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

By Takayoshi Sano, James M. Stone. 2002

155 citations recorded by the source corpus.

The effect of the Hall term on the evolution of the magnetorotational instability (MRI) in weakly ionized accretion disks is investigated using local axisymmetric simulations. First, we show that the Hall term has important effects on the MRI when the temperature and density in the disk is below a few thousand K and between 1013 and 1018 cm-3, respectively. Such conditions can occur in the quiescent phase of dwarf nova disks, or in the inner part (inside 10-100 AU) of protoplanetary disks. When the Hall term is important, the properties of the MRI are dependent on the direction of the magnetic field with respect to the angular velocity vector 𝛀. If the disk is threaded by a uniform vertical field oriented in the same sense as 𝛀, the axisymmetric evolution of the MRI is an exponentially growing two-channel flow without saturation. When the field is oppositely directed to 𝛀, however, small scale fluctuations prevent the nonlinear growth of the channel flow and the MRI evolves into MHD turbulence. These results are anticipated from the characteristics of the linear dispersion relation. In axisymmetry on a field with zero-net flux, the evolution of the MRI is independent of the size of the Hall term relative to the inductive term. The evolution in this case is determined mostly by the effect of ohmic dissipation.

Subfields: Astronomy and Astrophysics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/994904a4eb3c5b38140b16defa5d3b5f3ca5e6bf

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Citations in the corpus

Global Simulations of the Inner Regions of Protoplanetary Disks with Comprehensive Disk Microphysics (2017, background): “In the outer disk where the MRI is damped, the Hall effect can enhance/reduce turbulence depending on polarity (Sano & Stone 2002a, 2002b; Bai 2015; Simon et al. 2015), though not substantially.”
WIND-DRIVEN ACCRETION IN PROTOPLANETARY DISKS. I. SUPPRESSION OF THE MAGNETOROTATIONAL INSTABILITY AND LAUNCHING OF THE MAGNETOCENTRIFUGAL WIND (2013, methodology): “In the non-linear regime, so far all numerical simulations (all using the local shearing-box approach) focus on individual non-ideal MHD effects, such as MRI with Ohmic and Hall terms (Sano & Stone 2002a, 2002b) and MRI with AD (Hawley & Stone 1998; Bai & Stone 2011).”
The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability. II. Saturation Level and Critical Magnetic Reynolds Number (2002, unknown): “Detailed calculations reveal that the Hall term could be important in dwarf nova disks in quiescence, and in protoplanetary disks around young stellar objects (Sano & Stone 2002, hereafter Paper I).”
Angular Momentum Transport by Magnetohydrodynamic Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability (2003, methodology): “MRI turbulence is prevented by diffusion if the magnetic Reynolds number, defined using the MRI wavelength and the Alfvén speed, is less than unity (Sano & Stone 2002b).”
Local Magnetohydrodynamic Models of Layered Accretion Disks (2002, unknown): “The linear properties of the MRI are modified in unexpected ways in Hall – 4 – MHD (Wardle 1999; Balbus & Turquem 2001); the nonlinear saturation of the MRI in Hall MHD has recently been studied by Sano & Stone (2002a; 2002b).”
NON-IDEAL MHD EFFECTS AND MAGNETIC BRAKING CATASTROPHE IN PROTOSTELLAR DISK FORMATION (2011, methodology): “…was explored previously in the context of disk-driven outflows (Wardle & Königl 1993; see also Königl et al. 2010) and accretion disk dynamics (Sano & Stone 2002); it is only starting to be explored in the context of core collapse and disk formation (Krasnopolsky et al. 2011; C. Braiding…”
EFFECT OF AMBIPOLAR DIFFUSION ON THE NONLINEAR EVOLUTION OF MAGNETOROTATIONAL INSTABILITY IN WEAKLY IONIZED DISKS (2011, background): “…number equals one being the boundary between MRI permitted and suppressed regions identified in unstratified simulations (Sano et al. 1998; Fleming et al. 2000; Sano & Stone 2002b) do agree with results from stratified simulations (Fleming & Stone 2003; Turner et al. 2007; Ilgner & Nelson 2008).”
Turbulent Mixing and the Dead Zone in Protostellar Disks (2006, methodology): “Numerical results suggest that the strength of the saturated turbulence is largely unaffected by the Hall term and is determined by the ohmic term (Sano & Stone 2002b).”
Gaps, Rings, and Non-Axisymmetric Structures in Protoplanetary Disks - From Simulations to ALMA Observations (2014, background): “…an increase of accretion stress from a low-ionization region, the so-called dead zone, in which the MRI activity is suppressed (Blaes & Balbus 1994; Sano & Stone 2002; Turner et al. 2010; Flock et al. 2012b), to a zone with highly ionized gas in which the MRI is active (Dzyurkevich et al. 2013;…”
Enhanced Angular Momentum Transport in Accretion Disks (2003, methodology): “Nonlinear numerical simulations including ohmic resistivity have been done by Fleming, Stone, & Hawley (2000); Sano & Stone (2002) have done simulations including both the ohmic and Hall processes.”
Astrophysical magnetic fields and nonlinear dynamo theory (2004, background): “The ionization fraction at the ionization–recombination equilibrium is approximately given by xe=( / nn), where is the ionization 5 rate and = 3 × 10−6T −1/2 cm3 s−1 is the dissociative recombination rate [145,146].”