Magnetorotational instability in stratified, weakly ionised accretion discs

Abstract

We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionised accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and assumed constant with height. We obtained solutions for the structure and growth rate of global unstable modes for different conductivity regimes, strengths of the initial magnetic field and coupling between ionised and neutral components of the fluid. The envelopes of short-wavelenght perturbations are determined by the action of competing local growth rates at different heights, driven by the vertical stratification of the disc. Ambipolar diffusion perturbations peak consistently higher above the midplane than modes including Hall conductivity. For weak coupling, perturbations including the Hall effect grow faster and act over a more extended cross-section of the disc than those obtained using the ambipolar diffusion approximation. Finally, we derived an approximate criterion for when Hall diffusion determines the growth of the magnetorotational instability. This is satisfied over a wide range of radii in protostellar discs, reducing the extent of the magnetic `dead zone'. Even if the magnetic coupling is weak, significant accretion may occur close to the midplane, rather than in the surface regions of weakly-ionised discs.

19 pages, 13 figures, 3 tables. To appear in MNRAS

References in corpus (14)

• Magnetorotational Instability in Protoplanetary Disks. II. Ionization State and Unstable Regions
• Linear Analysis of the Hall Effect in Protostellar Disks
• Local Magnetohydrodynamical Models of Layered Accretion Disks
• The Balbus-Hawley instability in weakly ionised discs
• The ionization fraction in alpha-models of protoplanetary disks
• The Effect of Resistivity on the Nonlinear Stage of the Magnetorotational Instability in Accretion Disks
• The conductivity of dense molecular gas
• The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability: II. Saturation Level and Critical Magnetic Reynolds Number
• The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability: I. Local Axisymmetric Simulations
• On the origin of episodic accretion in Dwarf Novae
• Nonlinear Evolution of the Magnetorotational Instability in Ion-Neutral Disks
• Viscosity Mechanisms in Accretion Disks
• Dust grains and the structure of steady C-type magnetohydrodynamic shock waves in molecular clouds
• A Local One-Zone Model of MHD Turbulence in Dwarf Nova Disks

Cited by in corpus (45)

• Global simulations of protoplanetary disks with ohmic resistivity and ambipolar diffusion
• Thanatology in Protoplanetary Discs: the combined influence of Ohmic, Hall, and ambipolar diffusion on dead zones
• Hall magnetohydrodynamics of partially ionized plasmas
• Magnetorotational Instability Driven Accretion in Protoplanetary Disks
• Cooling Requirements for the Vertical Shear Instability in Protoplanetary Disks
• Magnetically driven accretion in protoplanetary discs
• Magnetic self-organisation in Hall-dominated magnetorotational turbulence
• Hall diffusion and the magnetorotational instability in protoplanetary discs
• Ambipolar Diffusion in the Magnetorotational Instability
• Self-Sustained Ionization and Vanishing Dead Zones in Protoplanetary Disks
• Saturation of the magnetorotational instability in the unstratified shearing box with zero net flux: convergence in taller boxes
• Diffusion coefficient of a passive contaminant in a local MHD model of a turbulent accretion disc
• The Role of Tiny Grains on the Accretion Process in Protoplanetary Disks
• On the First Generation of Stars
• Wind-driving protostellar accretion discs. I. Formulation and parameter constraints
• Angular momentum transport in protostellar discs
• On the Grain-Modified Magnetic Diffusivities in Protoplanetary Disks
• The ionising effect of low energy cosmic rays from a class II object on its protoplanetary disk
• The influence of the Hall effect on the global stability of cool protostellar disks
• Waves in the solar photosphere
• Dust segregation in Hall-dominated turbulent protoplanetary disks
• Finite Larmor Radius Effects on the Magnetorotational Instability
• Nonlinear Stability of Thin, Radially-Stratified Disks
• MRI channel flows in vertically-stratified models of accretion disks
• Magnetorotational instability in protoplanetary discs: The effect of dust grains
• Magnetorotational instability in magnetic diffusion dominated accretion discs
• The Weak Field Limit of the Magnetorotational Instability
• Multifluid simulations of the Magnetorotational Instability in protostellar disks
• Electron Heating in the Magnetorotational Instability: Implications for Turbulence Strength in Outer Regions of Protoplanetary Disks
• Centrifugally driven winds from protostellar accretion discs. I - Formulation and initial results
• Dynamics Near the Inner Dead-Zone Edges in a Proprotoplanetary Disk
• The Hall instability of thin weakly-ionized stratified Keplerian disks
• Hall equilibrium of thin Keplerian disks embedded in mixed poloidal and toroidal magnetic fields
• Ion dynamics and the magnetorotational instability in weakly-ionized discs
• The Hall instability of weakly ionized, radially stratified, rotating disks
• Disk evolution and the fate of water
• Global multifluid simulations of the magnetorotational instability in radially stratified protoplanetary disks
• Connecting Planetary Composition with Formation
• Gravitational instability of filamentary molecular clouds, including ambipolar diffusion; Non-isothermal filament
• Excitation of spiral density waves by convection in accretion discs
• Magnetorotational instability in weakly ionised, stratified accretion discs
• Formation of stars and planets: the role of magnetic fields
• Analysis of azimuthal magnetorotational instability of rotating MHD flows and Tayler instability via an extended Hain-Lust equation
• Radial and vertical angular momentum transport in protostellar discs
• The role of magnetic fields in star formation