A Mechanism for Producing Short-Period Binaries

When three point masses form a hierarchical triple system, the short-period orbit can be severely modified by the long-period orbit if the two orbits are inclined to each other by more than about 39^deg (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sin^{-1}\sqrt{2/5}$$\end{document}). Such an inclination can induce ‘Kozai cycles’ (Kozai, 1962), in which the eccentricity of the inner orbit cycles by a large amount while its period and therefore semimajor axis remains roughly constant. During those periastra when the eccentricity is largest, tidal friction may become important, and this can result in a secular shrinkage of the orbit, until it becomes circularised at a period of a few days.