Figure 1: Data from GRB 990308 with z=1.60 collected by BATSE trigger 7457 in a total number of 2^{11} 64 ms bins in the energy band 115-320 keV (top panel), and its Symmlet-10 (Mallat 1998) discrete wavelet transform (DWT) at the level L=6. The horizontal axis corresponds to the same time scale as in the original burst. Each level on the vertical axis shows the wavelet coefficients at a given resolution level (i.e., scale). The wavelet coefficients are represented by spikes whose size and direction (up or down) is determined by the magnitude and sign (+ or -) of the coefficient. | |
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Figure 2: The GRB 990308 light curve after preprocessing which sets the median absolute deviation of wavelet coefficients at the fine scale equal to unity, as described in more detail in Appendix A. The intensity profile estimated by the wavelet shrinkage procedure at the level L=6 is presented in the bottom panel. | |
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Figure 3: The CWT image (middle panel) of the GRB 990308 intensity profile (top panel). The horizontal and vertical axes give, respectively, the position u and (where s is the time scale in seconds), The shadings (colours from white to black) correspond to negative, zero and positive wavelet transforms respectively. Singularities create large amplitude coefficients in their cone of influence. The modulus maxima (bottom panel) of Wf(u,s) obtained from the matrix of CWT (middle panel) pointing towards the time positions of singularities at the fine scale. | |
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Figure 4: The light curve for GRB 990308 obtained by BATSE with trigger 7457, binned with 64 ms resolution in four spectral bands. | |
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Figure 5: The estimated intensity profiles of GRB 990308 - see Fig. 4 - obtained in four spectral bands by using a Symmlet-10 (Mallat 1998) basis at level L=6. The signal-to-noise ratios are at the levels SNR1=23.07, SNR2=22.71, SNR3=23.58 and SNR4=23.87 for each band, respectively. All variation points founded by CWT zoom are marked by circles. The behaviours of the Lipschitz exponents are estimated. Seven pairs of genuine variation points in the first and third spectral bands have been detected. | |
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Figure 6: Spectral time lags between the arrival times of pairs of genuine variation points detected in the third and first BATSE spectral bands. The analysis has been done for 9 GRB light curves collected with time resolution 64 ms. The solid line shows the best linear fit versus . | |
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Figure 7: The combination of 64 ms BATSE time-lag measurements shown in Fig. 6 with the measurement obtained from the BATSE-OSSE comparison and the TTE portion of the GRB 980329 light curve, with resolution 2.7 ms. | |
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Figure 8: The function defined in Eq. (35) as a function of the quantum gravity scale, for the scenario with a linear energy dependence of the vacuum refractive index, as obtained using different combinations of data sets. The solid line, which is used to establish the lower limit Eq. (36), corresponds to the combination of 64 ms BATSE data with both TTE and OSSE-BATSE data. | |
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Figure 9: The same function as in Fig. 8, which is defined in Eq. (35), now plotted as a function of the inverse quantum-gravity scale. The solid line corresponds the final lower limit Eq. (36). | |
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