Self-similar Solutions for Finite Size Advection-dominated Accretion Flows

We investigated effects on flow variables of transonic advection-dominated accretion flows (ADAFs) for different outer boundary locations (BLs) with a changing energy constant (E) of the flow. We used the ADAF solutions and investigated a general power index rule of a radial bulk velocity (v(r) proportional to r(-p)) with different BLs, but the power index with a radius for a rotation velocity and sound speed is unchanged. Here, p >= 0.5 is a power index. This power rule gives two types of self-similar solutions; first, when p = 0.5 gives a self-similar solution of a first kind and exists for infinite length, which has already been discovered for the ADAFs by Narayan & Yi, and second, when p. >. 0.5 gives a self-similar solution of a second kind and exists for finite length, which corresponds to our new solutions for the ADAFs. By using this index rule in fluid equations, we found that the Mach number (M) and advection factor (f(adv)) vary with the radius when p > 0.5. The local energies of the ADAFs and the Keplerian disk are matched very well at the BLs. So, this theoretical study is supporting a two-zone configuration theory of the accretion disk, and we also discussed other possible hybrid disk geometries. The present study can have two main implications with a variation of the p; first, one that can help with the understanding of outflows and nonthermal spectrum variations in black hole candidates, and second, one that can help with solving partial differential equations for any sized advective disk.