The role of cooling dust particles in gravitational turbulent protoplanetary disks

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.