Relativistic Diskoseismology. II. Analytical Results for c‐modes

Abstract

We first briefly review how we investigate the modes of oscillation trapped within the inner region of accretion disks by the strong-field gravitational properties of a black hole (or a compact, weakly magnetized neutron star). Then we focus on the "corrugation" (c-) modes, nearly incompressible perturbations of the inner disk. The fundamental c-modes have eigenfrequencies (ordered by radial mode number) which correspond to the Lense-Thirring frequency, evaluated at the outer trapping radius of the mode, in the slow rotation limit. This trapping radius is a decreasing function of the black hole angular momentum, so a significant portion of the disk is modulated only for slowly rotating black holes. The eigenfrequencies are thus strongly increasing functions of black hole angular momentum. The dependence of the eigenfrequencies on the speed of sound (or the luminosity) within the disk is very weak, except for slowly rotating black holes.