Low magnetic-Prandtl number flow configurations for cold astrophysical disk models: speculation and analysis

Abstract

Simulations of astrophysical disks in the shearing box that are subject to the magnetorotational instability (MRI) show that activity appears to be reduced as the magnetic Prandtl number (Pm) is lowered. On the other hand, calculations for laboratory experiments show that saturation is achieved through modification of the background shear for Pm << 1. Guided by the results of calculations appropriate for laboratory experiments when Pm is very low, the axisymmetric stability of inviscid disturbances in a shearing box model immersed in a constant vertical background magnetic field is considered under a variety of shear profiles and boundary conditions in order to evaluate the hypothesis that modifications of the shear bring about saturation of the instability. It is found that the emergence and stability of the MRI is sensitive to the boundary conditions adopted. Channel modes do not appear to be stabilized through any modification of the background shear whose average remains Keplerian. However, systems that have non-penetrative boundaries can saturate the MRI through modification of the background shear. Conceptually equating the qualitative results from laboratory experiments to the conditions in a disk may therefore be misleading.

To Appear in Astronomy and Astrophysics

References in corpus (9)

• Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks
• 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
• On the Magnetic Prandtl Number Behavior of Accretion Disks
• On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks
• A weakly nonlinear analysis of the magnetorotational instability in a model channel flow
• On the nonlinear saturation of the magnetorotational instability near threshold in a thin-gap Taylor-Couette setup
• Saturation of Magnetorotational Instability through Magnetic Field Generation
• Evolution of initially localized perturbations in stratified ionized disks

Cited by in corpus (5)

• Local instabilities in magnetized rotational flows: A short-wavelength approach
• Extending the range of the inductionless magnetorotational instability
• A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit
• Paradoxes of magnetorotational instability and their geometrical resolution
• Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD