Wave propagation in accretion disks - Axisymmetric case

Abstract

We study the propagation properties of 3D oscillating modes in a differentially rotating gaseous disk without self-gravity. We consider mainly axisymmetric waves in a locally vertically isothermal disk and show that the wave structure can be determined analytically. Low-frequency axisymmetric g-modes propagate in a region that lies somewhere inside the wave resonance radius defined by omega = Omega(r), for wave frequency omega and disk angular speed Omega(r). High-frequency axisymmetric p-modes propagate in a region that lies somewhere outside this resonance. Waves exist that cause the disk midplane to oscillate vertically (corrugation waves), as well as waves that keep the disk midplane fixed. For a Keplerian disk, the p-modes and g-modes are separated by a forbidden region for all modes, except for the mode with no vertical nodes (n = 0). Inwardly propagating g-modes become increasingly focused toward the disk midplane, experience a rapidly decreasing radial group velocity, and increasing perturbing velocities near the disk midplane. Such waves can never reach the disk radial center and must almost certainly shock near midplane.