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The onset of GRB afterglow is characterized by a smooth bump in the earlyafterglow lightcurve. We make an extensive search for such a feature. Twentyoptically selected GRBs and 12 X-ray selected GRBs are found, among which 17optically selected GRBs and 2 X-ray-selected GRBs have redshift measurements.We fit the lightcurves with a smooth broken power-law and measure the temporalcharacteristic timescales of the bumps at FWHM. Strong mutual correlationsamong these timescales are found, and a dimmer and broader bump tends to peakat a later peak time. The ratio of rising to decaying timescales is almostuniversal among bursts, but the ratio of the rising time to the peak timevaries from 0.3~1. The E_iso is tightly correlated with the peak luminosity andthe peak time of the bump in the burst frame. Assuming that the bumps signalthe deceleration of the GRB fireballs in a constant density medium, wecalculate the initial Lorentz factor (Gamma_0) and the deceleration radius(R_dec) of the GRBs in the optical-selected sample. It is found that Gamma_0are typically a few hundreds, and the typical deceleration radius isR_dec~10^{17} cm. More intriguingly, a tight correlation between the Gamma_0and E_iso is found, namely Gamma_0 ~ 195 E_iso, 52}^{0.27} (satisfied for boththe optical and X-ray z-known samples). It is helpful to understand GRBphysics, and may serve as an indicator of Gamma_0. We find that the earlybright X-rays are usually dominated by a different component from the externalshock emission, but occasionally (for one case) an achromatic decelerationfeature is observed. Components in X-rays would contribute to the diversity ofthe observed X-ray lightcurves (abridge).

Constraining GRB Initial Lorentz Factor with the Afterglow Onset Feature and Discovery of a Tight Gamma_0-E_iso Correlation