Advection-dominated accretion flow for the varied transition luminosities in black hole X-ray binaries
Li, J. and Qiao, E. May 2023, Monthly Notices of the Royal Astronomical Society, Volume 521, Issue 3, pp.3237–3246
Observationally, two main spectral states, i.e. the low/hard state and the high/soft state, are identified in black hole X-ray binaries (BH-XRBs). Meanwhile, the transitions between the two states are often observed. In this paper, we re-investigate the transition luminosities in the framework of the self-similar solution of the advection-dominated accretion flow (ADAF). Specifically, we search for the critical mass accretion rate m˙crit of ADAF for different radii r, respectively. It is found that m˙crit decreases with decreasing r. By testing the effects of BH mass m, the magnetic parameter β and the viscosity parameter α, it is found that only α has significant effects on m˙crit--r relation. We define the minimum m˙crit (roughly at the innermost stable circular orbit) as the hard-to-soft transition rate m˙tr:H--S, above which BH will gradually transit from the low/hard state to the high/soft state, and m˙crit at 30 Schwarzschild radii as the soft-to-hard transition rate m˙tr:S→H, below which BH will gradually transit from the high/soft state to the low/hard state. We derive fitting formulae of m˙tr:H→S and m˙tr:S→H as functions of α, respectively. By comparing with observations, it is found that the mean value of α are α ~ 0.85 and α ~ 0.33 for the hard-to-soft transition and the soft-to-hard transition, respectively, which indicates that two classes of α are needed for explaining the hysteresis effect during the state transition. Finally, we argue that such a constrained α may provide valuable clues for further exploring the accretion physics in BH-XRBs.
