CONSTRAINING GAMMA-RAY BURST INITIAL LORENTZ FACTOR WITH THE AFTERGLOW ONSET FEATURE AND DISCOVERY OF A TIGHT Γ₀-<i>E</i>_γ,isoCORRELATION

Abstract

The onset of GRB afterglow is characterized by a smooth bump in the early\nafterglow lightcurve. We make an extensive search for such a feature. Twenty\noptically selected GRBs and 12 X-ray selected GRBs are found, among which 17\noptically selected GRBs and 2 X-ray-selected GRBs have redshift measurements.\nWe fit the lightcurves with a smooth broken power-law and measure the temporal\ncharacteristic timescales of the bumps at FWHM. Strong mutual correlations\namong these timescales are found, and a dimmer and broader bump tends to peak\nat a later peak time. The ratio of rising to decaying timescales is almost\nuniversal among bursts, but the ratio of the rising time to the peak time\nvaries from 0.3~1. The E_iso is tightly correlated with the peak luminosity and\nthe peak time of the bump in the burst frame. Assuming that the bumps signal\nthe deceleration of the GRB fireballs in a constant density medium, we\ncalculate the initial Lorentz factor (Gamma_0) and the deceleration radius\n(R_dec) of the GRBs in the optical-selected sample. It is found that Gamma_0\nare typically a few hundreds, and the typical deceleration radius is\nR_dec~10^{17} cm. More intriguingly, a tight correlation between the Gamma_0\nand E_iso is found, namely Gamma_0 ~ 195 E_iso, 52}^{0.27} (satisfied for both\nthe optical and X-ray z-known samples). It is helpful to understand GRB\nphysics, and may serve as an indicator of Gamma_0. We find that the early\nbright X-rays are usually dominated by a different component from the external\nshock emission, but occasionally (for one case) an achromatic deceleration\nfeature is observed. Components in X-rays would contribute to the diversity of\nthe observed X-ray lightcurves (abridge).\n