Resonant capture in quadruple stellar systems

Abstract

ABSTRACT Some quadruple star systems in the hierarchical 2 + 2 configuration exhibit orbit–orbit resonances between the two compact binaries. We show that the most important resonances occur at period ratios of 1:1, 3:2, and 2:1. We describe the conditions required for capture and show that they can be satisfied at the 3:2 and 2:1 resonances in binaries that migrate significantly in semimajor axis after circularization, probably through magnetic braking or gravitational radiation.