Relativistic Diskoseismology. III. Low-Frequency Fundamental p-Modes

We extend our investigation of the normal modes of small adiabatic oscillations of relativistic barotropic thin accretion disks to the inertial-pressure (p) modes. We focus here on the lowest frequency fundamental p-modes, those with no axial or vertical nodes in their distribution. Through a variety of analyses, we obtain closed-form expressions for the eigenfrequencies and eigenfunctions. These depend on the luminosity and viscosity parameter of the disk as well as the mass and angular momentum of the black hole via detailed formulae for the speed of sound. The effect of a torque on the inner edge of the disk is also included. We compare the p-mode properties to those of the g- and c-modes.