Lidov-Kozai Mechanism in Hydrodynamical Disks: Linear Stability Analysis

TL;DR

This study performs a linear stability analysis to understand how gaseous disks in binary systems can develop eccentricity through Lidov-Kozai-like oscillations, considering gas pressure, viscosity, and tidal forces.

Contribution

It extends the classical Lidov-Kozai mechanism to gaseous disks by analyzing the effects of pressure and viscosity on eccentricity growth in binary systems.

Findings

Eccentricity growth depends on the ratio of sound speed squared to tidal torque.

Standard Lidov-Kozai behavior is recovered for thin disks with low S.

Eccentricity excitation can occur at low inclinations for certain disk profiles.

Abstract

Recent SPH simulations by Martin et al. (2014) suggest a circumstellar gaseous disk may exhibit coherent eccentricity-inclination oscillations due to the tidal forcing of an inclined binary companion, in a manner that resembles Lidov-Kozai oscillations in hierarchical triple systems. We carry out linear stability analysis for the eccentricity growth of circumstellar disks in binaries, including the effects of gas pressure and viscosity and secular (orbital-averaged) tidal force from the inclined companion. We find that the growth of disk eccentricity depends on the dimensionless ratio ($S$) between $c_{\rm s}^2$ (the disk sound speed squared) and the tidal torque acting on the disk (per unit mass) from the companion. For $S\ll 1$, the standard Lidov-Kozai result is recovered for a thin disk annulus: eccentricity excitation occurs when the mutual inclination $I$ between the disk and binary lies between $39^\circ$ and $141^\circ$. As $S$ increases, the inclination window for eccentricity growth generally becomes narrower. For $S\gtrsim$ a few, eccentricity growth is suppressed for all inclination angles. Surprisingly, we find that for $S\sim 1$ and certain disk density/pressure profiles, eccentricity excitation can occur even when $I$ is much less than $39^\circ$.