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J. A. Markiel (U. Rochester)
Models of the solar dynamo have traditionally assumed a rotation rate either varying only with radius, or constant on cylinders. We explore the effects of including a realistic solar rotation profile as determined by helioseismology.
Extensions of the Cartesian interface dynamo model of Parker (1993, ApJ, 408, 707) are considered through 2-d numerical simulations in spherical geometry. In this model the production of the poloidal and toroidal components of the magnetic field occur in two separate regions coupled by diffusion. By imposing a diffusivity contrast between the two regions, the required super-equipartition toroidal fields can be produced in an overshoot layer, while the alpha effect which produces the poloidal field acts only on weaker fields that diffuse into the convection zone, thus avoiding the difficulty of alpha quenching.
Our results show that, while solar-like dynamo modes are indeed found when the rotation is assumed to vary only radially, these modes do not survive when a solar-like rotation profile is used. In particular, if the alpha effect is assumed to be negative in the northern hemisphere to produce the correct direction of propagation of the dynamo wave, the latitudinal gradient of the rotation drives a steady mode which suppresses the interface mode driven by the radial gradient. Oscillatory dynamo modes with the correct direction of propagation can be found if the transition to a low diffusivity is placed in the middle of the rotational shear layer, but these solutions have peak field strengths only of the order of the equipartition value, and also have a more complicated spatial structure than the simple solar dipole field.
These results indicate that there is a serious difficulty with the interface model of the solar dynamo. In addition, they demonstrate that it is important that solar dynamo models include the full solar rotation profile.
This work was supported by NSF grant AST-9528398.
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