GRB Radiative Efficiencies Derived from the Swift Data: GRBs versus XRFs, Long versus Short

We systematically analyze the prompt emission and the early afterglow data of a sample of 31 GRBs detected by Swift before 2005 September and estimate the GRB radiative efficiency. BAT's narrow band inhibits a precise determination of the GRB spectral parameters, and we have developed a method to estimate these parameters with the hardness ratio information. The shallow decay component commonly existing in early X-ray afterglows, if interpreted as continuous energy injection in the external shock, suggests that the GRB efficiencies previously derived from the late-time X-ray data were not reliable. We calculate two radiative efficiencies using the afterglow kinetic energy EK derived at the putative deceleration time (tdec) and at the break time (tb), when the energy injection phase ends, respectively. At tb XRFs appear to be less efficient than normal GRBs. However, when we analyze the data at tdec, XRFs are found to be as efficient as GRBs. Short GRBs have similar radiative efficiencies to long GRBs despite of their different progenitors. Twenty-two bursts in the sample are identified to have the afterglow cooling frequency below the X-ray band. Assuming ϵe = 0.1, we find ηγ(tb) usually <10% and ηγ(tdec) varying from a few percent to >90%. Nine GRBs in the sample have the afterglow cooling frequency above the X-ray band for a very long time. This suggests a very small ϵB and/or a very low ambient density n.