Research on the Low Frequency Quasi-periodic Oscillations in Power Spectral Density of the Stochastic Oscillating Luminosity of Accretion Disk

In this paper, we improve the generalized Langevin equation model with fluctuating frequency and exponential function correlated stochastic force to describe the vertical oscillations of the accretion disk, then derive the analytical expression of the power spectrum density of stochastic oscillating luminosity, and discuss the influence of system parameters on low frequency quasi-periodic oscillations (LFQPOs) in power density spectrum. The results show that, for appropriate parameters, the double-peaked LFQPOs with a fundamental peak and a second harmonic peak can be found in the PSD curves, and the central frequency of primary peak corresponds to the characteristic frequency of accretion disk oscillation ν₀. Moreover, the correlation time of stochastic force determines the height and width of the primary peak, and frequency noise intensity and viscous coefficient only influence the second harmonic peak. These results confirm that the stochastic oscillation model of accretion disk should be an alternative interpretation for the origin of LFQPOs.