Analysis of self-similar solution of the advection dominated flows around a black hole

We analyze self-similar solution of advection dominated accretion flows around a black-hole. The effect of a pseudo-Newtonian potential is introduced perturbatively, i.e., by regarding the general relativistic effects to be small. Comparison is made with the exact global numerical solutions that exist in the literature. It is demonstrated that the perturbative analysis can give better representation and insight into the parameter space of the solution. We find over a large range of the viscosity parameter, that self-similarity could be an excellent approximation. However, for certain values of the viscosity parameter and the gas parameter gamma, the perturbation can have a singularity. Consequently, the assumption of self-similarity could be violated at distances far away from the central black hole. Implication of the perturbative analysis is discussed.