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Tidal Torques on Misaligned Disks in Binary Systems

We extend previous studies of the tidal truncation of coplanar disks in binary systems to the more general case of noncoplanar disks. As in the prograde coplanar case, Lindblad resonances play a key role in tidal truncation. We analyze the tidal torque acting on a misaligned nearly circular disk in a circular orbit binary system. We concentrate on the 2:1 inner Lindblad resonance associated with the m=2 tidal forcing (for azimuthal wavenumber m) that plays a major role in the usual coplanar case. We determine the inclination dependence of this torque, which is approximately cos^8(i/2) for misalignment angle i. Compared to the prograde coplanar case (i=0), this torque decreases by a factor of about 2 for i = pi/6 and by a factor of about 20 for i=pi/2. The Lindblad torque decreases to zero for a tilt angle of pi (counter-rotation), consistent with previous investigations. The effects of higher order resonances associated with m>2 tidal forcing may contribute somewhat, but are much more limited than in the i=0 case. These results suggest that misaligned disks in binary systems can be significantly extended compared to their coplanar counterparts. In cases where a disk is sufficiently inclined and viscous, it can overrun all Lindblad resonances and overflow the Roche lobe of the disk central object.