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Astron. Astrophys. 346, 922-928 (1999)

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4. Conclusions

We never find the traditional dipolar field geometry. The fields are always symmetric with respect to the equatorial plane. Small Coriolis numbers yield axisymmetric (S0) and large Coriolis numbers non-axisymmetric (S1) field geometries. While the S0-field consists of quadrupolar and higher modes with no dipolar contribution at all, the non-axisymmetric field found for realistic Coriolis numbers somewhat resembles a tilted dipole. Note, however, that it remains fully three-dimensional in the outer space, while an aligned dipole has no toroidal field component.

For the stellar model we have used, a Coriolis number of 2 would correspond to a rotation period of 220 days, much longer than the values of up to one week observed for weak-line T Tauri stars. We conclude that for this type of star the conditions for the excitation of the oscillating solutions are never met and the mean magnetic fields are thus always steady and non-axisymmetric.

It is a well-known result of linear dynamo theory, that non-axisymmetric modes can merely rotate, not oscillate (Rädler 1986). Although we deal with nonlinear dynamos, this is exactly the behavior we find. The fields are time-dependent, but their variation turns out to be a pure rotation.

The field geometry that results from our model is quite close to what MB found, although we deal with a different kind of object and a completely different [FORMULA]-tensor. This is due to the fact that [FORMULA]-type dynamos do not depend on the sign of [FORMULA]. Moreover, both [FORMULA]-tensors have essentially the same form because the gradients of density and turbulence velocity are aligned (with opposite signs). Both types of [FORMULA]-effect share the property that [FORMULA] vanishes for rapid rotation, while it dominates in case of slow rotation.

The field geometry appears not to depend significantly on the type of [FORMULA]-quenching used to limit the field generation. The field strength, however, does. While its order of magnitude is determined by the equipartition field strength, the actual value depends on the input parameters [FORMULA] and [FORMULA] as well as on the quenching function. The field strength inside the star typically ranges between [FORMULA] and [FORMULA] G. Its dependence on the Coriolis number implies that even in a pure [FORMULA]-type dynamo without any rotational shear, the magnetic field strength strongly depends on the stellar rotation rate.

The mechanism of field generation completely changes when the star contracts towards the main-sequence and the radiative core evolves. The strong rotational shear between the core and the convection zone should then turn the dynamo from the [FORMULA] to the [FORMULA]-regime. It is a challenge for the theories of differential rotation and stellar dynamos to make predictions about this transition.

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© European Southern Observatory (ESO) 1999

Online publication: June 17, 1999