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Astron. Astrophys. 362, 756-761 (2000)

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5. Discussion: dynamo-[FORMULA] and viscosity-[FORMULA]

In Table 1 a summary is given for the signs of the resulting MHD mean-field coefficients obtained by our turbulence model for the two cases of rigid rotation and Kepler rotation. The first line with positive [FORMULA]-effect, with positive kinetic helicity and negative current helicity (all in the upper disk plane) is just the same as given by Brandenburg & Schmitt (1998) for a simulation of the solar north pole. For a MHD shear flow simulated by Brandenburg (1999) the case `Kepler' in Table 1 is valid and there is also not even one exception from the general agreement. The kinetic helicity in the upper disk plane for Brandenburg's simulation is negative and the same is true in our flux tube model. It is interesting to formulate for Kepler disks the relation between both alphas. With (21) and (40) follows

[EQUATION]

so that the amplitude of the dynamo-[FORMULA] becomes

[EQUATION]

We have also used the relation [FORMULA] between the disk thickness and the temperature of a thin accretion disk. The magnetic Mach number Mm can be assumed to be of order unity.

We find the dynamo-[FORMULA] to be a rather small fraction of the turbulent velocity [FORMULA]. Ziegler & Rüdiger (2000) find with a box simulation that the dynamo-[FORMULA] is of order [FORMULA] in units of the sound velocity. The turbulent velocity is of the order of the sound velocity (of the midplane) so that the [FORMULA]-effect approaches [FORMULA] in units of the eddy velocity. This is indeed smaller than the viscosity-[FORMULA] which in the simulations was of order [FORMULA].

The dynamo-[FORMULA] proves to be negative in the upper disk plane and positive in the lower one. We can thus expect a dipolar symmetry with respect to the equator for the dynamo-maintained large-scale magnetic fields. In order to ensure self-excitation for the magnetic fields with such a small [FORMULA]-effect, the eddy diffusivity of the turbulence must be sufficiently small. As it works with uniform magnetic fields we can not compute this coefficient with our model. The same also holds for almost all numerical simulations so that here it must remain open whether a magnetic dynamo really works.

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© European Southern Observatory (ESO) 2000

Online publication: October 24, 2000
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