The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability. II. Saturation Level and Critical Magnetic Reynolds Number

By Takayoshi Sano, James M. Stone. 2002

157 citations recorded by the source corpus.

The nonlinear evolution of the magnetorotational instability (MRI) in weakly ionized accretion disks, including the effect of the Hall term and ohmic dissipation, is investigated using local three-dimensional MHD simulations and various initial magnetic field geometries. When the magnetic Reynolds number, ReM ≡ v/ηΩ (where vA is the Alfvén speed, η is the magnetic diffusivity, and Ω is the angular frequency), is initially larger than a critical value ReM,crit, the MRI evolves into MHD turbulence in which angular momentum is transported efficiently by the Maxwell stress. If ReM < ReM,crit, however, ohmic dissipation suppresses the MRI, and the stress is reduced by several orders of magnitude. The critical value is in the range of 1-30 depending on the initial field configuration. The Hall effect does not modify the critical magnetic Reynolds number by much but enhances the saturation level of the Maxwell stress by a factor of a few. We show that the saturation level of the MRI is characterized by v/ηΩ, where vAz is the Alfvén speed in the nonlinear regime along the vertical component of the field. The condition for turbulence and significant transport is given by v/ηΩ ≳ 1, and this critical value is independent of the strength and geometry of the magnetic field or the size of the Hall term. If the magnetic field strength in an accretion disk can be estimated observationally and the magnetic Reynolds number v/ηΩ is larger than about 30, this would imply that the MRI is operating in the disk.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

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Citations in the corpus

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).”
Radiation thermo-chemical models of protoplanetary disks I. Hydrostatic disk structure and inner rim (2009, background): “An electron concentration of∼10−10 is two orders of magnitude larger than the minimum value of∼10−12 required to sustain turbulence generation by magneto-rotational instability (MRI), see (Sano & Stone, 2002).”
ASSESSING QUANTITATIVE RESULTS IN ACCRETION SIMULATIONS: FROM LOCAL TO GLOBAL (2011, methodology): “…factors (e.g., Hawley et al. 1995, 1996; Brandenburg et al. 1995; Stone et al. 1996; Fleming et al. 2000; Miller & Stone 2000; Sano & Inutsuka 2001; Sano & Stone 2002; Sano et al. 2004; Fromang & Papaloizou 2007; Simon et al. 2009) The first shearing box simulations employed comparatively few…”
Thanatology in protoplanetary discs - The combined influence of Ohmic, Hall, and ambipolar diffusion on dead zones (2014, methodology): “It is well-known that the influence of the Hall effect on the linear stability of the disc depends upon the field polarity Ω · B (Wardle 1999; Balbus & Terquem 2001), a result we have found to hold true in the nonlinear regime as well (see also Sano & Stone 2002).”
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).”
Dead Zone Accretion Flows in Protostellar Disks (2008, background): “The resulting criterion for shear-p p 13/8 generated toroidal fields to grow to about 10 times the radial seed field strength, 2v /(hQ) 1 10, (1)f resembles the criterion (Sano & Stone 2002) for magnetorotational turbulence .”
GLOBAL SIMULATIONS OF PROTOPLANETARY DISKS WITH OHMIC RESISTIVITY AND AMBIPOLAR DIFFUSION (2015, background): “The potential importance of the other non-ideal effects has long been recognized (e.g. Sano & Stone 2002; Salmeron & Wardle 2003), but it is only recently that nonlinear shearing box simulations including ambipolar diffusion and the Hall term have been performed in relevant parameter regimes,…”
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).”
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.”
Theory of Star Formation (2007, background): “…for MRI to develop in partially-ionized disks is given in Gammie & Johnson (2005); Ohmic diffusion appears to be the main limiting effect, with the saturated-state value of α dropping when v2A,z/ηΩ <∼ 1, where η is the resistivity (Sano & Stone, 2002; Turner, Sano, & Dziourkevitch, 2007).”
Dynamics of Protoplanetary Disks (2010, background): “…the analytic expectation of a critical Reynolds number below which MRI activity is quenched (Fleming, Stone & Hawley 2000; Sano & Inutsuka 2001), and suggest that the primary criterion for quenching continues to be set by the resistivity even in the presence of the Hall effect (Sano & Stone 2002).”
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).”
Global simulations of protoplanetary disks with net magnetic flux: I. Non-ideal MHD case (2016, background): “In particular, it induces new branches of instability, and a polarity dependence on the large-scale magnetic field (Wardle 1999; Balbus & Terquem 2001; Sano & Stone 2002; O’Keeffe & Downes 2014).”