2017MNRAS.464.3945Z

Newly formed planets (or brown dwarfs) may possess discs or rings which occupy an appreciable fraction of the planet's Hill sphere and extend beyond the Laplace radius, where the tidal torque from the host star dominates over the torque from the oblate planet. Such a disc/ring can exhibit unique, detectable transit signatures, provided that the disc/ring is significantly misaligned with the orbital plane of the planet. There exists tentative evidence for an extended ring system around the young K5 star 1 SWASP J140747-354542. We present a general theoretical study of the inclination (warp) profile of circumplanetary discs under the combined influences of the tidal torque from the central star, the torque from the oblate planet, and the self-gravity of the disc. We calculate the equilibrium warp profile ('generalized Laplace surface') and investigate the condition for coherent precession of the disc. We find that to maintain a non-negligible misalignment between the extended outer disc and the planet's orbital plane, and to ensure coherent disc precession, the disc surface density must be sufficiently large so that the self-gravity torque overcomes the tidal torque from the central star. Our analysis and quantitative results can be used to constrain the parameters of transiting circumplanetary discs which may be detected in the future.