We investigate the β-prescription for viscosity in standard self-gravitating thin disks and predict that in a self-gravitating thin disk the β-model will have a different dynamical behavior compared to the well-known α-prescription.Methods. We used self-similar methods to solve the integrated equations that govern the dynamical behavior of the thin disk. Results. We present the results of self-similar solutions of the time evolution of axisymmetric, polytropic, self-gravitating viscous disks around a new-born central object. We apply a β-viscosity prescription derived from rotating shear flow experiments (ν = βr2Ω). Using reduced equations in a slow accretion limit, we demonstrate inside-out self-similar solutions after core formation in the center. Some physical quantities for β-disks are determined numerically. We compare our results with α-disks under the same initial conditions. The accretion rate onto the central object for β-disks is grater than for α-disks in the outer regions where β-disks are more efficient. Our results show that the Toomre instability parameter is less than one everywhere on the β-disk which means that in such disks gravitational instabilities can occur, so the β-disk model can be a good candidate for the origin of planetary systems. Our results show that the β-disks will decouple in the outer part of the disk where self-gravity plays an important role, in agreement with theoretical predictions.

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