Abstract
We present a non-kinematic axisymetric α2Ω mean-field dynamo model in which the complete α-tensor and mean differential rotation profile are both extracted from a global magnetohydrodynamical simulation of solar convection producing cycling large-scale magnetic fields. The nonlinear backreaction of the Lorentz force on differential rotation is the only amplitude-limiting mechanism introduced in the mean-field model. We compare and contrast the amplitude modulation patterns characterizing this mean-field dynamo, to those already well-studied in the context of non-kinematic αΩ models using a scalar α-effect. As in the latter, we find that large quasi-periodic modulation of the primary cycle are produced at low magnetic Prandtl number (Pm), with the ratio of modulation period to the primary cycle period scaling inversely with Pm. The variations of differential rotation remain well within the bounds set by observed solar torsional oscillations. In this low-Pm regime, moderately supercritical solutions can also exhibit aperiodic Maunder Minimum-like periods of strongly reduced cycle amplitude. The inter-event waiting time distribution is approximately exponential, in agreement with solar activity reconstructions based on cosmogenic radioisotopes. Secular variations in low-latitude surface differential rotation during Grand Minima, as compared to epochs of normal cyclic behavior, are commensurate in amplitude with historical inferences based on sunspot drawings. Our modeling results suggest that the low levels of observed variations in the solar differential rotation in the course of the activity cycle may nonetheless contribute to, or perhaps even dominate, the regulation of the magnetic cycle amplitude.
Highlights
The past decade has witnessed remarkable progress in the design of global magnetohydrodynamical (MHD) simulations of solar convection and dynamo action
Following Tobias (1996), we circumvent the specification of Reynolds stresses by separating the angular velocity into a temporally steady component X(r, h), and a time-dependent contribution X0(r, h, hBi(r, h, t)) driven by the Lorentz force: Xtðr; h; tÞ 1⁄4 Xðr; hÞ þ X0ðr; h; hBiðr; h; tÞÞ: ð8Þ. Underlying this separation is the implicit assumption that the Reynolds stresses powering the steady part of the differential rotation remain unaffected by the large-scale magnetic field produced by the dynamo, so that X represents a stationary solution of the unmagnetized momentum equation
We have developed a non-kinematic axisymmetric meanfield dynamo model of the a2X variety, i.e., a mean field model in which both the turbulent electromotive force and shearing by differential rotation contribute to the induction of the toroidal magnetic component
Summary
The past decade has witnessed remarkable progress in the design of global magnetohydrodynamical (MHD) simulations of solar convection and dynamo action. Studied far in the a2X context is the dynamical backreaction of the large-scale magnetic field produced by dynamo action on the large-scale inductive flows, the differential rotation This so-called Malkus-Proctor mechanism (Malkus & Proctor, 1975) has received a lot of attention in the context of aX models, as it has been shown capable to produce long timescale modulation of the primary cycle, including recurrent epochs of very low cycle amplitudes, reminiscent of Maunder Minimum-like episodes of suppressed surface magnetic activity (Tobias, 1996, 1997; Küker et al, 1999; Brooke et al, 2002; Bushby, 2006).
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