Astronomy and Astrophysics – Astronomy
Scientific paper
May 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993aas...182.4414t&link_type=abstract
American Astronomical Society, 182nd AAS Meeting, #44.14; Bulletin of the American Astronomical Society, Vol. 25, p.870
Astronomy and Astrophysics
Astronomy
Scientific paper
Differentially rotating magnetized disks are subject to the Balbus-Hawley instability. With the local approximation of the comoving frame, we study the stability of the disk with seed magnetic fields in either poloidal or toroidal direction. The Balbus-Hawley instability has no stability threshold with respect to {B}. Inclusion of the resistivity (kinematic viscosity is not essential), however, leads to the appearance of instability threshold. In the Keplerian disk with uniform vertical magnetic field with Alfven speed upsilon_A , the criterion for the instability is upsilon_A (2(k_z^2) upsilon_A (2-3Omega ^2)+(eta /4pi )^2) k_z(2Omega ^2) < 0, where Omega is the angular velocity, k_z the wavenumber in z-direction, and eta the resistivity. When eta != 0, there is a critical seed magnetic field Bzc = (rho /12pi )(1/2) eta k_z below which the Balbus-Hawley mode is stabilized. Since the resistivity depends on the instability-induced turbulent magnetic fields as eta =eta ( delta B(2) ), the alpha parameter of the angular momentum transport of the disk, alpha = delta B(2) /(4pi rho c_s(2)) is determined by the marginal stability condition. Using the resistivity expression by Ichimaru (1975), the marginal stability condition yields alpha = (6/beta_0 (1/2) ) (k_{perpendicular to }/k_z)max where (k_{perpendicular to }/k_z)max is the ratio of k_{perpendicular to } and k_z evaluated using the wavenumber at maximum growth, and beta_0 is the plasma beta due to the unperturbed B_z fields. The alpha value for the toroidal magnetic field is the order of 1/beta_0 . The above theory will be compared with the results of 2D and 3D MHD simulation.
Kaisig Michael
Matsumoto Ryo
Tajima Toshiki
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