Spectral and algebraic instabilities in thin Keplerian discs under poloidal and toroidal magnetic fields

Abstract

Linear instability of two equilibrium configurations with either poloidal (I) or toroidal (II) dominant magnetic field components are studied in thin vertically-isothermal Keplerian discs. Solutions of the stability problem are found explicitly by asymptotic expansions in the small aspect ratio of the disc. In both equilibrium configurations the perturbations are decoupled into in-plane and vertical modes. For equilibria of type I those two modes are the Alfvén-Coriolis and sound waves, while for equilibria of type II they are the inertia-Coriolis and magnetosonic waves. Exact expressions for the growth rates as well as the number of unstable modes for type I equilibria are derived. Those are the discrete counterpart of the continuous infinite homogeneous cylinder magnetorotational (MRI) spectrum. It is further shown that the axisymmetric MRI is completely suppressed by dominant toroidal magnetic fields (i.e. equilibria of type II). This renders the system prone to either non-axisymmetric MRI or non-modal algebraic growth mechanisms. The algebraic growth mechanism investigated in the present study occurs exclusively due to the rotation shear, generates the inertia-Coriolis driven magnetosonic modes due to non-resonant or resonant coupling that induces, respectively, linear or quadratic temporal growth of the perturbations.

correction of typos

References in corpus (12)

• 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
• MHD simulations of the magnetorotational instability in a shearing box with zero net flux. I. The issue of convergence
• Angular Momentum Transport in Accretion Disks: Scaling Laws in MRI-driven Turbulence
• Accretion Discs with Strong Toroidal Magnetic Fields
• Aspect ratio dependence in magnetorotational instability shearing box simulations
• On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks
• Destabilisation of hydrodynamically stable rotation laws by azimuthal magnetic fields
• Global transient dynamics of three-dimensional hydrodynamical disturbances in a thin viscous accretion disk
• Evolution of initially localized perturbations in stratified ionized disks
• Hall equilibrium of thin Keplerian disks embedded in mixed poloidal and toroidal magnetic fields
• Non-exponential hydrodynamical growth in density-stratified thin Keplerian discs

Cited by in corpus (6)

• Active modes and dynamical balances in MRI-turbulence of Keplerian disks with a net vertical magnetic field
• Non-Dissipative Saturation of the Magnetorotational Instability in Thin Disks
• Resonant instability of the nonlinearly-saturated magnetorotational mode in thin Keplerian discs
• The Magneto-Rotational Decay Instability in Keplerian Disks
• Regimes of the non-exponential temporal growth in thin Keplerian discs under toroidally-dominated magnetic fields
• Explosive magnetorotational instability in Keplerian disks