Variation of the gas and radiation content in the sub-Keplerian accretion disk around black holes and its impact to the solutions

Abstract

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 (β) and the underlying polytropic index (γ) should not be constant throughout the flow. We obtain that accretion flows exhibit significant variation of β and then γ, which affects solutions described in the standard literature based on constant β. Certain solutions for a particular set of initial parameters with a constant β do not exist when the variation of β 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 β. By solving the set of five coupled differential equations, we obtain the thermo-hydrodynamical properties of the flow. We show that during infall, β of the flow could vary upto ∼ 300%, while γ 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 γ and β should be taken with caution and corrected.

Hydromagnetics of Advective Accretion Flows Around Black Holes: Removal of Angular Momentum by Large-Scale Magnetic Stresses

“…Such flows have temperature T 10 9 K and ρ 10 −7 gm/cc (Sinha et al 2009;Rajesh & Mukhopadhyay 2010a), which were extensively explored in the context of the formation of shock in hot accretion disks and subsequent outflows and observed spectral states (Chakrabarti & Titarchuk 1995;Chakrabarti 1996). A relation of γ (and Ṁ ) with the ratio of the gas and radiation content of the flow and the corresponding variations have been discussed by Mukhopadhyay & Dutta (2012). Therefore, following previous authors and for the convenience of comparison of the previous results without magnetic fields, we choose γ = 1.335 along with the intermediate f vis and f m .…”

Dependence of acoustic surface gravity on geometric configuration of matter for axially symmetric background flows in the Schwarzschild metric ~

“…A more realistic flow model, however, perhaps requires the implementation of a non constant polytropic index having a functional dependence on the radial distance of the form γ ≡ γ(r). [41][42][43][44][45] We, nevertheless, have performed our calculations for a reasonably wide spectrum of γ and thus believe that the whole astrophysically relevant range of polytropic indices is covered in our analysis. The proportionality constant K in eq.…”