Low-order stellar dynamo models

Stellar magnetic activity – which has been observed in a diverse set of stars including the Sun – originates via a magnetohydrodynamic dynamo mechanism working in stellar interiors. The full set of magnetohydrodynamic equations governing stellar dynamos is highly complex, and so direct numerical simulation is currently out of reach computationally. An understanding of the bifurcation structure, likely to be found in the partial differential equations governing such dynamos, is vital if we are to understand the activity of solar-like stars and its evolution with varying stellar parameters such as rotation rate. Low-order models are an important aid to this understanding, and can be derived either as approximations of the governing equations themselves or by using bifurcation theory to obtain systems with the desired structure. We use normal-form theory to derive a third-order model with robust behaviour. The model is able to reproduce many of the basic types of behaviour found in observations of solar-type stars. In the appropriate parameter regime, a chaotic modulation of the basic cycle is present, together with varying periods of low activity such as that observed during the solar Maunder minima.