The excitation of density waves at the Lindblad and corotation resonances by an external potential

Abstract

The linear response of a differentially rotating two-dimensional gas disk, both with and without self-gravity, to a rigidly rotating external potential is calculated on the assumptions that the speed of sound is much smaller that the orbital velocity and that the external potential varies on the scale of the disk radius. The results show that: (1) the external potential exerts torques on the disk only at the Lindblad and corotation resonances; (2) the torque is positive at the outer Lindblad resonance and negative at the inner Lindblad resonance; (3) the torque at corotation has the sign of the radial vorticity gradient; and (4) the torques are of the same order of magnitude at both types of resonance and independent of the speed of sound in the disk. It is found that the external potential also excites density waves in the vicinity of the Lindblad and corotation resonances, that the long trailing wave is excited at a Lindblad resonance, and that short trailing waves are excited at the corotation resonance. The behavior of particle disks is briefly discussed, and the external torques on particle disks are proven to be identical to those on gas disks