Evolution of a Mode of Oscillation within Turbulent Accretion Disks

We investigate the effects of subsonic turbulence on a normal mode of oscillation (a possible origin of the high-frequency quasi-periodic oscillations (HFQPOs) within some black hole accretion disks). We consider perturbations of a time-dependent background (steady-state disk plus turbulence), obtaining an oscillator equation with stochastic damping, (mildly) nonlinear restoring, and stochastic driving forces. The (long-term) mean values of our turbulent functions vanish. In particular, turbulence does not damp the oscillation modes, so “turbulent viscosity” is not operative. However, the frequency components of the turbulent driving force near that of the mode can produce significant changes in the amplitude of the mode. Even with an additional (phenomenological constant) source of damping, this leads to an eventual “blowout” (onset of effects of nonlinearity) if the turbulence is sufficiently strong or the damping constant is sufficiently small. The infrequent large increases in the energy of the mode could be related to the observed low duty cycles of the HFQPOs. The width of the peak in the power spectral density (PSD) is proportional to the amount of nonlinearity. A comparison with observed continuum PSDs indicates the conditions required for the visibility of the mode.