The Coincidence Interval

As the automatic search for common bursts is based only on a temporal coincidence, a set of maximum delays between the trigger times of the GRBM and of the other catalogs, has been set (table ). Let $t_{auto}$ be the S/W trigger time of the burst candidate automatically detected; then, for every catalog with common bursts a search for simultaneous bursts in the time interval $[t_i, t_f]$ is performed: in table  the values defining the intervals for the different catalogs are reported. Furthermore, in order to know whether the burst candidate found from the scan of the GRBM 1 s ratemeters, triggered the on-board logic as well, a temporal coincidence is searched also with the GRBM on-board trigger times' catalog; in this specific case, the values for the boundaries of the coincidence interval have been determined from the HTR count rates times, so that, whenever an on-board trigger time is found to be inside $[t_i, t_f]$, it means that HTR count rates are available at $t_{auto}$; otherwise this is not true.

The max delays allowed for coincidence have been chosen to detect simultaneous bursts, even when the difference between the trigger times amounts to several seconds (for instance, when the burst is long and has a complex profile, strongly dependent on the detector energy band); on the other side, the max delay allowed cannot be too big, to avoid too many spurious common detections.

Table: Time intervals adopted for the search for common bursts

Catalog	$t_i - t_{auto}$	$t_f - t_{auto}$	$\Delta t$
	(s)	(s)	(s)
WFCs, IPN, ASM, HETE	-120	120	240
BATSE	-70	70	140
Kommers'	-70	70	140
Stern's	-70	70	140
GRBM on-board trigger	-98	8	106

Of course, a mere temporal coincidence does not suffice to establish the truthfulness of the common detection; first of all, in despite of the different energy bands, the two light curves must show consistent time profiles; further, the estimates for the arrival direction cannot be significantly different; also Earth blockage arguments are taken into account to reject possible spurious temporal coincidences. Nevertheless, since this kind of analysis has to be done by human intervention, it will be discussed in the next chapter, where the selection and the refinement of the off-line triggers' sample are treated in detail.