Boundary conditions at sonic radius for inertial-acoustic oscillations in transonic accretion disks

Abstract

Wave equations describing acoustic waves in transonic accretion flows have singular behaviors at the transonic point, because any acoustic informations cannot transport themselves upstream through the sonic radius. Under a simplified geometrically thin (relativistic) advection-dominated disk, the conditions that the singularity at the sonic radius is not a real singularity but a regular (apparent) one are derived for the inertial-acoustic oscillations (p-mode oscillations). A purpose of this derivation is to use the results as the inner boundary conditions in studying numerically the behaviors of the global trapped p-mode oscillations in transonic accretion disks. The p-mode oscillation, which is degenerated to a single mode in the disk with no accretion flow, is split into two ones by the effects of accretion flows. For each of these two split modes, the conditions of regular singularity at the sonic radius are derived. The derived conditions should be used as inner boundary conditions of oscillations when we examine trapping of global p-mode oscillations in transonic advection-dominated accretion disks.