GRBM Direction Matrix Behavior

As already tested in the previous section, the GRBM localization technique is reliable, since the $\sim$90% of the bursts lie within the GRBM 90% CL error region. Here the behavior of the direction matrix is studied: in other words, the purpose is to study how this localization technique locates a given set of bursts, to test if there are any trends and/or whether it clusters, and possibly what are the local directions where this clustering effect might work.

Figure: GRBM Direction Distribution of a sample of 446 GRBs localized with the GRBM localization technique. The frame of reference is local to BeppoSAX. The clustering tendency in the nearby of the BeppoSAX equatorial plane is apparent.

In fig.  the distribution of 446 directions, estimated with the GRBM localization technique, referred to the BeppoSAX local frame of reference is shown; for clarity, only the centroids have been spotted; although, on average, the error regions of the overall set of bursts would overlay also high elevation regions, nevertheless, a clear evidence for clustering of centroid positions in the nearby of the BeppoSAX equatorial plane. In particular, it is now well known that the GRBM localization capabilities dramatically get worse when approaching the local south pole, where the off-line trigger efficiency falls down to $\sim$24-25% (see table ).

At this stage, it is not possible to study the isotropy of the burst subset, that have been localized thanks to the GRBM only, owing to two facts: the first is apparent from fig. , because of this clustering effect; the second is that the 90% CL error regions of every GRBM-positioned burst is too large (15-40$\rm ^{\circ}$) for searching for a possible anyhow small anisotropy.

The clustering behavior of the GRBM direction matrix becomes more apparent in the two figg.  and , where the GRBM direction distributions for two GRB subset are shown: the first figure shows how the GRBM-BATSE (4B) common sample of 152 GRBs localized by both GRBM and BATSE, are distributed within the BeppoSAX local sky; both sets of directions are shown together, i.e. GRBM and BATSE directions of the same bursts: since the BATSE is much smaller (a systematic error of $1.6\rm ^{\circ}$ against the GRBM systematic error of $\sim 10\rm ^{\circ}$), these are taken as the true GRB positions. The clustering effect above claimed here is indeed clear.

Figure: Direction Distribution of the GRBM-BATSE (4B) common sample of 152 GRBs localized with the GRBM localization technique. The frame of reference is local to BeppoSAX. Both GRBM and BATSE positions are spotted. The clustering tendency in the nearby of the BeppoSAX equatorial plane is apparent, when compared with the BATSE distribution.

Figure: Direction Distribution of a sample of 45 GRBs, that have been localized with the GRBM localization technique, and whose position was already known thanks to other experiments, mainly WFC and IPN. The frame of reference is local to BeppoSAX. Both GRBM and true positions are shown. The clustering tendency in the nearby of the BeppoSAX equatorial plane is apparent.

The same operation has been made for the common sample of 45 well localized bursts, and the outcoming distribution is shown in fig. ; also in this case a kind of clustering effect is apparent near the local equatorial plane, although it should not be confused with the obvious clustering of bursts in the nearby of the fields of view of WFC1 and WFC2, at $\phi=270 (=-90)\rm ^{\circ}$, and $\phi=90\rm ^{\circ}$, respectively ( $\theta=0\rm ^{\circ}$), corresponding to the WFC local normal directions, given that the major contribution to this set of precisely localized GRBs comes from the WFCs' own detections.