The `amplitude' parameter of gamma-ray bursts and its implications for GRB classification

Traditionally, gamma-ray bursts (GRBs) are classified in the T₉₀-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<sub>eff</sub> and f<sub>eff, z</sub> 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 available data, we quantify the probability of a disguised short GRB below a certain f value is as P (<f)∼ 0.78^{+0.71}_{-0.4} f^{-4.33± 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.