Effects of local thermodynamics and of stellar mass ratio on accretion disc stability in close binaries

Abstract

Inflow kinematics at the inner Lagrangian point L1, gas compressibility, and physical turbulent viscosity play a fundamental role on accretion disc dynamics and structure in a close binary (CB). Physical viscosity supports the accretion disc development inside the primary gravitational potential well, developing the gas radial transport, converting mechanical energy into heat. The Stellar-Mass-Ratio (SMR) between the compact primary and the secondary star (M1/M2) is also effective, not only in the location of the inner Lagrangian point, but also in the angular kinematics of the mass transfer and in the geometry of the gravitational potential wells. In this work we pay attention in particular to the role of the SMR, evaluating boundaries, separating theoretical domains in compressibility-viscosity graphs where physical conditions allow a well-bound disc development, as a function of mass transfer kinematic conditions. In such domains, the lower is the gas compressibility (the higher the polytropic index γ), the higher is the physical viscosity (α) requested. In this work, we show how the boundaries of such domains vary as a function of M1/M2. Conclusions as far as dwarf novae outbursts are concerned, induced by mass transfer rate variations, are also reported. The smaller M1/M2, the shorter the duration of the active-to-quiet and vice-versa transitional phases. Time-scales are of the order of outburst duration of SU Uma, OY Car, Z Cha and SS Cyg-like objects. Moreover, conclusions as far as active-quiet-active phenomena in a CB, according to viscous-thermal instabilities, in accordance to such domains, are also reported.

An approach to the Riemann problem in the light of a reformulation of the state equation for SPH inviscid ideal flows: a highlight on spiral hydrodynamics in accretion discs

“…The EoS in the form of introduces physical dissipation only when real local gas compression occurs. Hence, for accretion problems, if the velocity field is mainly Keplerian then either a real physical turbulent viscosity (Flebbe et al 1994; Lanzafame 2003, 2008, 2009) in the Navier–Stokes approach or an EoS in the Euler approach in the form of or should be considered. The α and β () counterparts of the SPH+EoS in the form of or are generally larger than those values largely adopted in SPH techniques ∼1. This leads us to think that and are a compromise, allowing description of both a Riemann‐problem case and a shear flow at the same time, at the price of including some small shortcomings.…”

“…Examples of SPH spread on this argument can be found in Flebbe et al (1994), Speith & Riffert (1999) and Speith & Kley (2003), as well as in Costa et al (2010) in SPH physically inviscid hydrodynamics on the basis that the SPH shear dissipation in Eulerian non‐viscous flows can be compared with physical dissipation (Molteni et al 1991; Murray 1996; Okazaki et al 2002) in a full Navier–Stokes approach. In particular, an exhaustive comparison can also be found in Lanzafame (2008) and Lanzafame (2009).…”

“…The central accretor mass is normalized to M = 1. The kinematic shear dissipation is estimated as (Molteni et al 1991; Murray 1996; Okazaki et al 2002; Lanzafame 2008, 2009). SPH results of this test are comparable with those of Speith & Riffert (1999), Speith & Kley (2003) and Costa et al (2010).…”

An approach to solving the boundary free edge difficulties in SPH modelling: application to a viscous accretion disc in close binaries

“…In our physically viscous disc modelling, the Shakura and Sunyaev prescription (Shakura 1972, 1973; Shakura & Sunyaev 1973) is adopted with the largest α SS = 1 value to lay stress on the numerical reliability of results (Lanzafame et al 2006; Lanzafame 2009). The SPH formulation of viscous contributions in the Navier–Stokes and energy equations has been developed by Flebbe et al (1994a,b).…”

“…A too small h value does not prevent particle interpenetration, destroying any fluid behaviour, because of lack of artificial viscosity. Molteni et al (1991), Lanzafame et al (1992, 2006) and Lanzafame (2003, 2009) discuss what we statistically define as a well‐defined and bound accretion disc. As far as the numerical resolution is concerned, a number of disordered neighbour particles of the order of 10 (more or less) are considered, in principle, the minimum number of neighbours in order to achieve an adequate 3D numerical interpolation, although a number of neighbours larger than 30 are currently adopted to achieve a higher accuracy.…”