Resonant behavior of stochastic oscillations of general relativistic disks driven by a memory-damped friction

By using a generalized Langevin equation to describe the vertical oscillations of a general relativistic disk subjected to a memory-damped friction and a stochastic force, we derive the power spectrum density (PSD) of accretion disk oscillating luminosity by the method of Laplace transform, and discuss the influence of the system parameters on the resonant behavior in PSD curves. The results show that as the damping strength α and memory time τ of the friction increase, the variation of PSD with spectrum frequency f from monotonous decreasing to occurring maximums, and the phenomenon of a general stochastic resonance (SR) with a single peak and multi-peaks can be found in PSD curves. The radial distance parameter n, the mass M, and spin parameter a* of the black hole determine the inherent frequency of vertical oscillations in the disk, and they have significant influences on the SR phenomena in a system of black hole binaries.