Variation of the gas and radiation content in the sub-Keplerian
  accretion disk around black holes and its impact to the solutions
  We investigate the variation of the gas and the radiation pressure in
accretion disks during the infall of matter to the black hole and its effect to
the flow. While the flow far away from the black hole might be
non-relativistic, in the vicinity of the black hole it is expected to be
relativistic behaving more like radiation. Therefore, the ratio of gas pressure
to total pressure (beta) and the underlying polytropic index (gamma) should not
be constant throughout the flow. We obtain that accretion flows exhibit
significant variation of beta and then gamma, which affects solutions described
in the standard literature based on constant beta. Certain solutions for a
particular set of initial parameters with a constant beta do not exist when the
variation of beta is incorporated appropriately. We model the viscous
sub-Keplerian accretion disk with a nonzero component of advection and pressure
gradient around black holes by preserving the conservations of mass, momentum,
energy, supplemented by the evolution of beta. By solving the set of five
coupled differential equations, we obtain the thermo-hydrodynamical properties
of the flow. We show that during infall, beta of the flow could vary upto
~300%, while gamma upto ~20%. This might have a significant impact to the disk
solutions in explaining observed data, e.g. super-luminal jets from disks,
luminosity, and then extracting fundamental properties from them. Hence any
conclusion based on constant gamma and beta should be taken with caution and
corrected.
