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Astron. Astrophys. 322, 177-182 (1997)

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7. The average of five "resonance" spectra

We also computed [FORMULA] separately for each of the five CBS's catalogues. Those functions were averaged, and the resulting [FORMULA] -spectrum - analogue to the former spectrum [FORMULA] - is plotted in Fig. 7. The numbers of objects in the 5 catalogues are very different, but the averaging procedure is justified because the [FORMULA] -functions are normalized.) The strongest peak corresponds to [FORMULA] min, with a formal [FORMULA] ; accounting for the effects of "quasi-persistency" and overlap of catalogues, the empirical C.L. is estimated to be [FORMULA].

[FIGURE] Fig. 7. The average resonance spectrum [FORMULA] computed for five catalogues of CBS's (compare it with Fig. 1; see also text).

The [FORMULA] -effect cannot be explained in this case also by the presence of some peculiarity (e.g., a sharp excess, deep gap or distinct boundary) in the distribution of binary periods. One might imagine that the 160-min peak (Figs. 1 and 7) is a mere artifact of the upper limit of 5.5 d for periods that we applied for the sake of calculation. This explanation however does not hold, as was shown by many computations with various upper boundaries. Namely, when we changed the long-period boundary from 3 to 10 d, the amplitude of the primary peak - at the frequency [FORMULA] Hz - always emerged as significant, its formal statistical significance varying between [FORMULA] and [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998