Interpretations of gamma-ray burst spectroscopy. I. Analytical and numerical study of spectral lags

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Abstract
We describe the strong spectral evolution that occurs during a gamma-ray burst pulse and the means by which it can be analyzed. Based on observed empirical correlations, an analytical model is constructed which is used to describe the pulse shape and quantize the spectral lags and their dependences on the spectral evolution parameters. We find that the spectral lag depends mainly on the pulse-decay time-scale and that hard spectra (with large spectral power-law indices alpha) give the largest lags. Similarly, large initial peak-energies, Eo, lead to large lags, except in the case of very soft spectra. The hardness ratio is found to depend only weakly on alpha and the HIC index, eta. In particular, for low Eo, it is practically independent, and is determined mainly by Eo. The relation between the hardness ratio and the lags, for a certain Eo are described by power-laws, as alpha varies. We also discuss the expected signatures of a sample of hard spectral pulses (e.g. thermal or small pitch-angle synchrotron emission) versus soft spectral pulses (e.g. optically-thin synchrotron emission). Also the expected differences between a sample of low energetic bursts (such as X-ray flashes) and of high energetic bursts (classical bursts) are discussed.

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