ar X iv : a st ro - p h / 98 08 24 5 v 1 2 2 A ug 1 99 8 1 DISSIPATION INSTABILITIES IN THE ACCRETION DISK

The model of a geometrically thin gaseous disk in the external gravitational potential is considered. The dinamics of small nonaxisymmetric perturbations in the plane of the accretion disk with dissipative effects is investigated. It is showed, that conditions of development and parameters of unstable oscillation modes in the opticaly thick accretion disk are strongly depended on the models of viscosity and opacity. The possibility of the development of various types of instabilities in a thin gaseous disks is very attractive one for understanding different aspects of the accretion-disk (AD) phenomenon. In order to explain the required large values of dissipative coefficients, the concept of the turbulent viscosity has been used, which may be caused by the developed turbulence of a gaseous medium arising from the loss of stability. On the other hand, the nonlinear evolution of unstable oscillation modes may be responsible for many nonstationary phenomena in accreting systems. There are four unstable oscillation modes in the framework of the standard α-model of an accretion disk [1]. Two of then are acoustic [6-11], one is viscous and the other one is thermal [2-11]. A distinctive feature of the dynamic viscosity η = σν in the model of the accretion disks is it's dependence on the surfase density σ and on the disk half-thicness h (ν is the kinematic viscosity). The perturbation of the dynamic viscosity˜η is responsible for the formation of all unstable four modes. However, in all the above-cited papers on the dynamic of linear perturbation is suggested that viscosity simultaneously changes with changing of accretion-disk parameters. In our present work, we extend our research to time delay of the viscosity influence on the thermal, viscous and acoustic instabilities. In the construction of a different viscous models AD is suggested that viscosity caused by the developed turbulence η ∼ σu t ℓ t , where u t and ℓ t is the characteristic velocity of the large-scale turbulent pulsations and it's characteristic size, respectively [12]. The fundamental energy is contained in the large-scale pulsations, however dissipation of the energy is the case in the small-scale pulsations. By this means, as the local conditions changes in the accretion disk, there are two factors, which involves the change delay of the turbulent viscosity. Firstly, since the turbulence may be caused by the nonlinear evolution of unstable oscillation modes, that for formation of the developed turbulence is required of the characteristic time …