Linear Analysis of the Hall Effect in Protostellar Disks

By Steven Balbus, C. Terquem. 2000

315 citations recorded by the source corpus.

The effects of Hall electromotive forces (HEMFs) on the linear stability of protostellar disks are examined. Earlier work on this topic focused on axial field and perturbation wavenumber geometry. Here we treat the problem more generally. Both axisymmetric and nonaxisymmetric cases are treated. Though seldom explicitly included in calculations, HEMFs appear to be important whenever Ohmic dissipation is. They allow for the appearance of electron whistler waves, and since these have right-hand polarization, a helicity factor is also introduced into the stability problem. This factor is the product of the components of the angular velocity and magnetic field along the perturbation wavenumber, and it is destabilizing when negative. An important finding of our more general calculation is that unless the field and angular velocity are exactly aligned, it is always possible to find destabilizing wavenumbers. HEMFs can destabilize any differential rotation law, even those with angular velocity increasing outward. Regardless of the sign of the angular velocity gradient, the maximum growth rate is always given in magnitude by the local Oort A value of the disk, as in the standard magnetorotational instability. The role of HEMFs may prove crucial to understanding how turbulence is maintained in the "low state" of eruptive disk systems.

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

View Paper: https://www.semanticscholar.org/paper/28f322169273e79b9fb0f502aa79e149fda73ae9

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Citations in the corpus

On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics (2013, background): “, space plasmas, star formation, neutron stars and geo-dynamo (see [2, 6, 7, 12, 15, 17] and references therein).”
GLOBAL SIMULATIONS OF PROTOPLANETARY DISKS WITH OHMIC RESISTIVITY AND AMBIPOLAR DIFFUSION (2015, background): “…(Umebayashi & Nakano 1988), non-ideal MHD effects such as Ohmic resistivity, ambipolar diffusion (AD) and Hall drift are expected to be important due to the low ionization levels of the gas (e.g. Blaes & Balbus 1994; Wardle 1999; Sano, Miyama, Umebayashi, & Nakano 2000; Balbus & Terquem 2001).”
Ambipolar diffusion in low-mass star formation - I. General comparison with the ideal magnetohydrodynamic case (2015, background): “…of the present calculations, of the characterisation of plasma β, and of the detailed topology of the field is the major role of these quantities in determining viscous Article number, page 10 of 20 transport in disks, in particular for the magneto-rotational instability (Balbus & Terquem 2001).”
Enhanced Angular Momentum Transport in Accretion Disks (2003, methodology): “The effects of Hall electromotive forces on the MRI have been studied by Wardle (1999) and by Balbus & Terquem (2001).”
Global Simulations of the Inner Regions of Protoplanetary Disks with Comprehensive Disk Microphysics (2017, methodology): “Linear modes are damped by resistivity and AD (Blaes & Balbus 1994; Jin 1996; Kunz & Balbus 2004), whereas the Hall effect modifies the dispersion relation depending on the polarity of the vertical field threading the disk (Wardle 1999; Balbus & Terquem 2001).”
The ionization fraction in α models of protoplanetary discs (2001, unknown): “…of the linear stability of protostellar discs including the effects of Hall electromotive forces suggest that ReM,crit may be smaller (Wardle 1999; Balbus & Terquem 2001), and preliminary results from non-linear Hall simulations appear to back this finding (Sano & Stone, private communication).”
Dynamics of Protoplanetary Disks (2010, background): “It is much easier to assess the relative magnitude of the non-ideal terms, which depend only upon the temperature, T , and total number density n. Balbus & Terquem (2001) estimate these ratios by assuming that electrons and singly-ionized ions are the charge carriers, that the typical fluid…”
Well-posedness for Hall-magnetohydrodynamics (2012, background): “The Hall-MHD is indeed needed for such problems as magnetic reconnection in space plasmas [7, 9], star formation [17, 2], neutron stars [14] and geo-dynamo [12].”
EFFECT OF AMBIPOLAR DIFFUSION ON THE NONLINEAR EVOLUTION OF MAGNETOROTATIONAL INSTABILITY IN WEAKLY IONIZED DISKS (2011, methodology): “Linear analysis of the MRI in the Hall regime have been performed by Wardle (1999) and Balbus & Terquem (2001).”
Wave turbulence in incompressible Hall magnetohydrodynamics (2006, background): “The Hall effect is relevant in many astrophysical problems to understand, for example, the presence of instabilities in protostellar disks (Balbus and Terquem 2001), the magnetic field evolution in neutron star crusts (Goldreich and Reisenegger 1992; Cumming et al.”
Thanatology in protoplanetary discs - The combined influence of Ohmic, Hall, and ambipolar diffusion on dead zones (2014, background): “The Hall effect impacts the disc dynamics in a polaritydependent way (Wardle 1999; Balbus & Terquem 2001).”
The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability. I. Local Axisymmetric Simulations (2002, methodology): “Recently, linear analyses of the MRI in the Hall regime have been presented by Wardle (1999) and Balbus & Terquem (2001).”
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).”
Accretion onto Pre-Main-Sequence Stars (2016, background): “Although the potential importance of the Hall effect in protoplanetary disks has been recognized for some time (Wardle 1999, Balbus & Terquem 2001, Kunz 2008), it has only recently been included in time-dependent numerical simulations (Lesur et al. 2014; Bai 2014, 2015; Simon et al. 2015).”
Hall magnetohydrodynamics of partially ionized plasmas (2007, background): “…the dominant mechanism for plasma drift against the magnetic field, from flux expulsion in neutron star crusts (Goldrich & Reisenegger 1992) to angular momentum trans- port in weakly ionized protoplanetary discs (Wardle, 1999; Balbus and Terquem, 2001; hereafter W99 and BT01 respectively).”
Planet-Disk Interaction and Orbital Evolution (2012, background): “Disk structure can also be influenced by non-ideal MHD processes such as the Hall effect and ambipolar diffusion (Wardle, 1999; Balbus & Terquem, 2001), increasing substantially the complexity and computational expense of simulating the non linear evolution of such disks.”
The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability. II. Saturation Level and Critical Magnetic Reynolds Number (2002, unknown): “The properties of the MRI are strongly affected by the Hall term (Wardle 1999; Balbus & Terquem 2001).”
Astrophysical magnetic fields and nonlinear dynamo theory (2004, background): “In protostellar discs, the ratio of the Hall term to microscopic diffusion is ∼ e en ∼ (8 × 10(17)/nn)(vA/cs), where vA and cs are the 25 Alfvén and sound speeds respectively [144,146,170].”