## 6. DiscussionA main result of the study is that a model based on the DM distributions (Duquennoy & Mayor 1991) predicts too few resolved systems (by a factor ) as well as long-period astrometric binaries (by a factor ). To obtain agreement with the observed counts requires an increased multiplicity, at least for -100 AU, by roughly a factor 2. Depending on the shape of the distribution curve, this translates to a total multiplicity of 0.9 to 1.2, compared with 0.57 found by DM for solar-type stars. Alternative explanations could be (i) that a substantial fraction of the binary solutions in the Hipparcos Catalogue are spurious, or (ii) that our model underestimates the actual sensitivity of Hipparcos to binarity. Consider first possible spurious solutions. Concerning the resolved binaries, it can be noted that only 10% of them were actually discovered by Hipparcos; the rest were known from ground-based surveys. Most of the `new' systems have separations less than 0.5 arcsec, and most have solution quality flag `A' (Field H61 in the Hipparcos Catalogue). The only binaries that can reasonably be doubted are the `new' ones with less than `A' quality solutions, of which there are 68. Eliminating these reduces the ratio of observed to predicted C systems from 1.54 to 1.49. Similar assertions cannot easily be made concerning the G and delta-mu systems, as most of them were discovered as astrometric binaries by Hipparcos. However, we consider it very unlikely that more than 20% of them are spurious, which would still leave twice as many observed systems as predicted from the DM distributions. Concerning alternative (ii) we do not see how the model could faithfully reproduce the observed distribution of acceleration terms (Fig. 4) if the actual sensitivity of Hipparcos to orbital curvature was much higher than in the model. In conclusion we find that these explanations can only account for a small part of the observed discrepancy with respect to the DM distributions. Considering that the composition of the present sample
(Table 1) is very different from that of DM, it is perhaps not
unreasonable that the total multiplicity and the distribution in
Another result is the narrower distribution in compared with DM. We note that the dashed curves in Fig. 2 are not unlike the distribution derived by Abt (1988) for bright () main-sequence visual binaries of spectral type F3 to G2. One prediction from this narrow distribution is that there should be relatively few binaries in our sample with AU (corresponding to arcsec at typical distances, i.e. generally not counted among the C solutions). This appears consistent with a direct count of wide visual binaries in the Hipparcos Input Catalogue (Turon et al. 1992): less than 1% in our sample have a listed companion beyond a projected separation of 3000 AU, while the DM distribution would predict ten times as many. In the classical study by Heintz (1969), binary statistics of nearby stars brighter than 9th magnitude were examined. These are mainly stars earlier than spectral type G, and thus much closer to the present Hipparcos sample than the DM sample. Heintz derived a total multiplicity between 0.95 and 1.12, similar to the results found here, and a narrower distribution in compared to that of DM. Our distribution is not unlike that of Heintz, if we make the reasonable assumption that some systems with -10 AU are missing in his data. The analysis described in this paper can be seen as a simple
application of a general method to derive statistical information on
binaries from astrometric measurements. The method can be extended to
provide more detailed information on the distributions by dividing the
counts according to, for instance, linear separation
(), magnitude difference and the
size of the acceleration terms. The delta-mu binaries could probably
be more extensively analysed by comparing with the Tycho-2 Catalogue
(Hog et al. 2000) instead of FK5. Perhaps the most important
aspect of the method, which has been demonstrated in this paper, is
that it allows to probe an interval in © European Southern Observatory (ESO) 2000 Online publication: October 2, 2000 |