The "amplitude" parameter of Gamma-Ray Bursts and its implications for GRB classification

Traditionally gamma-ray bursts (GRBs) are classified in the $T_{90}$-hardness ratio two-dimensional plane into long/soft and short/hard GRBs. In this paper, we suggest to add the "amplitude" of GRB prompt emission as the third dimension as a complementary criterion to classify GRBs, especially those of short durations. We define three new parameters $f$, $f_{\rm eff}$ and $f_{\rm eff,z}$ as ratios between the measured/simulated peak flux of a GRB/pseudo-GRB and the flux background, and discuss the applications of these parameters to GRB classification. We systematically derive these parameters to 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 a relatively small $f$ (e.g. $f<1.5$), since the chance for an intrinsically long GRB to appear as a "disguised" short GRB is higher. Based on avaialble data, we quantify the probability of a disguised short GRB below a certain $f$ value is as $P (<f)\sim 0.78^{+0.71}_{-0.4} f^{-4.33\pm 1.84}$. By progressively "moving" a long GRB to higher redshifts through simulations, we also find that most long GRBs would show up as rest-frame short GRBs above a certain redshift.