Mean GRBM Efficiency

In order to estimate the number of GRBs that have been detected by BATSE, and missed by the GRBM, the overall BATSE 4B catalog ([Paciesas et al., 1999]) has been analysed, to select all the GRBs that should have been detected by the GRBM. For this selection, some points have been considered: first of all, the selection only regarded those GRBs occurred during the time intervals covered by the GRBM 1 s ratemeters currently available, from which this GRBM catalog has been extracted. A further selection concerned the bursts not Earth-blocked: the visibility (sec. ) of each burst has been calculated by using the BATSE direction and the GRBs have been split into four classes: ``surely visible'', ``surely occulted'', ``probably visible'', and ``probably occulted'', according to the visibility definition. Only the ``surely visible'' GRBs have been chosen, i.e. those GRBs, whose entire error circle is not Earth-blocked. On the GRB sample so selected, a final selection, aimed to exclude all the GRBs occurred in the nearby of the SAGA, where the off-line quest could not work, has been applied. At this stage, both the number of bursts detected with the GRBM by applying the SWTCs and the number of BATSE missed GRBs by the GRBM are known; typically, there are two possibilities for a burst to be missed by the off-line quest within the GRBM data: first, the BATSE burst brightness is below the GRBM sensitivity, so that no signal can be found at the burst time in the GRBM data; second, the BATSE burst can be identified by visual inspection within the GRBM ratemeters, but it nevertheless did not trigger any off-line quest. The comparison between the number of detected bursts and the number of expected bursts, according to the BATSE catalog, therefore allows to estimate the GRBM off-line trigger efficiency, accounting for both the GRBM intrinsic sensitivity and for the off-line quest algorithms used to extract this catalog of GRBs.

The results of this procedure are summarized in table .

Table: GRBM & BATSE GRBs: detected and expected.

Catalog	# Expected	# Detected	# Missed	$\epsilon_{\mbox{\small {off}}}$
BATSE 4B	409	283	126	$69 \pm 4$ %
Kommers'	53	18	35	$34 \pm 8$ %
Stern's	223	61	162	$27 \pm 4$ %
Total	685	362	323	$53 \pm 3$ %

In table  the parameter $\epsilon_{\mbox{\small {off}}}$ expresses the GRBM off-line quest efficiency, and it is calculated as the ratio of the number of off-line detected bursts over the number of expected bursts. This estimate has been calculated also in the cases of the two BATSE non-triggered bursts taken into consideration previously. From BATSE 4B to Stern's catalog, the efficiency $\epsilon_{\mbox{\small {off}}}$ falls from an initial $\sim$69% down to $\sim$27%; if one accepts the assumption that the non-triggered catalogs are affected by a negligible contamination of non-burst events, the following observations can be made: from BATSE 4B to Stern's, the minimum peak flux decreases down to $\sim 0.1$ photons s$^{-1}$ cm$^{-2}$ ([Stern et al., 2000b]), and correspondingly the number of GRBs, whose peak fluxes are below the GRBM sensitivity, increases, thus lowering the peak-flux-averaged GRBM efficiency. According to this value, one may conclude that, on average, any GRB, with a peak flux greater the above value of $\sim 0.1$ photons s$^{-1}$ cm$^{-2}$ in the BATSE energy band 50-300 keV has a $\sim 53$% probability of being detected within the GRBM data by means of the off-line quest algorithms, provided that it is not hidden by the Earth.