The structure and stability of extended, inclined circumplanetary disc or ring systems

Large dips in the brightness for a number of stars have been observed, for which the tentative explanation is occultation of the star by a transiting circumplanetary disc or ring system. In order for the circumplanetary disc/rings to block the host star's light, the disc must be tilted out of the planet's orbital plane, which poses stability problems due to the radial extent of the disc required to explain the brightness dip durations. This work uses N-body integrations to study the structure and stability of circumplanetary disc/ring systems tilted out of the planet's orbital plane by the spinning planet's mass quadrupole. Simulating the disc as a collection of test particles with orbits initialized near the Laplace surface (equilibrium between tidal force from host star and force from planet's mass quadrupole), we find that many extended, inclined circumplanetary discs remain stable over the duration of the integrations ( $\sim 3\!-\!16 \, {\rm Myr}$ ). Two dynamical resonances/instabilities excite the particle eccentricities and inclinations: the Lidov-Kozai effect which occurs in the disc's outer regions, and ivection resonance which occurs in the disc's inner regions. Our work places constraints on the maximum radial extent of inclined circumplanetary disc/ring systems, and shows that gaps present in circumplanetary discs do not necessarily imply the presence of exomoons.