Advection-Dominated Accretion Flows with Causal Viscosity

Aims. We present the basic equations and sample solutions for the steady-state global transonic solutions of the advection-dominated accretion flows (ADAFs) with causal viscosity prescription. The procedures of the stable numerical calculations and all explicit formula to obtain the solutions of ADAFs are also presented. Methods. We solve the transonic solutions of ADAFs by using the explicit numerical integrations, such as the Runge-Kutta method. In this calculation method, we firstly solve the physical values at the sonic radius where L’Hopital’s rule is used. Then, we numerically solve the coupled differential equations of the radial velocity, the angular momentum and the sound speed from the sonic radius to the inward and outward directions. Results. By the calculation procedures presented in this paper, we can cover the all parameter spaces of the transonic solutions of ADAFs. Sample transonic solutions for ADAF-thick disk and ADAF-thin disk are presented. The explicit formula for the analytical expansion around the singular points, the sonic point and the viscous point, are presented. If we set the diffusion timescale to be null, the formalism in this study become the formalism of the acausal viscosity which is usually used in the past study for the calculation of the ADAF structure.