Temporal variability from the two-component advective flow solution and its observational evidence

In the propagating oscillatory shock model, the oscillation of the post-shock region, i.e., the Compton cloud, causes the observed low-frequency quasi-periodic oscillations (QPOs). The evolution of QPO frequency is explained by the systematic variation of the Compton cloud size, i.e., the steady radial movement of the shock front, which is triggered by the cooling of the post-shock region. Thus, analysis of energy-dependent temporal properties in different variability time scales can diagnose the dynamics and geometry of accretion flows around black holes. We study these properties for the high inclination black hole source XTE J1550-564 during its 1998 outburst and the low-inclination black hole source GX 339-4 during its 2006-07 outburst using RXTE/PCA data, and we find that they can satisfactorily explain the time lags associated with the QPOs from these systems. We find a smooth decrease of the time lag as a function of time in the rising phase of both sources. In the declining phase the time lag increases with time. We find a systematic evolution of QPO frequency and hard lags in these outbursts. In XTE J1550-564, the lag changes from hard to soft (i.e., from a positive to a negative value) at a crossing frequency ($\nu_C$) of $\sim 3.4$ Hz. We present possible mechanisms to explain the lag behavior of high and low-inclination sources within the framework of a single two-component advective flow model (TCAF).