Gamma-Ray Bursts: Temporal Scales and the Bulk Lorentz Factor

For a sample of Swift and Fermi GRBs, we show that the minimum variability timescale and the spectral lag of the prompt emission is related to the bulk Lorentz factor in a complex manner: For small $\Gamma$'s, the variability timescale exhibits a shallow (plateau) region. For large $\Gamma$'s, the variability timescale declines steeply as a function of $\Gamma$ ($\delta T\propto\Gamma^{-4.05\pm0.64}$). Evidence is also presented for an intriguing correlation between the peak times, t$_p$, of the afterglow emission and the prompt emission variability timescale.