Extended Transiting Disks and Rings Around Planets and Brown Dwarfs:   Theoretical Constraints
  Newly formed planets (or brown dwarfs) may possess disks or rings that 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 disk/ring can exhibit unique, detectable transit signatures, provided that the disk/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 disks under the combined influences of the tidal torque from the central star, the torque from the oblate planet and the self-gravity of the disk. We calculate the steady-state warp profile ("generalized Laplace Surface") and investigate the condition for coherent precession of the disk. We find that to maintain non-negligible misalignment between the extended outer disk and the planet's orbital plane, and to ensure coherent disk precession, the disk 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 disks that may be detected in the future. 
J. J. Zanazzi and Dong Lai
astro-ph.EP