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Kozai-Lidov oscillations triggered by a tilt instability of detached circumplanetary discs

Circumplanetary discs can be linearly unstable to the growth of disc tilt in the tidal potential of the star-planet system. We use three-dimensional hydrodynamical simulations to characterize the disc conditions needed for instability, together with its long term evolution. Tilt growth occurs for disc aspect ratios, evaluated near the disc outer edge, of $H/r\gtrsim 0.05$, with a weak dependence on viscosity in the wave-like regime of warp propagation. Lower mass giant planets are more likely to have circumplanetary discs that satisfy the conditions for instability. We show that the tilt instability can excite the inclination to above the threshold where the circumplanetary disc becomes unstable to Kozai--Lidov (KL) oscillations. Dissipation in the Kozai--Lidov unstable regime caps further tilt growth, but the disc experiences large oscillations in both inclination and eccentricity. Planetary accretion occurs in episodic accretion events. We discuss implications of the joint tilt--KL instability for the detectability of circumplanetary discs, for the obliquity evolution of forming giant planets, and for the formation of satellite systems.