Lidov-Kozai Mechanism in Hydrodynamical Disks: Linear Stability Analysis

Recent SPH simulations by Martin et al. suggest that a circumstellar gaseous disc 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 discs 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 disc eccentricity depends on the dimensionless ratio (S) between c_s^2 (the disc sound speed squared) and the tidal torque acting on the disc (per unit mass) from the companion. For S ≪ 1, the standard Lidov-Kozai result is recovered for a thin disc annulus: Eccentricity excitation occurs when the mutual inclination I between the disc and binary lies between 39° and 141°. As S increases, the inclination window for the eccentricity growth generally becomes narrower. For S ≳ a few, eccentricity growth is suppressed for all inclination angles. Surprisingly, we find that for S ∼ 1 and certain disc density/pressure profiles, eccentricity excitation can occur even when I is much less than 39°.