Damping of orbital inclinations by bending waves

An inclined secondary orbiting in a disk will launch bending waves from resonance sites where the Doppler shifted forcing frequency matches the disk's natural frequency for vertical oscillations. These vertical resonances are of two types: external resonances falling interior and exterior to the perturber's semimajor axis that excite its inclination and coorbiting resonances that fall at the perturber's orbit and damp its inclination. We show that torques from coorbiting resonances dominate the bending wave interaction for a constant density disk. In this case the inclination ultimately decay and an estimate of the characteristic time scale for this process is made.