The local stability of accretion disk models with considering the role of various viscosity and cooling mechanisms

The standard thin accretion disk model can explain the soft X-ray spectra of Galactic black hole systems and AGN successfully. However, there are still a few observational documents for Radiation pressure theory in X-ray novae in black hole binary systems and AGN. The luminosity in accretion onto black holes is corresponds to L>0.01L _E . According to standard thin disk model, when the accretion rate is over a small fraction of the Eddington rate, L>0.01L _E , the inner region of the disk is radiation-pressure-dominated and thermally unstable. However, observations of the high/soft state of black hole X-ray binaries with luminosity within (0.01L _E <L<0.5L _E ) show that the disk is quite stable. Thus, this contradiction shows the objection of this model and maybe it is essential to change the standard viscosity law or one of the other basic assumptions in order to get a stable disk models. In this paper, we revisit and recalculate the thermal instability with a different models of viscosity and cooling functions and show that the choosing of an arbitrary cooling and viscosity functions can affect on the stability of a general disk model and hence maybe answer to a this problem in accretion disk theory. We choose an arbitrary functions of surface density Σ and half thickness of disk H for cooling and viscosity. Also, we discuss a general disk with thermal conduction, radial force and advection. Then, we solve the equations numerically. We obtain a fourth degree dispersions relation and discuss solutions and instability modes. This analysis shows the great sensitivity of stability of disk to the form of viscosity, so there are various effective factors to stabilize the disk. For example the exist of advection and thermal conduction can effect to stability of disks also.