s for GRB 1440 and maximum of 140 s for GRB 8101, the hardness ratio (HR) which is the ratio of fluence in BATSE channels 3 and 4 above 100 keV to that in channels 1 and 2 below 100 keV, the percentage of the total integrated counts (%C) in the fitted region, the index $\beta $ and the coefficient $c \times 10^{-4}$ for the fit with $\beta = 2$. GRBs 3247, 6353, 6903, 8101 and 7660 are from the fainter sample with T90 > 100 s.

Burst
$N/N^{\prime}$ t1,t2 HR $\%$ C $\beta $ c

394
25/12 0, 25 4.6 42 $1.9 \pm0.2$ 6.8
1122 10/8 0, 11 3.2 62 $1.9 \pm0.2$ 49.0
1440 15/9 10, 17 5.3 70 $2.1\pm0.2$ 147.1
2450 22/11 45, 65 3.4 49 $2.1\pm0.3$ 12.0
3035 21/12 5, 75 4.7 52 $2.1\pm0.3$ 1.1
3105 30/30 -10, 30 6.5 98 $2.1\pm0.2$ 6.3
3247 25/17 80, 180 7.7 79 $2.1\pm0.2$ 0.9
3489 12/5 -2, 11 6.6 56 $2.0\pm0.2$ 35.4
3860 13/8 -5, 22 22.4 72 $1.9\pm0.3$ 9.6
5526 34/14 -6, 16 4.4 36 $2.1\pm0.2$ 7.6
6353 9/5 -10, 50 1.7 53 $2.2\pm0.2$ 1.5
6453 25/12 -5, 52 1.7 46 $2.0\pm0.3$ 1.4
6587 28/20 3, 25 7.6 73 $2.1\pm0.2$ 15.8
6593 20/11 -10, 14 4.7 60 $2.1\pm0.3$ 10.2
6903 13/5 -25, 15 1.6 47 $2.1\pm0.2$ 3.3
6963 17/10 0, 17 4.1 52 $2.0\pm0.2$ 18.4
7318 12/7 -3, 10 21.8 78 $2.0\pm0.2$ 48.0
7575 30/20 135, 165 12.9 78 $2.1\pm0.2$ 9.1
8101 11/9 -40, 100 10.4 95 $1.9 \pm0.2$ 0.5

678
52/44 1, 36 42.6 86 $1.9 \pm0.2$ 6.2
2891 18/14 0.5, 20 23.1 89 $2.1\pm0.3$ 22.0  
2929 44/36 12, 50 13.5 83 $2.2 \pm 0.3$ 5.7
2984 22/12 6, 20 14.2 72 $2.1\pm0.2$ 37.2
2993 17/11 0, 20 31.1 75 $2.2\pm0.2$ 16.4
2994 36/22 6, 35 19.3 58 $2.3 \pm 0.2$ 6.3
3408 44/35 10, 60 6.4 77 $1.9 \pm0.2$ 3.2
4039 33/31 0, 40 21.5 91 $1.9\pm0.3$ 5.1
6694 10/9 1, 16 18.3 91 $2.1\pm0.2$ 39.5
7660 7/5 25, 140 8.4 77 $2.0\pm0.3$ 0.7
7766 22/11 0, 20 48.2 85 $2.0\pm0.2$ 18.1


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