On the dynamo driven accretion disks

We add the $\alpha-$ effect in the dynamo driven accretion disk model proposed by Tout & Pringle (1992), i.e., a dynamo model depends on the physical processes such as Parker instability, Balbus-Hawley instability, magnetic field reconnection and $\alpha-\omega$ mean field dynamo as well. The $\alpha-$ effect in the dynamo mechanism is determined by the strength of turbulence of the accretion flow. When the turbulent Mach number $M_t$ is less than 0.25, the solutions of the magnetic fields oscillate around their equilibrium values. The increase of the value of $M_t$ makes the amplitude of the oscillation smaller and the period longer, but does not affect the equilibrium values. The Shakura-Sunyaev viscosity parameter $\alpha_{SS}$ oscillates around the equilibrium value of 0.33. When the turbulent Mach number $M_t$ is larger than 0.25, the magnetic field components reach a stable state. In the non-linear dynamo region, the critical turbulent Mach number $M_t$ is 0.44 rather than 0.25. The oscillating magnetic fields and viscosity parameter can explain the basic properties of the dwarf nova eruptions and some properties of quiescent disks (Armitage et al. 1996).