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.
Highlights
The statistics of multiple star systems are quite incomplete and suffer from discovery biases, many observational studies have reported a significant proportion of triple-star systems with an inner binary period smaller than six days (e.g., Duquennoy & Mayor 1991; Tokovinin 1997, 2001, 2014)
For an inner binary perturbed by an outer inclined stellar companion, the eccentricity of the inner orbit can reach values close to unity during the Lidov-Kozai cycles, for which the periastron distance can be very small
An over-abundance of short-period binaries result from their Monte-Carlo simulations, in agreement with the observations, and could be interpreted as a possible indication of the presence of a distant tertiary companion in short-period binaries. They have noticed that tertiary companions leading to LidovKozai migration have preferably a final mutual inclination around ∼ 40◦ or ∼ 140◦ with respect to the inner binary plane
Summary
The statistics of multiple star systems are quite incomplete and suffer from discovery biases, many observational studies have reported a significant proportion of triple-star systems with an inner binary period smaller than six days (e.g., Duquennoy & Mayor 1991; Tokovinin 1997, 2001, 2014). In line with the work of Fabrycky & Tremaine (2007), extensive numerical simulations are carried out, using the vectorial secular equations of Correia et al (2016) for the spin and orbital evolution (octupole approximation) with general relativity corrections, including the effects of tides, stellar oblateness and magnetic spin-down braking. Semi-major axis aj (AU) Eccentricity ej Argument of pericenter ωj (deg) Longitude of the node Ωj (deg)
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