Stochastic modeling of kHz QPO light curves

Abstract

The Kluzniak & Abramowicz model explains high frequency, double peak, "3:2" QPOs observed in neutron star and black hole sources in terms of a non-linear parametric resonance between radial and vertical epicyclic oscillations of an almost Keplerian accretion disk. The 3:2 ratio of epicyclic frequencies occurs only in strong gravity. Rebusco (2004) and Horak (2004) studied the model analytically: they proved that a small forcing may indeed excite the parametric 3:2 resonance, but they have not explained the physical nature of the forcing. Here we integrate their equations numerically, dropping the ad hoc forcing, and adding instead a stochastic term to mimic the action of the very complex processes that occur in disks as, for example, MRI turbulence. We demonstrate that the presence of the stochastic term triggers the resonance in epicyclic oscillations of nearly Keplerian disks, and influences their pattern.