Duration Distribution

Only for 891 out of 944 GRBs from this GRBM catalog the duration estimate has been possible, since short duration bursts, for which no HTR data were available, prevent from measuring either $T_{90}$ or $T_{50}$.

Figure: $T_{90}$ and $T_{50}$ Distributions of 891 GRBs detected by the GRBM (40-700 keV).

In fig.  the $T_{90}$ and $T_{50}$ distributions of 891 GRBM bursts, are shown. By comparing them with the analogous BATSE distributions (fig. ), it can be noted that in the GRBM case, the bimodality distribution found by BATSE ([Kouveliotou et al., 1993,Fishman et al., 1994]) is less apparent, probably because of a lack of short duration bursts ($T_{90}<2$ s), that causes a bias in the distribution.

Figure: $T_{90}$ Distribution of 777 GRBs and $T_{50}$ Distribution of 689 GRBs (40-700 keV). Only durations known with at least 3$\sigma$ significance have been taken.

Like in the case of BATSE, the sample has been split into the short ($T_{90}<2$ s) and long ($T_{90}>2$ s) burst classes, with the following results: 124 short and 767 long GRBs, corresponding to $\sim$ 14% and 86%, respectively. For comparison, in the case of BATSE bursts, the corresponding fractions were $\sim$ 26% and $\sim$ 74%, respectively ([Kouveliotou et al., 1993]). To some extent, these values suggest the lack of short GRBs in the GRBM catalog when compared to BATSE. The logarithmic mean $T_{90}$ has turned out to be $0.52$ s $\pm 0.03$ s and $24.1$ s $\pm 0.5$ s for the short and long subset, respectively; in the BATSE case, $0.33$ s $\pm 0.21$ s and $26.2$ s $\pm 1.7$ s had been obtained, respectively ([Kouveliotou et al., 1993]). In spite of the different energy bands (40-700 keV for the GRBM, $>$ 25 keV for BATSE), these values look perfectly consistent each other.

A possible explanation of the lack of short GRBs in the GRBM catalog might be the following: out of $\sim$ 1/3 of the entire catalog, that did not trigger the GRBM on-board logic (sec. ), the duration could have been estimated only for the long bursts, owing to the 1 s time resolution. Therefore, for several non-triggered short bursts detected by the GRBM and recognized as true GRBs thanks to the simultaneous detections by other experiments, the duration estimate was not feasible. In addition, it is possible that a proportionally greater fraction of off-line triggered short GRBs than long ones, has been discarded or not classified as GRBs, afterwards, since the lack of HTR data prevented from inspecting their resolved time profiles.

In other words, two sources of bias are thought to act against the short bursts detection and identification in the GRBM case: during the classification of the off-line triggered events, and within the duration estimation for the classified GRBs, for which HTR data are required only for the short bursts.

Figure: HR-Duration Correlation of 891 GRBM bursts. In the upper panel, duration is expressed in terms of $T_{90}$, while $T_{50}$ has been used in the lower panel.

Finally, it is possible to show that, when the on-board short integration time (sec. ) is 1 or 2 s, the GRBM on-board trigger efficiency is worse for short than for long bursts: let us suppose that the efficiency does not significantly change for short and long bursts; then, since the short GRB population, contributing to the duration distribution, includes only on-board triggered events, if one takes into account the energy-averaged on-board trigger efficiency $\epsilon_{\mbox{\small {onb}}}$ estimated in eq. , $\sim$ ($64 \pm 3$)%, the number of short bursts that should have been detected raises to $124/0.64 \simeq 194 \pm 9$, i.e. other 70 short bursts that did not trigger the on-board logic. Then, the fraction of short burst would be $194/(891+70) \simeq (20 \pm 1)$%. Nevertheless, since the BATSE corresponding fraction amounts to $\sim$ 26%, this strongly suggests that the true GRBM on-board trigger efficiency is lower for short bursts than its average value of ($64 \pm 3$)%, found for the overall catalog (sec. ).

Moreover, the same distributions have been obtained, by excluding all the GRBs, whose duration estimates were not at least 3$\sigma$ significant; this selection reduced the sample of $T_{90}$ durations from 891 to 777, and the $T_{50}$ durations from 891 down to 689; the new duration distributions are shown in fig. . In this case, there are 82 (11%) short and 695 (89%) long GRBs: this shows that the short GRBs are known with worse accuracy than the long ones, on average; the logarithmic mean $T_{90}$ is $0.68$ s $\pm 0.01$ s and $26.7$ s $\pm 0.2$ s for the short and long subset, respectively.