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Viscous accretion of a polytropic self-gravitating disk in the presence of wind

Self-similar and semi-analytical solutions are found for the height-averaged equations govern the dynamical behavior of a polytropic, self-gravitating disk under the effects of winds, around the nascent object. In order to describe time evolution of the system, we adopt a radius dependent mass loss rate, then highlight its importance on both the traditional $α$ and innovative $β$ models of viscosity prescription. In agreement with some other studies, our solutions represent that Toomre parameter is less than one in most regions on the $β$-disk which indicate that in such disks gravitational instabilities can occur in various distances from the central accretor and so the $β$-disk model might provide a good explanation of how the planetary systems form. The purpose of the present work is twofold. First, examining the structure of disk with wind in comparison to no-wind solution; and second, to see if the adopted viscosity prescription affects significantly the dynamical behavior of the disk-wind system. We also considered the temperature distribution in our disk by a polytropic condition. The solutions imply that, under our boundary conditions, the radial velocity is larger for $α$-disks and increases as wind becomes stronger in both viscosity models. Also, we noticed that the disk thickness increases by amplifying the wind or adopting larger values for polytropic exponent $γ$. It also may globally decrease if one prescribe $β$-model for the viscosity. Moreover, in both viscosity models, surface density and mass accretion rate reduce as wind gets stronger or $γ$ increases.