Recent analyses of the helioseismic data, from both the Michelson Doppler Imager (MDI) instrument on board the SOHO spacecraft (Howe et al. 2000a) and the Global Oscillation Network Group (GONG) project (Antia & Basu 2000) have provided strong evidence which indicates that the earlier observed time variations of the differential rotation on the solar surface, the so called `torsional oscillations' with periods of about 11 years (e.g. Howard & LaBonte 1980; Snodgrass, Howard & Webster 1985; Kosovichev & Schou 1997; Schou et al. 1998), penetrate into the convection zone, to depths of at least 8 percent in radius.
Furthermore, these data have provided some evidence to suggest that variations in the differential rotation are also present around the tachocline at the bottom of the convection zone (Howe et al. 2000b). An important feature that distinguishes these variations from those observed at the upper parts of the convection zone is that they possess markedly different modes of behaviour: either possessing distinctly lower periods (of 1.3 years), or being non-periodic (Antia & Basu 2000). Clearly, to firmly establish the precise nature of these variations, future observations are required. Whatever the outcome of such observations, however, both these sets of results point to the very interesting possibility that the variations in the differential rotation can have different periodicities/behaviours at different depths in the solar convection zone. It is therefore important to ask whether such different variations can in principle occur at different parts of the convection zone and, if so, what could be the possible mechanism(s) for their production.
The aim of this letter is to suggest that a natural mechanism for the production of such different dynamical modes of behaviour in the convection zone is through what we call spatiotemporal fragmentation , i.e. the occurrence of dynamical regimes at (given) values of the control parameters of the system, which possess different temporal behaviours at different spatial locations. This is to be contrasted with the usual temporal bifurcations, with identical temporal behaviour at each spatial point, which require changes in parameters to occur.
We find evidence for this mechanism in the context of a two dimensional axisymmetric mean field dynamo model in a spherical shell, with a semi-open outer boundary condition, in which the only nonlinearity is the action of the azimuthal component of the Lorentz force of the dynamo generated magnetic field on the solar angular velocity. The underlying angular velocity is chosen to be consistent with the most recent helioseismic data.
In addition to producing different dynamical variations in the differential rotation, including different periods, at the top and the bottom of the convection zone, this model is also capable of producing butterfly diagrams which are in qualitative agreement with the observations as well as displaying torsional oscillations that penetrate into the convection zone, as recently observed by Howe et al. 2000a and Antia & Basu 2000 and studied by Covas et al. (2000).
© European Southern Observatory (ESO) 2000
Online publication: December 5, 2000