Fractal analysis of short and intermediate GRB and the fireball model

In the present work the possibility of the fractal analysis application for GRB temporal profiles was studied. We have analysed the 4B revised BATSE catalog: temporal profiles of GRB with t₉₀ < 3 s (287 short and 100 intermediate) were studied on TTE data, a sample of 278 intermediate GRB with t₉₀  3 s were studied on DISCSC data. An analysis of the background fractal dimension distributions obtained using TTE and DISCSC data (143 and 110 background regions, respectively), indicates that for both datasets background fractal dimensions D_bgr = 1.5 that the fractal dimension distributions obtained by using these data can be processed simultaneously. The change of the fractal index D_bgr for Poisson statistics – dominated sets with different coefficients of error in counting (up to 10) was studied and D_bgr = 1.5. The ranges of fractal dimension (0.80  D  2.25 for short and 0.85  D  2.01 for intermediate GRB) are shifted over range for theoretical fractal curve (1 < D < 2) due to the finite detector time resolution. There are four subgroups in fractal dimension distribution for short GRB (D = 1.05 ± 0.03, D = 1.31 ± 0.05, D = 1.51 ± 0.04, D = 1.90 ± 0.03) and six subgroups for intermediate one (D = 1.05 ± 0.09, D = 1.24 ± 0.08, D = 1.44 ± 0.07, D = 1.51 ± 0.08, D = 1.64 ± 0.07, D = 1.91 ± 0.1). Time profiles with fractal dimension smaller then background can be obtained by using models with many short chaotic processes in sources, for example, fireball model with shock waves. The range of fractal dimensions for the modelled temporal profiles is 1.213  D  1.400, which can correspond to subgroups of short and intermediate GRB with D = 1.31 and D = 1.24; moreover, the fractal dimension of a simulated indented event and GRB990208 are equal within the error limits for some model parameters and it is possible to obtain smooth temporal profiles with D = D_bgr.