Local and global aspects of the linear MRI in accretion disks

Abstract

We revisit the linear MRI in a cylindrical model of an accretion disk and uncover a number of attractive results overlooked in previous treatments. In particular, we elucidate the connection between local axisymmetric modes and global modes, and show that a local channel flow corresponds to the evanescent part of a global mode. In addition, we find that the global problem reproduces the local dispersion relation without approximation, a result that helps explain the success the local analysis enjoys in predicting global growth rates. MRI channel flows are nonlinear solutions to the governing equations in the local shearing box. However, only a small subset of MRI modes share the same property in global disk models, providing further evidence that the prominence of channels in local boxes is artificial. Finally, we verify our results via direct numerical simulations with the Godunov code RAMSES.

13 pages, 9 figures, MNRAS accepted

References in corpus (5)

• A High Order Godunov Scheme with Constrained Transport and Adaptive Mesh Refinement for Astrophysical MHD
• Aspect ratio dependence in magnetorotational instability shearing box simulations
• Convection Causes Enhanced Magnetic Turbulence in Accretion Disks in Outburst
• A weakly nonlinear analysis of the magnetorotational instability in a model channel flow
• Saturation of the MRI in Strongly Radiation Dominated Accretion Disks

Cited by in corpus (16)

• Vortices and the saturation of the vertical shear instability in protoplanetary disks
• Rings and gaps produced by variable magnetic disk winds and avalanche accretion streams: I. Axisymmetric resistive MHD simulations
• On the Nature of Magnetic Turbulence in Rotating, Shearing Flows
• The magnetorotational instability in debris-disc gas
• Instability in strongly magnetized accretion discs: A global perspective
• Saturation of the magnetorotational instability and the origin of magnetically elevated accretion discs
• HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. II. Magnetohydrodynamic simulations
• The weakly nonlinear magnetorotational instability in a local geometry
• Active modes and dynamical balances in MRI-turbulence of Keplerian disks with a net vertical magnetic field
• HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. I. Hydrodynamic simulations
• The weakly nonlinear magnetorotational instability in a global, cylindrical Taylor-Couette flow
• Quasi-periodic oscillations and the global modes of relativistic, MHD accretion discs
• Magnetohydrodynamics in a Cylindrical Shearing Box
• On the appearance of non-local MRI in Keplerian accretion discs
• Parametric Survey of Nonaxisymmetric Accretion Disk Instabilities: Magnetorotational Instability to Super-Alfvénic Rotational Instability
• Gravitoturbulent dynamo in global simulations of gaseous disks