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

TL;DR

This study derives self-similar solutions for a polytropic, self-gravitating accretion disk with wind, analyzing how different viscosity models and wind strength influence disk structure, stability, and evolution.

Contribution

It introduces semi-analytical solutions for disk-wind systems considering both $eta$ and $ ext{alpha}$ viscosity models, highlighting the impact of wind and viscosity prescriptions on disk stability and structure.

Findings

Toomre parameter is less than one in most regions, indicating potential gravitational instabilities.

Radial velocity increases with wind strength and is higher in $ ext{alpha}$-disks.

Disk thickness and surface density are affected by wind strength, polytropic exponent, and viscosity model.

Abstract

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 $\alpha$ and innovative $\beta$ 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 $\beta$-disk which indicate that in such disks gravitational instabilities can occur in various distances from the central accretor and so the $\beta$-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 $\alpha$-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 $\gamma$. It also may globally decrease if one prescribe $\beta$-model for the viscosity. Moreover, in both viscosity models, surface density and mass accretion rate reduce as wind gets stronger or $\gamma$ increases.