A given direction is considered to belong to the -th face, whenever the mininum angular distance between the given direction and the normal direction to the -th face ( or 12, depending on whether the cube or the dodecahedron grid is considered, respectively), occurs when . In the case of the cube grid, the six cube faces, corresponding to the six sky regions, are so numbered: face # 1 corresponds to GRBM unit 1, and so on till # 4 facing GRBM 4; then face # 5 refers to the top face (pointing along the same direction of the NFIs), while # 6 faces the opposite direction, i.e. the BeppoSAX local south pole. For the dodecahedron faces, their local coordinates can be read from table .
In the following table the results are reported in two cases: first, by taking into account only the BATSE 4B catalog; second, the three merged catalogs: BATSE 4B, Kommers' and Stern's (4B+K+S, in the table). Both the cube and the dodecahedron grid cases are reported; in the latter case, only the merged catalogs have been considered, otherwise the statistics would be poor.
Local Sky | Det | Exp | Det | Exp | ||||
Region | () | () | (4B) | (4B) | (4B) | (4B+K+S) | (4B+K+S) | (4B+K+S) |
(Cube) | ||||||||
GRBM 1 | 270 | 0 | 55 | 65 | 75 | 112 | ||
GRBM 2 | 0 | 0 | 59 | 75 | 75 | 129 | ||
GRBM 3 | 90 | 0 | 43 | 58 | 62 | 103 | ||
GRBM 4 | 180 | 0 | 34 | 51 | 43 | 92 | ||
North Pole | 0 | +90 | 43 | 55 | 52 | 94 | ||
South Pole | 0 | -90 | 28 | 84 | 32 | 132 | ||
Total | - | - | 262 | 388 | 339 | 662 |
Local Sky | Det | Exp | |||
Region | () | () | (4B+K+S) | (4B+K+S) | (4B+K+S) |
(Dodecahedron) | |||||
Face 1 | 0 | +90.00 | 24 | 48 | |
Face 2 | 90 | +26.56 | 25 | 46 | |
Face 3 | 162 | +26.56 | 26 | 45 | |
Face 4 | 234 | +26.56 | 32 | 52 | |
Face 5 | 306 | +26.56 | 54 | 68 | |
Face 6 | 18 | +26.56 | 36 | 52 | |
Face 7 | 0 | -90.00 | 17 | 67 | |
Face 8 | 270 | -26.56 | 28 | 64 | |
Face 9 | 342 | -26.56 | 26 | 60 | |
Face 10 | 54 | -26.56 | 33 | 59 | |
Face 11 | 126 | -26.56 | 26 | 51 | |
Face 12 | 198 | -26.56 | 12 | 50 | |
Total | - | - | 339 | 662 |
Finally, one might note that the number of BATSE 4B common bursts (262) reported in table and the number of total bursts, including the BATSE non-triggered catalogs (339), are smaller than the corresponding numbers 283 and 283+79=362, respectively, reported in tables and : actually, some bursts happened when the BeppoSAX spacecraft attitude was not known, during the time interval May - July 1997; hence, for these GRBs, the transformation from celestial to local coordinates was not feasible; owing to this, they have not been taken into account for estimating the GRBM efficiency as a function of the local direction.