Self-similar and semi-analytical solutions are found for the height-averaged equations governing the dynamical behavior of a polytropic, self-gravitating disk under the effects of winds around the nascent object. In order to describe the 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 the Toomre parameter is less than one in most regions on the β-disk, which indicates that in such disks gravitational instabilities can occur at various distances from the central accretor. So, the β-disk model might provide a good explanation of how the planetary systems form. The purpose of the present work is twofold: examining the structure of a disk with wind in comparison to a no-wind solution and seeing whether the adopted viscosity prescription significantly affects 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 the polytropic exponent γ . It also may globally decrease if one prescribes a β-model for the viscosity.Moreover, in both viscosity models, the surface density and mass accretion rate diminish as the wind gets stronger or γ increases.

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