The onset of GRB afterglow is characterized by a smooth bump in the early
afterglow lightcurve. We make an extensive search for such a feature. Twenty
optically selected GRBs and 12 X-ray selected GRBs are found, among which 17
optically selected GRBs and 2 X-ray-selected GRBs have redshift measurements.
We fit the lightcurves with a smooth broken power-law and measure the temporal
characteristic timescales of the bumps at FWHM. Strong mutual correlations
among these timescales are found, and a dimmer and broader bump tends to peak
at a later peak time. The ratio of rising to decaying timescales is almost
universal among bursts, but the ratio of the rising time to the peak time
varies from 0.3~1. The E_iso is tightly correlated with the peak luminosity and
the peak time of the bump in the burst frame. Assuming that the bumps signal
the deceleration of the GRB fireballs in a constant density medium, we
calculate 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_0
are typically a few hundreds, and the typical deceleration radius is
R_dec~10^{17} cm. More intriguingly, a tight correlation between the Gamma_0
and E_iso is found, namely Gamma_0 ~ 195 E_iso, 52}^{0.27} (satisfied for both
the optical and X-ray z-known samples). It is helpful to understand GRB
physics, and may serve as an indicator of Gamma_0. We find that the early
bright X-rays are usually dominated by a different component from the external
shock emission, but occasionally (for one case) an achromatic deceleration
feature is observed. Components in X-rays would contribute to the diversity of
the observed X-ray lightcurves (abridge).Comment: 15 pages, including 4 tables and 7 figures, Submitted to Ap
