Analytical solution for the structure of ADAFs

Abstract: The standard Advection-Dominated Accretion Flow (ADAF) is studied using a set of self-similar analytical solutions in the spherical coordinates. Our new solutions are useful for studying ADAFs without dealing with the usual mathematical complexity. We assume the $r\varphi$ component of the stress tensor dominates and the latitudinal component of the velocity is negligible. Moreover, the fluid is incompressible and the solutions are radially self-similar. We show that our analytical solutions display most of the important properties of ADAFs which have already been obtained by the detailed numerical solutions. According to our solutions, the density and the pressure of the flow decreases from the equator to the polar regions and this reduction depends on the amount of the advected energy. We also show analytically that an ADAF tends to a quasi-spherical configuration as more energy is advected with the radial flow.