The onset of GRB afterglow is characterized by a smooth bump in the early afterglow lightcurve caused by the deceleration of the gamma-ray burst ( GRB ) fireball by the circumburst medium .
We make an extensive search for such a deceleration feature , either from the literature for optical lightcurves , or from the X-ray afterglow lightcurve catalog established with the Swift/XRT .
Twenty optically selected GRBs and 12 X-ray selected GRBs are found to show the onset signature , among which 17 optically selected GRBs and 2 X-ray-selected GRBs have redshift measurements .
We study the optical z -known sample by fitting the lightcurves with a smooth broken power-law and measure the width ( w ) , rising timescale ( t _ { r } ) , and decaying timescale ( t _ { d } ) at full-width-at-half-maximum ( FWHM ) .
Strong mutual correlations among these timescales and with the peak time ( t _ { p } ) are found .
The optical peak luminosity ( L _ { p,O } ) at the lightcurve bump is anti-correlated with t _ { p } and correlated with w , indicating a dimmer and broader bump at a later peak time .
The ratio t _ { r } / t _ { d } is almost universal among bursts , but the ratio t _ { r } / t _ { p } varies from 0.3 \sim 1 .
The isotropic gamma-ray energy ( E _ { \gamma, { iso } } ) is tightly correlated with L _ { { p,O } } and t _ { p } 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 _ { d } ) 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 } \sim 10 ^ { 17 } cm .
More intriguingly , a tight correlation between the initial Lorentz factor and the isotropic gamma-ray energy is found , namely \Gamma _ { 0 } \simeq 195 E _ { \gamma, { iso } , 52 } ^ { 0.27 } ( satisfied for both the optical and X-ray z -known samples ) .
This correlation is helpful to understand GRB physics , and may serve as an indicator of \Gamma _ { 0 } for other long GRBs .
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 .