Fluctuations in Babcock-Leighton dynamos. I. Period doubling and transition to chaos

We present a large series of numerical simulations of the solar magnetic activity cycle based on the Babcock-Leighton mechanism for the regeneration of the solar poloidal magnetic field. While the primary cycle period changes very little as the dynamo number is increased, the model shows a well-defined transition to chaos through a sequence of period-doubling bifurcations, i.e., the sequential appearance of modulations of the primary cycle's amplitude, with associated periods equal to twice the periods characterizing the amplitude variations prior to a given bifurcation. This behavior arises through the unavoidable time delay built into this type of solar dynamo model, rather than through the effects of complex, nonlinear magnetic back-reaction on the fluid motions driving the dynamo process. It is noteworthy that a chaotic regime exists in this numerical model, given that the only non-linearity present is a simple algebraic amplitude-quenching factor in one of the governing partial differential equations. The results also represent a rare instance in which the complex dynamical behavior of a spatially extended, diffusive solar dynamo model can be reproduced in detail on the basis of the simplest of low-order dynamical systems, namely a one-dimensional iterative map. The numerical results also demonstrate the central role of meridional circulation in setting the primary cycle period in this class of dynamo models; despite variations by many orders of magnitude in the dynamo number and concomitant large and sometimes even chaotic variations in amplitude, the cycle period remains tightly locked to the meridional circulation turnover time.