The Early Trigger Conditions

Differently from the late SWTCs, the early criteria have been applied only to the off-line quest. The reason is explained below. Like the OBTCs, also the early SWTCs ([Guidorzi et al., 2000a]) are based on the search for an excess in the count rates above a background, which is continuously estimated as follows: let $C_u^{(e)}(i)$ the counts measured in the $u$th unit ($u$ = 1,2,3,4), in the energy band $(e)$ ($e$ = G, A, where 'G' and 'A' correspond to the 40-700 keV, or GRBM band, and $>$100 keV, or AC band, respectively) and for the $i$th time bin; let $B_u^{(e)}(i)$ be the background counts estimated for the same time bin, and Let $N$ be the number of contiguous time bins used for the background estimate. The bacground counts are estimated through an averaging process that involves only the time bins previous to the scanned bin:

$$B_u^{(e)}(i) = \frac{\displaystyle \sum_{k=i-N}^{i-1} C_u^{(e)}(k)}{\displaystyle N} \qquad\qquad \forall i > N$$ (8)

The choice $N = 100$ was adopted. The moving average described by the eq.  is the same as the average counts computed by the on-board logic, except for some points: the SWTCs apply to 1 s bins, and, most important, both the GRBM and the AC energy bands are taken into account.

Eq.  applies to the bins following at least $N$ contiguous bins; the background estimate for the other bins, in the nearby of the data gaps, like the SAGA transits or other less frequent gaps in the telemetry, and for the bins close to the boundaries of the time interval, is computed with the same averaging process, but applied to the same $N$-bin long interval to which the scanned bins themselves belong: obviously, this estimate is biased, since every scanned bin contributes to the estimate of its own background; however, this rough background estimate method for the ``more difficult'' bins, limits the number of several bursts, that, otherwise, would be missed.

Once the background in every light curve for a given bin has been estimated, a set of eight $\sigma_u^{(e)}(i)$, nearly equal to the poissonian standard deviations of the single bin counts , with their correponding net signals $S_u^{(e)}(i)$ are defined as follows (eq. ):

$$\sigma_u^{(e)}(i) = \sqrt{B_u^{(e)}(i)}, \qquad S_u^{(e)}(i) = C_u^{(e)}(i)-B_u^{(e)}(i)$$ (9)

Let $n^{(G)}=6$ and $n^{(A)}=3$ be two threshold parameters, one for each energy band. There are three SWTCs, defined by the following equations:

$$\textrm{SWTC 1} \left\{\begin{array}{l} S_{u_1}^{(G)}(i) \quad > ... ..._2}^{(A)}(i) \end{array}\right. \qquad u_1, u_2=1,\dots,4 \qquad u_1 \not = u_2$$ (10)

$$\textrm{SWTC 2} \left\{\begin{array}{l} S_{u}^{(G)}(i) \quad > \q... ...is to unit $u$\ is NOT pointing to Earth} \end{array}\right. \qquad u=1,\dots,4$$ (11)

$$\textrm{SWTC 3} \left\{\begin{array}{l} S_{u_1}^{(G)}(i) \quad > ... ...(i) \end{array}\right. \qquad u_1,u_2,u_3=1,\dots,4 \qquad u_j\not=u_k, j\not=k$$ (12)

When at least one among SWTC1, SWTC2, SWTC3, is satisfied, the $i$th bin is tagged ``good event''.

The choice of a lower threshold ($n^{(A)}=3$) for the $>$ 100 keV band than the 40-700 keV band ($n^{(G)}=6$) is supported by the lower noise in the harder range (fig. ). An important peculiarity of the GRBs is their spectral hardness: generally, the GRB spectra are harder than other transient events; this property makes the AC band fundamental in the their identification among the other events. The SWTCs involving the AC counts are SWTC1 and SWTC2 (eqq. ,); in particular, SWTC2 relaxes the strong request of a detection in at least two units of SWTC1, but, in addition, it requires that the normal direction to the single triggered unit has to point to the sky, thus preventing from taking several weak events coming from the Earth atmosphere.

Eventually, SWTC3 (eq. ) is useful to catch soft GRBs and, in general, other transient events which are a bit softer than typical GRBs; since the noise in the GRBM band is stronger, the conditions on this band must be matched simultaneously in at least three units, in order to automatically reject the majority of events triggering the on-board logic, due to particles crossing the detectors.

Figure: Time history of NTB 960723, UT 04:46:03, (also BATSE trigger 5551) in all the GRBM units, both energy bands. Only unit 2 detected it. This NTB was caught trough SWTC 2: actually, its BATSE direction was $\sim$70$^\circ$above the Earth limb and $\sim$11$^\circ$off-axis with respect to unit 2.