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Register a new userTurbulent viscosity by convection in accretion discs - a self-consistent approach
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Added by
Dominikus Heinzeller
Publication date
2009
fields
Physics
and research's language is
English
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The source of viscosity in astrophysical accretion flows is still a hotly debated issue. We investigate the contribution of convective turbulence to the total viscosity in a self-consistent approach, where the strength of convection is determined from the vertical disc structure itself. Additional sources of viscosity are parametrized by a beta-viscosity prescription, which also allows an investigation of self-gravitating effects. In the context of accretion discs around stellar mass and intermediate mass black holes, we conclude that convection alone cannot account for the total viscosity in the disc, but significantly adds to it. For accretion rates up to 10% of the Eddington rate, we find that differential rotation provides a sufficiently large underlying viscosity. For higher accretion rates, further support is needed in the inner disc region, which can be provided by an MRI-induced viscosity. We briefly discuss the interplay of MRI, convection and differential rotation. We conduct a detailed parameter study of the effects of central masses and accretion rates on the disc models and find that the threshold value of the supporting viscosity is determined mostly by the Eddington ratio with only little influence from the central black hole mass.
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We conduct a series of numerical experiments into the nature of three-dimensional (3D) hydrodynamics in the postbounce stalled-shock phase of core-collapse supernovae using 3D general-relativistic hydrodynamic simulations of a $27$-$M_odot$ progenitor star with a neutrino leakage/heating scheme. We vary the strength of neutrino heating and find three cases of 3D dynamics: (1) neutrino-driven convection, (2) initially neutrino-driven convection and subsequent development of the standing accretion shock instability (SASI), (3) SASI dominated evolution. This confirms previous 3D results of Hanke et al. 2013, ApJ 770, 66 and Couch & Connor 2014, ApJ 785, 123. We carry out simulations with resolutions differing by up to a factor of $sim$4 and demonstrate that low resolution is artificially favorable for explosion in the 3D convection-dominated case, since it decreases the efficiency of energy transport to small scales. Low resolution results in higher radial convective fluxes of energy and enthalpy, more fully buoyant mass, and stronger neutrino heating. In the SASI-dominated case, lower resolution damps SASI oscillations. In the convection-dominated case, a quasi-stationary angular kinetic energy spectrum $E(ell)$ develops in the heating layer. Like other 3D studies, we find $E(ell) propto ell^{-1}$ in the inertial range, while theory and local simulations argue for $E(ell) propto ell^{-5/3}$. We argue that current 3D simulations do not resolve the inertial range of turbulence and are affected by numerical viscosity up to the energy containing scale, creating a bottleneck that prevents an efficient turbulent cascade.
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Self-gravity becomes competitive as an angular momentum transport process in accretion discs at large radii, where the temperature is low enough that external irradiation likely contributes to the thermal balance. Irradiation is known to weaken the strength of disc self-gravity, and can suppress it entirely if the disc is maintained above the threshold for linear instability. However, its impact on the susceptibility of the disc to fragmentation is less clear. We use two-dimensional numerical simulations to investigate the evolution of self-gravitating discs as a function of the local cooling time and strength of irradiation. In the regime where the disc does not fragment, we show that local thermal equilibrium continues to determine the stress - which can be represented as an effective viscous alpha - out to very long cooling times (at least 240 dynamical times). In this regime, the power spectrum of the perturbations is uniquely set by the effective viscous alpha and not by the cooling rate. Fragmentation occurs for cooling times tau < beta_crit / Omega, where beta_crit is a weak function of the level of irradiation. We find that beta_crit declines by approximately a factor of two, as irradiation is increased from zero up to the level where instability is almost quenched. The numerical results imply that irradiation cannot generally avert fragmentation of self-gravitating discs at large radii; if other angular momentum transport sources are weak mass will build up until self-gravity sets in, and fragmentation will ensue.
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