Lidov-Kozai Mechanism in Hydrodynamical Disks: Linear Stability Analysis

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 $39^\circ$.