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 $Gamma$ ($delta TproptoGamma^{-4.05pm0.64}$). Evidence is also presented for an intriguing correlation between the peak times, t$_p$, of the afterglow emission and the prompt emission variability timescale.