Stochastic Fluctuations in a Babcock‐Leighton Model of the Solar Cycle

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Abstract
We investigate the effect of stochastic fluctuations on a flux transport model of the solar cycle based on the Babcock-Leighton mechanism. Specifically, we make use of our recent flux transport model (Dikpati & Charbonneau) to investigate the consequences of introducing large-amplitude stochastic fluctuations in either or both the meridional flow and poloidal source term in the model. Solar cycle-like oscillatory behavior persists even for fluctuation amplitudes as high as 300%, thus demonstrating the inherent robustness of this class of solar cycle models. We also find that high-amplitude fluctuations lead to a spread of cycle amplitude and duration showing a statistically significant anticorrelation, comparable to that observed in sunspot data. This is a feature of the solar cycle that is notoriously difficult to reproduce with dynamo models based on mean field electrodynamics and relying only on nonlinearities associated with the back-reaction of the Lorentz force to produce amplitude modulation. Another noteworthy aspect of our flux transport model is the fact that meridional circulation in the convective envelope acts as a "clock" regulating the tempo of the solar cycle; shorter-than-average cycles are typically soon followed by longer-than-average cycles. In other words, the oscillation exhibits good phase locking, a property that also characterizes the solar activity cycle. This shows up quite clearly in our model, but we argue that it is in fact a generic property of flux transport models based on the Babcock-Leighton mechanism, and relies on meridional circulation as the primary magnetic field transport agent.