The Initial Lorentz Factors Of Gamma-Ray Burst Fireballs And The Lifetimes Of The Central Engines

Both observational and theoretical progresses on gamma-ray bursts (GRBs) in recent years, especially since the launches of Swift and Fermi satellites, are briefly summarized, and our analysises on the initial Lorentz factor of the GRB fireballs and the lifetime of the GRB central engines are presented in this article.The GRB fireballs are extremly relativistic, and initial Lorentz factors of the fireballs are a crucial parameter to understand the GRB physics. The onset of the GRB afterglows is characterized by a smooth bump in the early afterglow light curve as the GRB fireball is decelerated by the circumburst medium in the thin shell case. We extensively search for GRBs with such an onset feature in their optical and X-ray light curves. Twenty optically-selected GRBs and 12 X-ray-selected GRBs are obtained. We calculate the initial Lorentz factor (Γ0) and the deceleration radius (Rd) of the GRBs with redshift measurements. The derivedΓ0 is typically a few hundreds, and the deceleration radius is Rd～2×1017cm. More intriguingly, a tight correlation betweenΓ0 and Eiso,r is found, namelyΓ0≈182 Eiso,γ,52,0.25 which can be very useful to understand GRB physics. The relation could also roughly estimate the initial Lorentz factor of the other long bursts.The time scale of central engine is a crucial parameter for GRB classification. The observed erratic X-ray flares post the prompt gamma-ray phase indicates that the lifetimes of the GRB central engines (TCE) are much longer than the duration of prompt gamma-rays. We collect a unified sample of the XRT lightcurves and measure the lifetime TCE of the central engines with the X-ray flares. It is found that no any significant flare is observed in the XRT lightcurves for about one-third of the GRBs in our sample and a steep decay segment post the prompt gamma-ray phase is usually seen in their XRT lightcurves. The duration of the prompt gamma-rays T90 would be a good indicator of the TCE, of these GRBs. Significant flares following the prompt gamma-ray phases are observed for two-third of the bursts in our sample. These flares are erratically superimposed in the underlying X-ray afterglows. We estimate the TCE, with the peak time of the last flare. It is interesting that the XRT lightcurves of 5 GRBs (including the well-known short-type GRB 050724) are dominated by flares without detection of a clear afterglow component, likely indicating that the density of the medium surrounding these busts may be much lower than the other bursts. The distribution of TCE, of the bursts in our sample spans from several seconds to days without any bimodal features. The typical value of TCE is 100-1000 seconds. Our results suggest that the lifetimes of the GRB central engines are much longer than T90 and the bimodal distribution of T90 may be due to a selection effect of the BATSE.