| Abstract
| - A dynamic model of dynamo and rotation is investigated to understand the observational data of the dependence of the magnetic activities and the differential rotation ΔΩ on the rotation rate Ω. Specifically, we propose a minimal seventh-order nonlinear dynamical system for magnetic fields and differential rotation ΔΩ by parameterizing the generation and destruction of magnetic fields by α-Ω effect and magnetic flux loss from stars and by including quenching of α-effect and differential rotation ΔΩ due to the Lorentz force. By examining different forms of α-quenching and flux loss, we study how the strength and frequency ω of magnetic fields and the differential rotation ΔΩ change with the rotation rate Ω through dynamo number. In particular, among the three cases with (i) α-quenching and no flux loss; (ii) flux loss and no α-quenching; (iii) α-quenching and flux loss, our results show that the best agreement with observations is obtained in case (iii) with equal amounts of α-quenching and poloidal and toroidal magnetic flux losses with quadratic nonlinear dependence on | B|. Specifically, in this case, the frequency spectrum of the magnetic field has a well-localized frequency of the maximum intensity which scales as ω ∝ Ω 0.80, in agreement with a previous observation. The magnetic field and mean differential rotation exhibit the tendency of saturation for high rotation. The implication of our results in light of necessary dynamic balance is discussed.
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