The Dependence of Spectral State Transition and Disk Truncation on Viscosity Parameter $\alpha

TL;DR

This study explores how the viscosity parameter $oldsymbol{lpha}$ influences spectral state transitions and disk truncation in black hole X-ray binaries, revealing a strong dependence of transition luminosity on $oldsymbol{lpha}$ within the disk-corona model.

Contribution

It provides a quantitative analysis of the impact of $oldsymbol{lpha}$ on transition luminosity and disk truncation, including fitting formulae and comparison with observations.

Findings

Transition luminosity scales as $oldsymbol{lpha}^{2.34}$.

Transition luminosity varies from 0.001 to 0.2 Eddington for $oldsymbol{lpha}$ between 0.1 and 0.6.

Model results agree with observed transition luminosities and inferred $oldsymbol{lpha}$ values.

Abstract

A wealth of Galactic accreting X-ray binaries have been observed both in low/hard state and high/soft state. The transition between these two states was often detected. Observation shows that the transition luminosity between these two states is different for different sources, ranging from 1% to 4% of the Eddington luminosity. Even for the same source the transition luminosity at different outbursts is also different. The transition can occur from 0.0069 to 0.15 Eddington luminosity. To investigate the underlying physics, we study the influence of viscosity parameter $\alpha$ on the transition luminosity on the basis of the disk-corona model for black holes. We calculate the mass evaporation rate for a wide range of viscosity parameter, $0.1\le \alpha\le 0.9$. By fitting the numerical results, we obtain fitting formulae for both the transition accretion rate and the corresponding radius as a function of $\alpha$. We find that the transition luminosity is very sensitive to the value of $\alpha$, $L/L_{\rm Edd}\propto\alpha^{2.34}$. For $0.1\le\alpha\le 0.6$, the transition luminosity varies by two orders of magnitude, from 0.001 to 0.2 Eddington luminosity. Comparing with observations we find that the transition luminosity can be fitted by adjusting the value of $\alpha$, and the model determined values of $\alpha$ are mostly in the range of observationally inferred value. Meanwhile we investigate the truncation of the disk in the low/hard state for some luminous sources. Our results are roughly in agreement with the observations.