2017ApJ...850...47M

In a two component advective flow around a compact object, a high-viscosity Keplerian disk is flanked by a low angular momentum and low-viscosity flow that forms a centrifugal, pressure-supported shock wave close to the black hole. The post-shock region that behaves like a Compton cloud becomes progressively smaller during the outburst as the spectra change from the hard state (HS) to the soft state (SS), in order to satisfy the Rankine-Hugoniot relation in the presence of cooling. The resonance oscillation of the shock wave that causes low-frequency quasi-periodic oscillations (QPOs) also allows us to obtain the shock location from each observed QPO frequency. Applying the theory of transonic flow, along with Compton cooling and viscosity, we obtain the viscosity parameter α_SK required for the shock to form at those places in the low-Keplerian component. When we compare the evolution of α_SK for each outburst, we arrive at a major conclusion: in each source, the advective flow component typically requires an exactly similar value of α_SK when transiting from one spectral state to another (e.g., from HS to SS through intermediate states and the other way around in the declining phase). Most importantly, these α_SK values in the low angular momentum advective component are fully self-consistent in the sense that they remain below the critical value α_cr required to form a Keplerian disk. For a further consistency check, we compute the α_K of the Keplerian component, and find that in each of the objects, α_SK < α_cr < α_K.