Possible range of viscosity parameter to trigger black hole candidates to exhibit different states of outbursts

TL;DR

This paper investigates the viscosity parameter range in accretion flows around black holes that triggers different outburst states, using theoretical models and QPO observations to determine flow properties.

Contribution

It introduces a method to estimate the viscosity parameter in low-angular momentum flows during black hole outbursts, demonstrating its consistency across spectral states.

Findings

The viscosity parameter remains below the critical value during state transitions.

Similar viscosity values are required for shock formation across different outburst phases.

The viscosity in the advective flow is consistent with the formation of a Keplerian disk.

Abstract

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 which forms a centrifugal pressure supported shock wave close to the black hole. The post-shock region which behaves as a Compton cloud becomes progressively smaller during the outburst as the spectra change from the hard state to the soft state in order to satisfy Rankine-Hugoniot relation in presence of cooling. The resonance oscillation of the shock wave which 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 with Compton cooling and viscosity, we obtain the viscosity parameter $\alpha_{SK}$ required for the shock to form at those places in the low-Keplerian component. When we compare the evolution of $\alpha_{SK}$ for each outburst, we arrive at a major conclusion: In each source, the advective flow component typically requires exactly a similar value of $\alpha_{SK}$ when transiting from one spectral state to another (e.g., from hard state to soft state through intermediate states and the other way around in the declining phase). Most importantly, these $\alpha_{SK}$ values in the low-angular momentum advective component are fully self-consistent in the sense that they remain below critical value $\alpha_{cr}$ required to form a Keplerian disk. For a further consistency check, we compute the $\alpha_K$ of the Keplerian component, and find that in each of the objects, $\alpha_{SK}$ $<$ $\alpha_{cr}$ $<$ $\alpha_K$.