Indications on the binary nature of individual stars derived from a comparison of their HIPPARCOS proper motions with ground-based data I. Basic principles

We present a method which provides some information on the possible binary nature of an apparently single star. The method compares the instantaneously measured HIPPARCOS proper motion with the long-term averaged, groundbased proper motion or with the proper motion derived from old ground-based positions and the HIPPARCOS position. Good sources for such ground-based data an the FK5 and the GC. If the proper-motion difference Delta mu is statistically significant with respect to its measuring error, the object is very probably a double star. We call then the object a 'delta-mu binary'. If the proper-motion difference is insignificant and if no other information on a binary nature of the object is available, we call such a star a 'single-star candidate'. We propose a quantitative test for the significance of the observed proper-motion difference. The sensitivity of our method is high: For nearby stars at a distance of 10 pc, the measuring accuracy of the proper-motion difference, expressed as a velocity, is of the order of 50 m/s (basic FK5 stars) or 80 m/s (GC stars). At 100 pc, the mean error of the two-dimensional difference is still 0.5 km/s or 0.8 km/s. For the FK5 stars, we provide indications on the probable period of the Delta mu binaries. If we adopt an orbital period and a mass-luminosity relation, we can use the observed velocity difference to estimate the separation and the magnitude difference between the two components of the binary. The present paper concentrates mainly on the basic principles of the method, but it provides also a few examples of delta-mu binaries and of single-star candidates for illustration: gamma UMa, epsilon Eri, Vir, 47 UMa,delta Pav.