Multiplicity among solar-type stars in the solar neighbourhood. II - Distribution of the orbital elements in an unbiased sample.

The results of a CORAVEL spectroscopic survey whose radial velocities have been published in Paper I are presented. 37 spectroscopic orbits are derived, of which 23 are for stars without previously known orbit or for stars with e-quality orbits in the recent catalogue of Batten, Fletcher and McCarthy. The duplicity of solar-like stars in the solar neighbourhood is then reconsidered, using a complete subsample of 164 primaries in the spectral range F7 to G9 IV-V, V, VI taken from Gliese's catalogue. Within this subsample represented by about 4200 CORAVEL radial-velocity measurements obtained in almost 13 years with a precision better than 0.3 km s ―1 , added to published data on visual binaries and common proper motion systems and allowing for detection biases, we derive significant new results on the present-day distribution of orbital elements and of mass-ratios ; i) The period distribution is unimodal and can be remarkably appoximated by a Gaussian-type relation with a median period of 180 yr. ii) The tight binaries with P < 11 d are all circularized due to tidal effects occurring during their evolution on the main sequence. This result can be used as an age indicator of the galactic disk, which is found to be statistically in agreement with the current estimations. However, it is thought that such a clock is not presently reliable and that the agreement obtained here is merely due to chance. iii) The tight binaries not affected by tidal effects (11 ≤ P ≤ 1000d) may reflect the initial binary formation process and have an observed mean eccentricity of e = 0.31 ± 0.04. iv) Less tight binaries (P ≥ 1000 d) are probably subject to large scale dynamical interactions and have an eccentricity distribution, when corrected for detection biases, which tends roughly towards f(e) = 2e, expected if that distribution is a function of energy only (Ambartsumian). v) The secondary-mass distribution shows no maximum toward values close to unity, but a continuous increase toward small secondary masses. In fact, this distribution is found remarkably similar to the mass-function found recently by Kroupa, Tout and Gilmore for low-mass field stars. It seems that binaries, on average, can be formed by random association of stars from the same IMF. Although this result may be surprising for binaries of shortest period, we think it premature to claim a difference in the observed mass-ratio distribution among nearby G-dwarf stars on one side or the other of any cut-off period. vi) The proportion of very low mass secondaries with M 2 = 0.01 ― 0.10 M ⊙ for which we have no firm detection yet, may be estimated as (8 ± 6)% of the primaries in our sample. Such new distributions should be useful as constraints on stellar formation processes, keeping in mind that binaries are found in a proportion which varies from 65% to 100% at the middle of the MS, following the most recent studies. From the present one, only about one third of the G-dwarf primaries may be real single stars, i.e. having no companion above 0.01 M ⊙ . Besides, the recent and exciting search for brown dwarfs led us to investigate our CORAVEL radial velocity data base to produce a first sample of 11 spectroscopic binaries with probable very low mass secondaries (M 2min < 0.10 M ⊙ ) extracted from velocity standards and dM stars samples. Including 8 astrometric candidates, we observe that the mean orbital eccentricity for 11 < P < 1000 d is e = 0.34 ± 0.07. Our preliminary conclusion is that the binary formation process seems to be the same for stars and for brown dwarfs. This dominant process would be fragmentation, according to the most recent views on the subject. Conversely, giant planets seem to form only with very small eccentricities which would result from different processes. We can also estimate the proportion of very low mass secondaries among the IAU velocity standard sample to be about 10% which is in reasonable agreement with that found among the nearby G-dwarfs.