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Title: Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion

Abstract

The effect of magnetic field diffusion on the stability of accretion disks is a problem that has attracted considerable interest of late. In particular, the Hall effect has the potential to bring about remarkable changes in the dynamical behavior of disks that are without parallel. In this paper, we conduct a systematic examination of the linear eigenmodes in a weakly magnetized differentially rotating gas with a special focus on Hall diffusion. We first develop a geometrical representation of the eigenmodes and provide a detailed quantitative description of the polarization properties of the oscillatory modes under the combined influence of the Coriolis and Hall effects. We also analyze the effects of magnetic diffusion on the structure of the unstable modes and derive analytical expressions for the kinetic and magnetic stresses and energy densities associated with the non-ideal magnetorotational instability (MRI). Our analysis explicitly demonstrates that, if the dissipative effects are relatively weak, the kinetic stresses and energies make up the dominant contribution to the total stress and energy density when the equilibrium angular momentum and magnetic field vectors are anti-parallel. This is in sharp contrast to what is observed in the case of the ideal or dissipative MRI. We conduct shearingmore » box simulations and find very good agreement with the results derived from linear theory. Because the modes under consideration are also exact solutions of the nonlinear equations, the unconventional nature of the kinetic and magnetic stresses may have significant implications for the nonlinear evolution in some regions of protoplanetary disks.« less

Authors:
;  [1]
  1. Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen Ø (Denmark)
Publication Date:
OSTI Identifier:
22661250
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 838; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; ANGULAR MOMENTUM; DIFFUSION; ENERGY DENSITY; EQUATIONS; EQUILIBRIUM; EVOLUTION; EXACT SOLUTIONS; HALL EFFECT; INSTABILITY; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NMR IMAGING; POLARIZATION; PROTOPLANETS; SIMULATION; STABILITY; STRESSES

Citation Formats

Mohandas, Gopakumar, and Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk. Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion. United States: N. p., 2017. Web. doi:10.3847/1538-4357/AA6118.
Mohandas, Gopakumar, & Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk. Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion. United States. doi:10.3847/1538-4357/AA6118.
Mohandas, Gopakumar, and Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk. Mon . "Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion". United States. doi:10.3847/1538-4357/AA6118.
@article{osti_22661250,
title = {Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion},
author = {Mohandas, Gopakumar and Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk},
abstractNote = {The effect of magnetic field diffusion on the stability of accretion disks is a problem that has attracted considerable interest of late. In particular, the Hall effect has the potential to bring about remarkable changes in the dynamical behavior of disks that are without parallel. In this paper, we conduct a systematic examination of the linear eigenmodes in a weakly magnetized differentially rotating gas with a special focus on Hall diffusion. We first develop a geometrical representation of the eigenmodes and provide a detailed quantitative description of the polarization properties of the oscillatory modes under the combined influence of the Coriolis and Hall effects. We also analyze the effects of magnetic diffusion on the structure of the unstable modes and derive analytical expressions for the kinetic and magnetic stresses and energy densities associated with the non-ideal magnetorotational instability (MRI). Our analysis explicitly demonstrates that, if the dissipative effects are relatively weak, the kinetic stresses and energies make up the dominant contribution to the total stress and energy density when the equilibrium angular momentum and magnetic field vectors are anti-parallel. This is in sharp contrast to what is observed in the case of the ideal or dissipative MRI. We conduct shearing box simulations and find very good agreement with the results derived from linear theory. Because the modes under consideration are also exact solutions of the nonlinear equations, the unconventional nature of the kinetic and magnetic stresses may have significant implications for the nonlinear evolution in some regions of protoplanetary disks.},
doi = {10.3847/1538-4357/AA6118},
journal = {Astrophysical Journal},
number = 1,
volume = 838,
place = {United States},
year = {Mon Mar 20 00:00:00 EDT 2017},
month = {Mon Mar 20 00:00:00 EDT 2017}
}