A Time Delay Model for Solar and Stellar Dynamos

Magnetohydrodynamic dynamos operating in stellar interiors produce the diverse range of magnetic activity ob- served in solar-like stars. Sophisticated dynamo models including realistic physics of convection zone flows and flux tube dynamics have been built for the Sun, for which appropriate observations exist to constrain such models. Nevertheless,significantdifferencesexistinthephysicsthatthemodelsinvoke,themostimportantbeingthenature and location of the dynamo -effect and whether it is spatially segregated from the location of the -effect. Spatial segregation of these source layers necessitates a physical mechanism for communication between them, involving unavoidable time delays. We construct a physically motivated reduced dynamo model in which, through the use of time delays, we mimic the generation of field components in spatially segregated layers and the communication between them. The model can be adapted to examine the underlying structures of more complicated and spatially extended numerical dynamo models with diverse -effect mechanisms. Avariety of dynamic behaviors arise as a direct consequence of the introduction of time delays in the system. Various parameter regimes give rise to periodic andaperiodicoscillations.Amplitudemodulationleadstoepisodesofreducedactivity,suchasthatobservedduring the Maunder minima, the length and duration of which depend on the dynamo number. Regular activity is more easily excited in the fl ux transportYdominated regime (when the time delay is smaller than the dissipative time- scale), whereas irregular activity characterizes solutions in the diffusion-dominated regime (when the time delay is larger than the dissipative timescale).