Smoothed particle hydrodynamic simulations of viscous accretion discs around black holes

Abstract

A B S T R A C TViscous Keplerian discs become sub-Keplerian close to a black hole since they pass through sonic points before entering into it. We study the time evolution of polytropic viscous accretion discs (both in one-and two-dimensional flows) using smoothed particle hydrodynamics. We discover that for a large region of the parameter space spanned by energy, angular momentum and polytropic index, when the flow viscosity parameter is less than a critical value, standing shock waves are formed. If the viscosity is very high then the shock wave disappears. In the intermediate viscosity, the disc oscillates very significantly in the viscous time-scale. Our simulations indicate that these centrifugally supported high density regions close to a black hole play an active role in the flow dynamics, and consequently, the radiation dynamics.

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“…Physical viscosity, combined together with the angular momentum, produces a shock front capable of pushing out part of the accreting flow from the disc. For low viscosity values, the subsonic post-shock region, close to the BH, develops in a radially, more-extended zone where the higher the viscosity the farther the steady shock front where the RH jump conditions are satisfied (Lanzafame et al 1998;Chakrabarti & Das 2004). Such a result has been pointed out in Chakrabarti & Molteni (1995), Lanzafame et al (1998), and in Chakrabarti & Das (2004).…”

“…Such a result has been pointed out in Chakrabarti & Molteni (1995), Lanzafame et al (1998), and in Chakrabarti & Das (2004). Moreover, Lanzafame et al (1998), and Chakrabarti & Das (2004), have shown that, when the Article published by EDP Sciences RH condition is not satisfied, the shock front shows a periodical behaviour instead of a stationary one.…”

“…In Lanzafame et al (1998), simulations have been carried out with λ = 1.6 and 0 ≤ α ≤ 1.5 × 10 −3 . These simulations refer to a stationary shock front development due to a centrifugal barrier formed during accretion onto a SMBH.…”

“…SMBH (M SMBH = 10 6 ÷ 10 9 M ) in the axisymmetric case. Following Lanzafame et al (1998), we adopted cylindrical coordinates, and assume all derivatives d/dφ equal to zero. In such formulation, each SPH particle is represented by a torus whose thickness is equal to the SPH resolution h. Exhaustive descriptions of cylindrical SPH, adopted to solve axially symmetric problems, can be found in Petschek & Libersky (1993) and in Omang et al (2006).…”

“…For low viscosity values, the subsonic post-shock region, close to the BH, develops in a radially, more-extended zone where the higher the viscosity the farther the steady shock front where the RH jump conditions are satisfied (Lanzafame et al 1998;Chakrabarti & Das 2004). Such a result has been pointed out in Chakrabarti & Molteni (1995), Lanzafame et al (1998), and in Chakrabarti & Das (2004). Moreover, Lanzafame et al (1998), and Chakrabarti & Das (2004), have shown that, when the Article published by EDP Sciences RH condition is not satisfied, the shock front shows a periodical behaviour instead of a stationary one.…”