Correlation Analysis of Temporal Variation of Spectral Parameters of Prompt GRB Emission

Prompt emission from a gamma-ray burst (GRB) exhibits very rapid and complicated temporal and spectral evolution, which likely contains a lot of information about the GRB origin. Using the BATSE time- resolved spectral fit data, we performed a number of correlation tests for individual bursts and for the entire sample. We report on the strong correlations between the low-energy power law index, $\alpha$, and the observed photon flux, $F$, in some GRBs. Since, however, the observed flux is a poor measure of the intrinsic flux (because of dust extinction, unknown distances, etc.), we calculate the normalized flux $F_*$ assuming that the correlation of $\alpha$ and $F$ is unique for all GRBs. We carefully examine statistical biases this technique may produce. We speculate that the observed $F-\alpha$ and $F_*-\alpha$ correlations support the predictions of an anisotropic jitter radiation theory from Weibel-generated magnetic fields.