Magnetic Viscosity in Accretion Disks
**Previous
abstract**
**Next abstract**

**Session 44 -- Radio Galaxies, Jets and Disks**
*Display presentation, Wednesday, 9:20-6:30, Pauley Room*

## [44.14] Magnetic Viscosity in Accretion Disks

*T.Tajima, R.Matsumoto (UT Austin), M.Kaisig (Univ.Wuerzburg)*
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 Alfv\'en speed $\upsilon_A$, the criterion for the
instability is
$\upsilon_A^2(k_z^2 \upsilon_A^2-3\Omega^2)+(\eta/4\pi)^2 k_z^2\Omega^2 < 0$,
where $\Omega$ is the angular velocity, $k_z$ the wavenumber
in $z$-direction, and $\eta$ the resistivity. When $\eta \ne 0$,
there is a critical seed magnetic field
$B_{zc} = (\rho/12\pi)^{1/2}
\eta k_z$ 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, $\alpha= \delta B^2 /(4\pi\rho c_s^2)$
is determined by the marginal stability condition. Using the
resistivity expression by Ichimaru (1975), the marginal stability
condition yields $\alpha = (6/\beta_0^{1/2}) (k_{\perp}/k_z)_{max}$
where $(k_{\perp}/k_z)_{max}$ is the ratio of $k_{\perp}$ 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.

**Wednesday
program listing**