Spiral and shock front development in accretion discs in close binaries: Physically viscous and non-viscous SPH modelling

Abstract

Abstract.A comparison between an accretion disc model, whose transport mechanisms are driven only by artificial viscosity, and a physically viscous accretion disc model for the same close binary system is performed here by adopting the same parameters and boundary conditions. These assumptions mean that artificial viscosity, included in both models, shares, together with physical viscosity, mass and angular momentum transport in the second disc model. The Smooth Particle Hydrodynamics (SPH) Lagrangian scheme has been adopted in both models and α ss = 1 has been considered as for the viscous model according to the well-known Shakura and Sunjaev formulation. Physical viscosity is represented by the viscous force contribution as a divergence of the symmetric viscous stress tensor in the Navier-Stokes equation, whilst the viscous energy contribution is given by a symmetric combination of the symmetric shear tensor times to the particle velocity. Adopting a supersonic particle inflowing at the inner lagrangian point L1, clear spiral strong shocks in the radial flux develop from the inviscid 3D model. Extended spirals and shock fronts are even more evident in the viscous accretion disc model, which is larger than the non-viscous one in the XY orbital plane. Characteristics of the two disc structures as well as observational consequences are discussed.

Low compressibility accretion disc formation in close binaries: the role of physical viscosity

“…For the α = 0.1 case no evident differences appear with respect to the inviscid reference model. A similar result was also reported in Lanzafame (2003). Instead, a well bound accretion disc is seen for the α = 0.5 case.…”

“…In the case of a well bound and defined physically viscous accretion disc, we also investigated the possibility of spiral shock front development from its outer edge in spite of the physical viscosity degradation effect on gas dynamics and shock front discontinuities. Spiral shock fronts coming out in the disc radial flow have clearly been shown in a previous paper (Lanzafame 2003) for γ = 1.01 in the case of a physically viscous disc. In this paper a γ = 5/3 polytropic index has been adopted and a comparison among three stationary SPH accretion disc models has been performed, adopting the same binary system parameters such as stellar masses and their separation.…”

“…Indeed, physical viscosity implies a degradation and smoothing effect both on dynamical and thermodynamical discontinuities, so disfavouring shocks. As shown in Lanzafame (2003), high compressibility (γ ≤ 1.01) is a quite favourable condition to develop spirals and shock fronts in the radial flow according to some suitable dynamical and thermodynamical initial outer edge conditions at L1. Accretion disc models around massive black holes, as in Lanzafame & Belvedere (2005), are an exception.…”

“…Gas compressibility is fixed by the adiabatic index γ of 5/3. In models a) and b) we chose a highly supersonic injection velocity at L1, to verify whether, by adopting a high angular momentum injection condition, spiral structures and shocks in the radial flow would appear in low compressibility 3D modelling, as shown by Lanzafame et al (2000 in 2D, and by Lanzafame (2003) in 3D, high compressibility models. We and other authors (Meglicki et al 1993;Yukawa et al 1997) have found that spirals and shock fronts in the radial flow do not develop in high compressibility 3D SPH accretion disc models if subsonic injection conditions at L1 are adopted, in spite of the fact that tidally induced spiral patterns should develop (Murray 1996;Blondin 2000;Truss et al 2000Truss et al , 2001, at least in 2D modelling.…”

Hydrodynamic simulations of outburst events in accretion discs in close binaries

“…[12,8]) do not produce well-bound accretion discs within the primary's gravitational potential well by the fact that blobs of gas escape from the disc outer edge because the ejection rate is comparable to the injection rate from the inner Lagrangian point L1. High compressibility viscous gas dynamics in accretion discs was investigated in [5]. In a high compressibility modelling, accretion discs would form anyway, even in physically inviscid conditions.…”