The Frequency Distribution of Semi-major Axis of Wide Binaries. Cosmogony and Dynamical Evolution

Abstract

The frequency distribution f(a) of semi-major axis of double and multiple systems, as well as their eccentricities and mass ratios, contain valuable fossil information about the process of star formation and the dynamical history of the systems. In order to advance in the understanding of these questions, we have made an extensive analysis of the frequency distribution f (a) for wide binaries (a>25 AU) in the various published catalogues, as well as in our own (Poveda et al., 1994; Allen et al., 2000; Poveda & Hernandez, 2003). Based upon all these studies we have established that the frequency f(a) is function of the age of the system and follows Oepik's distribution f(a) ~ 1/a in the range of 100 AU < a < a[c](t), where a[c](t) is a critical semi-major axis beyond which binaries have dissociated by encounters with massive objects. We argue that the physics behind the distribution f(a) ~ 1/a is a process of energy relaxation, analogous to that present in stellar clusters (secular relaxation) or in spherical galaxies (violent relaxation). The frequency distribution of mass ratios in triple systems as well as the existence of runaway stars, indicate that both types of relaxation are important in the process of binary and multiple star formation.