SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


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

Previous Section Next Section Title Page Table of Contents

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.
Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
helpdesk.link@springer.de