GRB Radiative Efficiencies Derived from the<i>Swift</i>Data: GRBs versus XRFs, Long versus Short

Abstract

We systematically analyze the prompt emission and the early afterglow data of a sample of 31 GRBs detected by&#13;\nSwift 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&#13;\nhardness 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&#13;\nfrom the late-time X-ray data were not reliable. We calculate two radiative efficiencies using the afterglow kinetic&#13;\nenergy EK derived at the putative deceleration time (tdec) and at the break time (tb), when the energy injection phase&#13;\nends, respectively. At tb XRFs appear to be less efficient than normal GRBs. However, when we analyze the data at&#13;\ntdec, XRFs are found to be as efficient as GRBs. Short GRBs have similar radiative efficiencies to long GRBs despite&#13;\nof their different progenitors. Twenty-two bursts in the sample are identified to have the afterglow cooling frequency&#13;\nbelow the X-ray band. εe = 0.1, we find ηγ(tb) usually &lt;10% and ηγ(tdec) varying from a few percent to&#13;\n&gt;90%. Nine GRBs in the sample have the afterglow cooling frequency above the X-ray band for a very long time.&#13;\nThis suggests a very small εB and/or a very low ambient density n.