Multiplicity among solar-type stars III. Statistical properties of the F7-K binaries with periods up to 10 years

Two CORAVEL radial velocity surveys - one among stars in the solar neighbourhood, the other in the Pleiades and in Praesepe - are merged to derive the statistical properties of main-sequence binaries with spectral types F7 to K and with periods up to 10 years. A sample of 89 spectroscopic orbits was finally obtained. Among them, 52 relate to a free-of-bias selection of 405 stars (240 field stars and 165 cluster stars). The statistics corrected for selection effects yield the following results: (1) No discrepancy is found between the binaries among field stars and the binaries in open cluster. The distributions of mass ratios, of periods, the period-eccentricity diagram and the binary frequencies are all within the same error intervals. (2) The distribution of mass ratios presents two maxima: a broad peak from q ~~ 0.2 to q ~~ 0.7, and a sharp peak for q > 0.8 (twins). Both are present among the early-type as well as among the late-type part of the sample, indicating a scale-free formation process. The peak for q > 0.8 gradually decreases when long-period binaries are considered. Whatever their periods, the twins have eccentricities significantly lower than the other binaries, confirming a difference in the formation processes. Twins could be generated by in situ formation followed by accretion from a gaseous envelope, whereas binaries with intermediate mass ratios could be formed at wide separations, but they are made closer by migration led by interactions with a circumbinary disk. (3) The frequency of binaries with P<10 years is about 14%. (4) About 0.3% of binaries are expected to appear as false positives in a planet search. Therefore, the frequency of planetary systems among stars is presently 7^+4 -2%. The extension of the distribution of mass ratios in the planetary range would result in a very sharp and very high peak, well separated from the binary stars with low mass ratios.