3. Results and discussion
As it can be seen in Fig. 2, the mean value of the "added correlation" for the simulated catalogues, , is even larger than the "added correlation" for the real WATCH and BATSE catalogues, namely . This implies that our results agree qualitatively with the absence of common sources.
The fact that we have preferred to simulate WATCH catalogues instead of BATSE ones is only due to the computing time, because it is more efficient to simulate sets of 57 bursts in comparison with groups of 1906 members. In spite of this fact, the roles of both catalogues were exchanged in order validate the method, applying the process explained in Sect. 2 to 50 BATSE simulated catalogues. Only with 50 catalogues the values obtained for and differ by less than 5% from those obtained when WATCH catalogues were simulated.
The probability distributions are shown in Fig. 3 and the deduced values of are given in Table 1 and displayed in Fig. 4. As it is shown in Table 1, decreases with N, showing the maximum value when BATSE and WATCH do not share any source. Thus, our results support the lack of common sources. Furthermore, the number of common sources is with a 94% confidence level (see Table 1), which means a 15.8% of the whole sample. This percentage is similar to the 20% upper limit imposed to the 1B catalogue (Strohmayer et al. 1994). The results are also in good agreement with the studies carried out with the BATSE 3B (Tegmark et al. 1996) and 4B catalogues (Hakkila et al. 1998), which did not find evidence of repetition. A possible reason to explain our results could be due to the different sensitivity of the experiments, as WATCH is sampling the strongest bursts and BATSE is also detecting a fainter population. The different populations of objects found inside WATCH and BATSE error boxes could support this idea (Gorosabel and Castro-Tirado 1998a, 1998b).
Table 1. The first and third column represent the number of repeaters, N. The second and the fourth ones give the probability of having N repeaters.
© European Southern Observatory (ESO) 1998
Online publication: July 7, 1998