The effect of different models of viscosity on the Rossby wave and Toomre instability in accretion disks with self gravity

Rossby Wave Instability (RWI) has a noteworthy effect on the evolution of proto planetary accretion disks. This instability depends on the density and extremum of vorticity in differentially rotating disks. The role of self gravity in this unstable mode has also been considered and studies have shown that self gravity can affect the stability of systems noticeably. Self gravity can also produce a new unstable mode in systems (Toomre instability). However, all of the studies so far have been concentrated on non-viscose systems. In this paper, the effect of viscosity on RWI and Toomre instability has been investigated. Both alpha and radial viscosities as well as the viscosity of second type turbulence due to self gravity have been considered. The results show that alpha viscosity leads to an increase in the growth rate of Toomre instability. This effect becomes significant in high viscosity limits. However, alpha viscosity can lead to a decrease in RWI growth rates. Assuming a viscosity of second turbulent due to self gravity causes the decrease of RWI growth rate mode to become faster. This unstable mode will disappear in high viscosity limits for small azimuthal mode numbers. For a radial viscosity (nu alpha r(n)), it has been found that the effect of viscosity is dependent upon parameter n and dimensionless parameter R. The effect of radial viscosity on RWI mode at smaller radii (R < 1) is less than larger ones (R > 1). With regard to the findings of this study, it can be suggested that the viscosity and the viscosity of second type turbulence due to self gravity be included in the simulation of RWI, planetesimal formation and dispersal of accretion disks around different objects, especially in accretion disks with moderate viscosity (young binary stars) where both viscosity and self gravity can be significant.