Magnetic viscosity by localized shear flow instability in magnetized accretion disks

Details Magnetic viscosity by localized shear flow instability in magnetized accretion disks Magnetic viscosity by localized shear flow instability in magnetized accretion disks

Jan 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995mvls.book.....m&link_type=abstract

Unknown

Mathematics

3

Accretion Disks, Angular Momentum, Dwarf Novae, Flow Stability, Gas Viscosity, Magnetohydrodynamic Turbulence, Magnetohydrodynamic Waves, Magnetohydrodynamics, Momentum Transfer, Rotating Disks, Shear Flow, Space Plasmas, Angular Velocity, Azimuth, Computerized Simulation, Doppler Effect, Eigenvectors, Magnetic Fields, Singularity (Mathematics), Three Dimensional Models

Scientific paper

Differentially rotating disks are subject to the axisymmetric instability for perfectly conducting plasma in the presence of poloidal magnetic fields. For nonaxisymmetric perturbations, the authors find localized unstable eigenmodes whose eigenfunction is confined between two Alfven singularities at omega(d) = +/- omega(A), where omega(d) is the Doppler-shifted wave frequency, and omega(A) = k(parallel bars)v(A) is the Alfven frequency. The radial width of the unstable eigenfunction is Delta x approximately to omega(A)/(Ak(y)), where A is the Oort's constant, and k(y) is the azimuthal wave number. The growth rate of the fundamental mode is larger for smaller value of k(y)/k(z). The maximum growth rate when k(y)/k(z) approximately 0.1 is approximately 0.2 Omega for the Keplerian disk with local angular velocity Omega. It is found that the purely growing mode disappears when k(y)/k(z) greater than 0.12. In a perfectly conducting disk, the instability grows even when the seed magnetic field is infinitesimal. Inclusion of the resistivity, however, leads to the appearance of an instability threshold. When the resistivity eta depends on the instability-induced turbulent magnetic fields delta B as eta ((delta B(exp 2))), the marginal stability condition self-consistently determines the alpha parameter of the angular momentum transport due to the magnetic stress. For fully ionized disks, the magnetic viscosity parameter alpha(B) is between 0.001 and 1. The authors' three-dimensional MHD simulation confirms these unstable eigenmodes. It also shows that the alpha parameter observed in simulation is between 0.01 and 1, in agreement with theory. The observationally required smaller alpha in the quiescent phase of accretion disks in dwarf novae may be explained by the decreased ionization due to the temperature drop.

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