Nonlinearity, time delay, and Grand Maxima in supercritical Babcock-Leighton Dynamos

The physical origin of centennial and millennial-scale variations in solar activity remains ill-understood. Although stochastic fluctuations of the solar dynamo are unavoidable in view of the turbulent nature of the solar convection zone, the quasiperiodic long timescale modulations revealed by the cosmogenic radioisotope records are suggestive of a deterministic process. In this paper, we investigate the nonlinear behavior of two solar cycle models based on the Babcock-Leighton mechanism, with particular emphasis on deterministic amplitude modulation patterns materializing in the moderately to strongly supercritical dynamo regimes. Although formulated quite differently, both models show common long timescale modulation patterns arising from the interaction between the time-delay dynamics inherent to these flux transport dynamos, with the threshold non-linearity characterizing the Babcock-Leighton mechanism of poloidal field regeneration. In particular, we demonstrate the existence of multiple co-existing dynamo branches in the supercritical regime, each retaining a finite-sized basin of attraction over a substantial range in dynamo number. Transition from one branch to another is shown to be possible via the introduction of low-amplitude stochastic noise with short coherence time. On this basis, we propose a novel physical scenario potentially accounting for the occurrence of both Grand Minima and Maxima of solar activity.