The reliability of the Titius–Bode relation and its implications for the search for exoplanets

The major semiaxes of the planets in our solar system obey a simple geometric progression known as the Titius–Bode (TB) relation, whose physical origin remains disputed. It has been shown that the exoplanetary systems follow a similar (but not identical) progression of the form $a_n= a_0$ e$^{bn}$, where $a_0$ and b are constants to be determined for each system. Since its formulation, the TB relation has proved to be highly predictive in our solar system. Using data from 27 exoplanetary systems with five or more planets and applying a proposed method, we conclude that reliable TB-like fits can be obtained for systems with at least four planets and that the precision of the TB relation is $78\%$. By means of a statistical test we show that the periods of planets in real exoplanetary systems are not consistent with a random distribution. Rather, they show signs that their configuration is shaped by their mutual interactions.

The Distribution of Separations of Wide Binaries of Different Ages

For the purpose of understanding how the distribution of major semiaxes of double and multiple stars has evolved from the earliest ages up to the ages of the oldest systems, we have studied a number of different groups of such systems. We review and expand our previous work on the following groups of stars: (a) The wide binaries in the IDS; (b) Luyten’s common proper motion pairs (the LDS catalogue), (c) Our catalogue of nearby wide binaries divided into two groups: the youngest and the oldest; (d) The common proper motion pairs in the Orion Nebula cluster; (e) Our sample of high velocity, low metallicity binaries that represents a population of very old systems. From the very young binaries (Orion Nebula Cluster) to the oldest (thick disk and halo), all groups show a distribution of major semiaxes following Oepik, i.e., f(a) da ∝ da/a (where a is the major semiaxis), valid over an interval of a between 60 AU and am(t), am(t) being a maximum semiaxis which depends on the age of the binaries as well as on the number density and velocities of the massive objects they encounter as they travel in the Galaxy. Strong gravitational encounters in recently formed multiple systems were found to produce an Oepik distribution, which at small separations (a ≤ 40 − 60 AU) gets truncated by circumstellar disks and close binaries, and at large separations gets depleted by encounters with massive objects.

On the Distribution of Young Spectroscopic Binary Stars Over the Major Semiaxes of their Orbits

About 60% of stars of the disc population in our Galaxy are close binary systems (CBS). Half of the known CBS are spectroscopic binary stars (Kraitcheva et al., 1978).To know the distribution of a correlation between the masses of CBS components and semiaxes of their orbits is necessary for the investigation of the origin and evolution of CBS. For such statistical investigations, a catalogue of CBS was compiled at the Astronomical Council. The catalogue is based on the 6th Batten catalogue (Batten, 1967), its extensions (Pedoussant and Ginestet, 1971; Pedoussant and Carquillat, 1973) and data published up to the end of 1980 (Popova et al., 1981). Now it is recorded on magnetic tape and contains data on 1041 spectroscopic binaries; 333 of them are stars with two visible spectra. The latter are mostly systems prior to mass exchange and the distribution of physical parameters in these systems reflects the distribution and presumably conditions at the time of formation. Using some assumptions, we can obtain for spectroscopic binaries masses of the components M1 and M2 (or the ratio q = M1/M2) and semiaxes of their orbits. Masses of components with the known sin i were obtained by the usual technique; when sin i was not known, masses were estimated from the spectra. We shall discuss here the distribution of CBS in the M-a plane.