Warping and tearing of misaligned circumbinary disks around eccentric
  SMBH binaries
  We study the warping and tearing of a geometrically thin,
non-self-gravitating disk surrounding binary supermassive black holes on an
eccentric orbit. The circumbinary disk is significantly misaligned with the
binary orbital plane, and is subject to the time-dependent tidal torques. In
principle, such a disk is warped and precesses, and is torn into mutually
misaligned rings in the region, where the tidal precession torques are stronger
than the local viscous torques. We derive the tidal-warp and tearing radii of
the misaligned circumbinary disks around eccentric SMBH binaries. We find that
in disks with the viscosity parameter, alpha, larger than a critical value
depending on the disk aspect ratio, the disk warping appears outside the
tearing radius. This condition is expressed as alpha > sqrt{H/3r} for H/r
~<0.1, where H is the disk scale height. If alpha < sqrt{H/3r}, only the disk
tearing occurs because the tidal warp radius is inside the tearing radius,
where most of disk material is likely to rapidly accrete onto SMBHs. In warped
and torn disks, both the tidal-warp and the tearing radii most strongly depend
on the binary semi-major axis, although they also mildly depend on the other
orbital and disk parameters. This strong dependence enables us to estimate the
semi-major axis, once the tidal warp or tearing radius is determined
observationally: For the tidal warp radius of 0.1 pc, the semi-major axis is
estimated to be ~10^{-2} pc for 10^7 Msun black hole with typical orbital and
disk parameters. We also briefly discuss the possibility that central objects
of observed warped maser disks in active galactic nuclei are supermassive black
hole binaries.
