1 Introduction

The knowledge of the statistics of multiple star orbital and physical parameters is important for the studies of their formation processes. A variety of mechanisms invoked for modeling of the multiple star formation processes result in different shapes of the eccentricity distribution f(e) and its dependence on the orbital period, which can be checked against the statistics of observed systems.

Visual double stars have been observed for many years mainly with the aim to determine stellar masses. Selection affects heavily the discovery and success of orbit computation for them (e.g. Ruymaekers 1999), hampering especially the study of highly inclined or eccentric orbits. Respective biases in statistics are very difficult to assess.

For the systems with periods P>500-1000 years, the computation of orbits becomes almost impossible and hence there is no way to obtain f(e)directly. Meanwhile, bound systems with periods up to 10⁵-10⁶ years do exist (e.g. Palasi 2000), so more than three orders of magnitude in period escape from the study of orbital parameter statistics.

Tokovinin (1998) proposed to determine the shape of f(e) for wide visual binaries from the distribution of the angle $\gamma$between the radius vector of a secondary companion and the vector of its apparent relative motion in the system (Fig. 1). For a sample of Hipparcos binaries studied by Brosche et al. (1992, BDS92), such a distribution $f(\gamma )$ is approximately flat. According to Tokovinin (1998), this corresponds to the linear distribution of eccentricities, f(e)=2e predicted by stellar dynamics (Ambartsumian 1937). Duquennoy & Mayor (1991) affirm that f(e)=2e applies to the visual binaries in the solar neighborhood. However, as we show below, this is not the case for multiple systems.

Figure 1: Definition of angle $\gamma$ for the motion of the star B in the system A-B. In the sky plane, radius vector r connects the gravity centers of A and B; $\Delta \mu$ shows the direction of the apparent relative motion of B with respect to A.

With the new data from Hipparcos and the database of the Multiple Star Catalogue (MSC, Tokovinin 1997) we address the question about the f(e) for long-period outer subsystems of multiple ($N\!>\!2$) stars. MSC is a unique collection of high-order systems which are confirmed to be physical by a combination of several criteria.

Our basic idea is to obtain some constraints on f(e) for this previously unstudied domain of long periods dealing with definitely non-optical pairs. Also, it is intriguing to test whether the multiple ($N\!>\!2$) stars differ in orbital characteristics from the whole ensemble of non-single objects, most of which contain, apparently, only two stars.