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.
We study a warping instability of a geometrically thin, non-self-gravitating, circumbinary disk around young binary stars on an eccentric orbit. Such a disk is subject to both the tidal torques due to a time-dependent binary potential and the radiati
ve torques due to radiation emitted from each star. The tilt angle between the circumbinary disk plane and the binary orbital plane is assumed to be very small. We find that there is a radius within/beyond which the circumbinary disk is unstable to radiation-driven warping, depending on the disk density and temperature gradient indices. This marginally stable warping radius is very sensitive to viscosity parameters, a fiducial disk radius and the temperature measured there, the stellar luminosity, and the disk surface density at a radius where the disk changes from the optically thick to thin for the irradiation from the central stars. On the other hand, it is insensitive to the orbital eccentricity and binary irradiation parameter, which is a function of the binary mass ratio and luminosity of each star. Since the tidal torques can suppress the warping in the inner part of the circumbinary disk, the disk starts to be warped in the outer part. While the circumbinary disks are most likely to be subject to the radiation-driven warping on a AU to kilo-AU scale for binaries with young massive stars more luminous than 10^4Lsun, the radiation driven warping does not work for those around young binaries with the luminosity comparable to the solar luminosity.
We investigate the tidal interactions of a red giant with a main sequence in the dense stellar core of globular clusters by Smoothed Particle Hydrodynamics method. Two models of $0.8 msun$ red giant with the surface radii 20 and $85 R_sun$ are used w
ith 0.6 or $0.8M_sun$ main sequence star treated as a point mass. We demonstrate that even for the wide encounters that two stars fly apart, the angular momentum of orbital motion can be deposited into the red giant envelope to such an extent as to trigger rotational mixing and to explain the fast rotation observed for the horizontal branch stars, and also that sufficient mass can be accreted on the main sequence stars to disguise their surface convective zone with the matter from the red giant envelope. On the basis of the present results, we discuss the parameter dependence of these transfer characteristics with non-linear effects taken into account, and derive fitting formulae to give the amounts of energy and angular momentum deposited into the red giant and of mass accreted onto the perturber as functions of stellar parameters and the impact parameter of encounter. These formulae are applicable to the encounters not only of the red giants but also of the main sequence stars, and useful in the study of the evolution of stellar systems with the star-star interactions taken into account.
