Dynamical evolution of triple-star systems by Lidov-Kozai cycles and tidal friction

TL;DR

This paper investigates how Lidov-Kozai cycles combined with tidal friction can lead to the formation of short-period inner binaries in triple-star systems, emphasizing the roles of initial eccentricity, argument of pericenter, and mutual inclination.

Contribution

It provides a comprehensive framework including general relativity, tides, and stellar effects, revealing the critical influence of initial conditions and the Kozai constant on system evolution.

Findings

Mutual inclination alone is insufficient to predict migration outcomes.

Initial eccentricity and argument of pericenter significantly affect Lidov-Kozai migration.

Phase portraits at fixed Kozai constants show different evolutionary pathways.

Abstract

Many triple-star systems have an inner pair with an orbital period of a few days only. A common mechanism to explain the short-period pile-up present in the observations is the migration through Lidov-Kozai cycles combined with tidal friction. Here, we revisit this mechanism and aim to determine the initial orbital configurations leading to this process. We show that the mutual inclination of the triple-star system is not the only critical parameter, since the eccentricity as well as the argument of the pericenter of the inner orbit also play an important role in the establishment of the Lidov-Kozai migration. Our framework is the secular hierarchical three-body problem (octupole order approximation) with general relativity corrections, including the effects of tides, stellar oblateness and magnetic spin-down braking. Both the orbital and the spin evolutions are considered. Extensive numerical simulations with uniform and non-uniform distributions of the initial orbital parameters are carried out, and unbiased initial conditions leading to Lidov-Kozai migration are revealed. Finally, we highlight the importance of the initial "Kozai constant" $h=\sqrt{(1-e^2)}\cos{i}$ in the dynamical evolution of triple-star systems, by showing that phase portraits at given $h$-values unveil different evolution paths.