The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability. I. Local Axisymmetric Simulations

Sano, Takayoshi; Stone, James M.

doi:10.1086/339504

Cited by 169 publications

(208 citation statements)

References 30 publications

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“…In this case the column density of the magnetically active region of the disk is Σ active ≈ 1700 g cm −2 . Hall diffusion dominates (Wardle & Ng 1999;Sano & Stone 2002) because the ions are decoupled form the magnetic field and electrons are not. Notably, the Hall effect imparts an implicit handedness to the fluid dynamics, which becomes sensitive to a global reversal of the magnetic field direction.…”

Section: Discussionmentioning

confidence: 99%

“…In addition, the Hall effect provides a dissipationless diffusion pathway that can maintain field gradients under a much broader range of conditions than would otherwise occur (Wardle & Ng 1999;Wardle 1999;Balbus & Terquem 2001). Finally, aggregation and settling of grains increases the number and mobility of charged species in the gas phase and reduces diffusivity to the point that magnetic stresses are important even at the disk midplane (Sano & Stone 2002).…”

Section: Introductionmentioning

confidence: 99%

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Magnetic fields in protoplanetary disks

Wardle

2007

Astrophys Space Sci

255

341

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Magnetic fields likely play a key role in the dynamics and evolution of protoplanetary disks. They have the potential to efficiently transport angular momentum by MHD turbulence or via the magnetocentrifugal acceleration of outflows from the disk surface. Magnetically-driven mixing has implications for disk chemistry and evolution of the grain population, and the effective viscous response of the disk determines whether planets migrate inwards or outwards. However, the weak ionisation of protoplanetary disks means that magnetic fields may not be able to effectively couple to the matter. I examine the magnetic diffusivity in a minimum solar nebula model and present calculations of the ionisation equilibrium and magnetic diffusivity as a function of height from the disk midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling by soaking up electrons and ions from the gas phase and reducing the conductivity of the gas by many orders of magnitude. However, once grains have grown to a few microns in size their effect starts to wane and magnetic fields can begin to couple to the gas even at the disk midplane. Because ions are generally decoupled from the magnetic field by neutral collisions while electrons are not, the Hall effect tends to dominate the diffusion of the magnetic field when it is able to partially couple to the gas, except at the disk surfaces where the low density of neutrals permits the ions to remain attached to the field lines.For a standard population of 0.1µm grains the active surface layers have a combined column Σ active ≈ 2 g cm −2 at 1 AU; by the time grains have aggregated to 3 µm, Σ active ≈ 80 g cm −2 . Ionisation in the active layers is dominated by stellar x-rays. In the absence of grains, x-rays maintain magnetic coupling to 10% of

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Magnetic fields in protoplanetary disks

Wardle

2007

Astrophys Space Sci

255

341

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“…The MHD equations are solved using ZeusTW, a 3D non-ideal MHD code based on Zeus3D (Clarke, Norman, & Fiedler 1994). We treat the Hall term in the induction equation using an explicit method based on Sano & Stone (2002) and Huba (2003), which includes subcycling to speed up the computation.…”

Section: Problem Setupmentioning

confidence: 99%

Disk Formation in Magnetized Clouds Enabled by the Hall Effect

Krasnopolsky

Shang

2011

ApJ

102

118

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Stars form in dense cores of molecular clouds that are observed to be significantly magnetized. A dynamically important magnetic field presents a significant obstacle to the formation of protostellar disks. Recent studies have shown that magnetic braking is strong enough to suppress the formation of rotationally supported disks in the ideal MHD limit. Whether non-ideal MHD effects can enable disk formation remains unsettled. We carry out a first study on how disk formation in magnetic clouds is modified by the Hall effect, the least explored of the three non-ideal MHD effects in star formation (the other two being ambipolar diffusion and Ohmic dissipation). For illustrative purposes, we consider a simplified problem of a non-self-gravitating, magnetized envelope collapsing onto a central protostar of fixed mass. We find that the Hall effect can spin up the inner part of the collapsing flow to Keplerian speed, producing a rotationally supported disk. The disk is generated through a Hall-induced magnetic torque. Disk formation occurs even when the envelope is initially non-rotating, provided that the Hall coefficient is large enough. When the magnetic field orientation is flipped, the direction of disk rotation is reversed as well. The implication is that the Hall effect can in principle produce both regularly rotating and counter-rotating disks around protostars. We conclude that the Hall effect is an important factor to consider in studying the angular momentum evolution of magnetized star formation in general and disk formation in particular.

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“…Considering a characteristic length of 1 AU and n % 10 5 cm À3 (Shu et al 1994), we obtain H=I % 10 À4 . In a dwarf nova disk, if T % 1500 K, n N % 10 16 cm À3 , and L % 10 10 cm, then H=I % 1 (Sano & Stone 2002) and can be even larger in some regions of protoplanetary disks. Finally, in the crust of a neutron star with B % 10 12 G, we find H=O % 10 3 (Hollerbach & Rü diger 2002).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, we expect an enhancement of the dynamo mechanism by the Hall currents. On the other hand, in some dwarf nova disks and protoplanetary disks, H=I % 1 or even larger (Sano & Stone 2002). Therefore, an inhibition of the dynamo is expected for these objects.…”

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confidence: 97%

Dynamo Action in Magnetohydrodynamics and Hall‐Magnetohydrodynamics

Mininni

Gomez

Mahajan

2003

ApJ

128

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The first direct numerical simulations of turbulent Hall dynamos are presented. The evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary regime of hydrodynamic turbulence (by a stirring force at a macroscopic scale) is studied to explore the conditions for exponential growth of the magnetic energy. The Hall current is shown to have a profound effect on turbulent dynamo action; it can strongly enhance or suppress the generation of the large-scale magnetic energy depending on the relative values of the length scales of the system.

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The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability. I. Local Axisymmetric Simulations

Cited by 169 publications

References 30 publications

Magnetic fields in protoplanetary disks

Magnetic fields in protoplanetary disks

Disk Formation in Magnetized Clouds Enabled by the Hall Effect

Dynamo Action in Magnetohydrodynamics and Hall‐Magnetohydrodynamics

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