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

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4. The data and "resonance" spectra

We analysed all available data on orbital periods of eclipsing and spectroscopic binaries with [FORMULA] d, taken from: i) the "General Catalogue of Variable Stars" with [FORMULA] binaries, compiled by Kholopov et al. (1985-1987), and ii) four other catalogues due to Kopal & Shapley (1956), Batten et al. (1978), Brancewicz & Dworak (1980), Popova & Kraicheva (1984), with [FORMULA] = 80, 540, 962 and 518 binaries respectively. The total number of binaries (with [FORMULA] d, and an error in the period not larger than [FORMULA] d) is 5845.

The resonance spectrum [FORMULA] computed for all binaries with [FORMULA] d ([FORMULA]) is shown in Fig. 1 where we see a peak at a period of [FORMULA] min (frequency [FORMULA] Hz; the uncertainties everywhere are [FORMULA]); its formal confidence level [FORMULA] (C.L.) is nearly [FORMULA]. Note that the chance probability p of this peak should not be multiplied by the number of independent frequencies tested, [FORMULA], since the period of the peak agrees within the error limits with a a priori period suggested by previous investigations (Brookes et al. 1976; Severny et al. 1976; Grec et al. 1980; Gough 1983; Scherrer & Wilcox, 1983; Kotov & Koutchmy 1985; Scherrer et al. 1993). This period also coincides with the "solar" value [FORMULA] min (Severny et al. 1976), or, more correctly, with [FORMULA] = [FORMULA] min (Scherrer et al. 1993). If we take into account the circumstance that there is some overlap between the five catalogues (for detailed discussion see below), - so that the true number of different binaries [FORMULA], - the confidence of the peak (estimated using random numbers) is still found to be of [FORMULA]. The probability of occurrence of the peak by chance is [FORMULA] [FORMULA]. There is no other significant peak in Fig. 1 for the frequency range 5 - 160 µHz (in periods, from about 1.7 hr to [FORMULA] 2.3 d).

[FIGURE] Fig. 1. The generalized commensurability spectrum [FORMULA] computed for close binary stars of the Galaxy (with orbital periods [FORMULA] d; the total number of periods [FORMULA]). The dashed line indicates the formal [FORMULA] level. The major peak corresponds to a period of [FORMULA] min, with nearly [FORMULA] significance.

One should also note that the period we have found is very close to the 1/9-th of a terrestrial day, suggesting the possibility of a mere observational artifact. This is ruled out by the following three arguments:

(a) the actual "solar" period deviates significantly from exactly 1/9-th of a day: [FORMULA] = [FORMULA] min (1/9-th of a day is 160.0000 min),

(b) there is no other peak in the [FORMULA] -spectrum which could be closely related to any other harmonic of a day.

(c) the primary effect relates to the [FORMULA] -min periodicity which is non-commensurate with a day.

It is interesting to know which of the A resonance or the B -resonance contributes most to the [FORMULA] -peak in the [FORMULA] -spectrum. To this aim we computed the simple resonance spectrum [FORMULA] - for orbital periods [FORMULA] d, i.e. for the same number of periods [FORMULA] ; the result is plotted on Fig. 2. We observe a positive peak at frequency [FORMULA] Hz (period [FORMULA] min, at about [FORMULA]) and a remarkable negative peak at frequency [FORMULA] Hz (period [FORMULA] min, at [FORMULA]). All other peaks have no relevance to the discussion: they might be real (but with low significance), or appear just by chance, with no noticeable correspondance in the generalized [FORMULA] -spectrum. One must conclude therefore that the strongest 160-min feature in Fig. 1 arises indeed from both resonance effects, A and B, as was supposed for the action of a hypothetical GW (QGW).

[FIGURE] Fig. 2. The simple resonance spectrum [FORMULA] for 5280 orbital periods of binaries with [FORMULA] d. The dashed lines correspond to the formal [FORMULA] level for positive (upper) and negative (lower) peaks of the [FORMULA] -spectrum. The A and B type resonances are associated with positive ([FORMULA] 160 min) and negative ([FORMULA] 321 min) peaks located at frequencies [FORMULA] 104.2 and [FORMULA] 52.0 µHz, respectively.
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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998