Analytical solution for the structure of ADAFs
  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.
