Behaviours of disco-seismological c-mode oscillations around the inner edge of discs

Abstract

ABSTRACT Accretion flows in the innermost region of relativistic discs are transonic. At the transonic radius, the differential equation describing wave motions with constant frequency becomes singular. This implies that for an oscillation of constant frequency to be realized in the innermost region of discs, the oscillation needs to satisfy some regularity conditions (boundary conditions) at the sonic radius. In this paper, under the assumption that the unperturbed disc structure around the sonic radius is rather smooth in the radial direction, behaviours of the fourth-order ordinary differential equation describing non-axisymmetric c-mode oscillations are examined around the sonic radius. Among four linearly independent wave solutions, one is always singular at the sonic radius and is outside of our interest. In remaining three wave modes satisfying boundary conditions, the advection term in equation of motion is a main contributor in determining the structure of the oscillations. Due to this, the waves are tightly wound or change their amplitude sharply in a narrow region around the sonic radius. This characteristic is especially notable in one of three wave modes. Possibility of the oscillations being swallowed into the central source with no reflection at the sonic radius is briefly discussed.