Stability of MRI turbulent Accretion Disks

Abstract

Based on the characteristics of the magnetorotational instability (MRI) and the MRI-driven turbulence, we construct a steady model for a geometrically thin disk using "non-standard" $\alpha$-prescription. The efficiency of the angular momentum transport depends on the magnetic Prandtl number, $Pm=\nu /\eta$, where $\nu$ and $\eta$ are the microscopic viscous and magnetic diffusivities. In our disk model, Shakura-Sunyaev's $\alpha$-parameter has a power-law dependence on the magnetic Prandtl number, that is $\alpha \propto P{m}^{\delta }$ where $\delta$ is the constant power-law index. Adopting Spitzer's microscopic diffusivities, the magnetic Prandtl number becomes a decreasing function of the disk radius when $\delta >0$. The transport efficiency of the angular momentum and the viscous heating rate are thus smaller in the outer part of the disk, while these are impacted by the size of index $\delta$. We find that the disk becomes more unstable to the gravitational instability for a larger value of index $\delta$. The most remarkable feature of our disk model is that the thermal and secular instabilities can grow in its middle part even if the radiation pressure is negligibly small in the condition $\delta >2/3$. In the realistic disk systems, it would be difficult to maintain the steady mass accretion state unless the $Pm$-dependence of MRI-driven turbulence is relatively weak.

9 pages, 6 figures, Accepted for publication in ApJ

References in corpus (10)

• Accretion disc viscosity: how big is alpha?
• MHD simulations of the magnetorotational instability in a shearing box with zero net flux. II. The effect of transport coefficients
• Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport
• Angular Momentum Transport in Accretion Disks: Scaling Laws in MRI-driven Turbulence
• On the Magnetic Prandtl Number Behavior of Accretion Disks
• Simulations of Magnetorotational Turbulence with a Higher-Order Godunov Scheme
• Viscous and Resistive Effects on the MRI with a Net Toroidal Field
• MRI-driven turbulent transport: the role of dissipation, channel modes and their parasites
• Viscous, Resistive Magnetorotational Modes
• Axisymmetric Magnetorotational Instability in Viscous Accretion Disks

Cited by in corpus (9)

• Explicit-Implicit Scheme for Relativistic Radiation Hydrodynamics
• An accretion disc instability induced by a temperature sensitive $\alpha$ parameter
• MRI turbulence in accretion discs at large magnetic Prandtl numbers
• Demonstration of a magnetic Prandtl number disc instability from first principles
• An investigation of magnetic field distortions in accretion discs around neutron stars - II. Analysis of the toroidal field component
• Inconsistency in the Standard Model for Thin Accretion Disks
• On the application of Jacobian-free Riemann solvers for relativistic radiation magnetohydrodynamics under M1 closure
• Neutrino-Dominated Accretion Flows with Magnetic Prandtl Number-Dependent MRI-driven Turbulence
• Properties of an accretion disc with a power-law stress-pressure relationship