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Astron. Astrophys. 356, 363-372 (2000) 8. Viscous evolution of advective diskAs we know, the structure of an accretion disk in the vertical direction, the relation between the viscous tensor and the surface density in particular, defines the type of its temporal evolution. In advective disks, which are the low-radiative accretion flows, the relations between their characteristic physical parameters differ significantly from those in standard disks. In this section, we discuss the results of Sect. 2 as applied to the disks which radial structure was presented by Spruit et al. (1987) and Narayan & Yi (1994, 1995, hereafter NY). The viscous stress and the surface density are related through the kinematic coefficient of turbulent viscosity. Integrating the component of viscous stress tensor one obtains (cf. (14) and (15)): where Recall that If one adopts for the structure of advection-dominated accretion flow (ADAF) the self-similar solution by NY, it can be easily inferred that such disks exhibit the exponential with time behaviour. The solution of NY is given by: Expressing Solution (48) enables deriving the relation between
where and Eq. (49) can be rewritten in the form: Solution to (52) is sought as a product of two functions
The exponential temporal behaviour of NY flow is evident. Generally
speaking, any disk possessing such properties of
The question is, would the confined NY disk keep such properties or it would not. The fact is that NY solution describes the infinite disk. Either the boundary conditions destroy the linearity of (52) or just the characteristic decay time changes, this problem requires further accurate numerical investigation. For instance, Narayan et al. (1997) calculated numerically the global structure of stationary advection-dominated flow with consistent boundary conditions; they noted that although the self-similar solution (48) makes significant errors close to the boundaries, it gives the reasonable description of the overall properties of the flow. Further we assume that exponential trend of solution persists.
Generally speaking, the equation determining
The accretion rate evolves with time as follows (cf. (20) and (53)): The value of accretion rate can be determined if an initial
condition is imposed at some t. Mahadevan (1997) showed
that ADAF luminosity We can estimate the characteristic time of evolution of such flow.
It can be obtained from (55). Let us compare the diffusion time
We use the expressions for We can see that the time-dependent advection-dominated disk is
quickly depleted if ![]() ![]() ![]() ![]() © European Southern Observatory (ESO) 2000 Online publication: March 28, 2000 ![]() |