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Astron. Astrophys. 363, L13-L16 (2000)

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4. Discussion

We have proposed spatiotemporal fragmentation as a natural mechanism for producing different types of variation in the differential rotation at the top and the bottom of the convection zone. To demonstrate the occurrence of such behaviour, we have studied a solar dynamo model, with a semi-open outer boundary condition, calibrated to have the correct cycle period, with a mean rotation law given by recent helioseismic observations. We note in passing that in a few simulations performed with the boundary condition [FORMULA] at the surface, we have not so far found this phenomenon, although we cannot yet make a definitive statement on this point. In addition to producing butterfly diagrams in qualitative agreement with those that are observed, as well as torsional oscillations that penetrate into the convection zone, we have shown that this model can also produce spatiotemporal fragmentation, resulting in different oscillatory modes of behaviour near the top and the bottom of the convection zone.

We emphasize that the main aim of this letter is to propose a mechanism that can be expected to operate in general nonlinear dynamo settings, and which is capable of producing multiple periods and/or non-periodic oscillations in parts of the convective zone. The specific results given here, such as the single period halving, are based on a particular dynamo model which inevitably includes many simplifying assumptions, not least of which is that the density is uniform. (It is unclear how the inclusion of a radial dependence [FORMULA] would affect our results - we note that current solar dynamo models commonly take a uniform density.) We expect that the mechanism is of quite general applicability, and so it is plausible that a more sophisticated model might exhibit further bifurcations, thus producing different reduced periods and oscillatory regimes. It may also be useful to bear in mind in this connection that three period halvings would result in 11 years[FORMULA] years! We shall return to a more detailed study of the underlying dynamics as well as a quantitative study of different dynamo models elsewhere. We have chosen [FORMULA] in order to obtain larger amplitude torsional oscillations near the surface. We have checked that fragmentation still occurs at smaller values of [FORMULA].

Inevitably the uncertainties associated with the inversion of the helioseismic data so deep in the convection zone are quite large. Thus we believe that the mechanism discussed here may, by demonstrating what modes of dynamical behaviour are theoretically possible, act as a conceptual aid in interpreting current and further observations.

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000