Resonant excitation of disk oscillations by warps: A model of kHz QPOs

Abstract

The amplification of disk oscillations resulting from non-linear resonant couplings between the oscillations and a warp is examined. The disks are geometrically thin and general relativistic with non-rotating central objects. By using a Lagrangian formulation, a general stability criterion is derived. The criterion is applied to horizontal and vertical resonances of g-mode oscillations and to horizontal resonances of p-mode oscillations. The results of analyses show that g-mode oscillations (including p-mode oscillations of n = 0) are amplified by horizontal resonances with the warp. Other modes of oscillations with other resonances are all damped by resonances. The amplified g-mode oscillations are located around the radius 4rg, the radius of the epicyclic frequency being maximum, i.e., κmax. The frequencies of amplified oscillations are harmonics of κmax, and well explain the 2 : 3 pairs of observed QPOs for reasonable masses (and spins) of the central objects.