Hou-Jun Lü, Bing Zhang, En-Wei Liang, Bin-Bin Zhang, Takanori Sakamoto
(abridged),In this paper, we suggest to add the "amplitude" of GRB prompt emission as the third dimension into the consideration of GRB classification with the prompt $\gamma$-ray data. We define three new parameters with the prompt emission data. The first parameter is defined as $f={F_{p}}/{F_{B}}$, where $F_{p}$ and $F_{B}$ are the peak flux and the background flux, respectively. The second parameter is defined by $f_{\rm eff}={F^{\prime}_{p}}/{F_{B}}$, where ${F^{\prime}_{p}}$ the peak flux of the a pseudo-GRB, which is generated by scaling the original lightcurve down until the measured $T_{90}$ above the background is just less than 2 s. This is an "effective amplitude" of a real long GRB that is observed as a "short" GRB with its "tip-of-iceberg" above the background. The third parameter is defined as $f_{\rm eff,z}={F^{\prime}_{p,z}}/{F_{B}}$, where ${F^{\prime}_{p,z}}$ is the peak flux of another pseudo-GRB, which is generated by progressively moving a GRB to a higher redshift $z$, until its measured "rest frame" duration $T_{90}/(1+z)$ is just below 2 s. We systematically derive these parameters for the {\em Swift} GRBs detected between December 2004 to December 2011. We find that most short GRBs are likely not "tip-of-iceberg" of long GRBs. However, one needs to be cautious if a short GRB has $f<2$, since it could be either intrinsically short or intrinsically long with the extended emission episodes buried beneath the background. We also find that most long GRBs would show up as rest-frame short GRBs if they have a high enough redshift. This interprets the interesting observational fact that the three highest-$z$ GRBs (080913, 090423, 090429B) all have a rest frame duration shorter than 2 s, but are all likely Type II GRBs.
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http://arxiv.org/abs/1211.1117
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