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

Abstract

Abstract A wealth of Galactic accreting X-ray binaries has been observed in both the low/hard and high/soft states. The transition between these two states has often been detected. Observations show that the transition luminosity between these two states is different for different sources, ranging from 1% to 4% of the Eddington luminosity $L_{\rm Edd}$. Even for the same source, the transition luminosity at different outbursts can be different. The transition can occur at luminosities from 0.0069 to 0.15 $L_{\rm Edd}$. In order 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 parameters such as 0.1 $\le$$\alpha $$\le$ 0.9. 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$L_{\rm Edd}$. Comparing with observations, we find that 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 values. We also investigate the truncation of the disk in the low/hard state for some luminous sources. Our results agree roughly with the observations.