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The static structure of a turbulent self-gravitational disk is investigated based on the effect of cooling due to the presence of dust particles. In agreement with the numerical simulations of self-gravitational disks that have been done so far, the cumulative parameter is assumed to be on the threshold of its critical value; however, the coefficient of turbulence is obtained from the system's cooling rate. The physical quantities of the disk are obtained as a function of the radial amplitude. We show that the overall structure of the disk is divided into two regions, such that the inner part is optically a thick one and the outer part is an optically thin one. On the other hand, the model we present shows that as the mass increase speed is raised, the role of dust becomes more important. We show that the turbulent viscosity coefficient increases with the distance, but this coefficient decreases in the inner region due to the cooling of the dust. We then determine the mass of gravitational instability particles in the self-gravitational radius. We show that cooling dust particles increases the self-gravitational radius in the high accretion, while in the low accretion, the cooling of dust reduces the self-gravitational radius.

The purpose of this paper is to consider the ring systems in the context of a modified gravity theory. In fact, the gravitational stability of a ring system consisted of N particle with the same mass m rotating around a massive object at the center is studied. After finding the equation of motion and considering the dynamics of the system in the equilibrium state, perturbative analysis is used in order to find the linearized version of the equations of motion. Finally using the Fourier analysis, the dispersion relation of the system is derived. At the end, using the observational values of the free parameters of the above mentioned theory and also the dispersion equation the stability criterion of the system for several cases is derived. Finally, the results have been compared with the corresponding results in Newtonian gravity. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider the ring systems in the context of a modified gravity theory. In fact, the gravitational stability of a ring system consisted of N particle with the same mass m rotating around a massive object at the center is studied. After finding the equation of motion and considering the dynamics of the system in the equilibrium state, perturbative analysis is used in order to find the linearized version of the equations of motion. Finally using the Fourier analysis, the dispersion relation of the system is derived. At the end, using the observational values of the free parameters of the above mentioned theory and also the dispersion equation the stability criterion of the system for several cases is derived. Finally, the results have been compared with the corresponding results in Newtonian gravity. [ABSTRACT FROM AUTHOR]