Simple model of a stochastically excited solar dynamo

The aim of this paper is to investigate the dynamical nature of the complexity observed in the time evolution of the sunspot number. We report a detailed analysis of the sunspot number time series, and use the daily records to build the phase space of the underlying dynamical system. The observed features of the phase space prompted us to describe the global behavior of the solar cycle in terms of a noise-driven relaxation oscillator. We find the equations whose solutions best fit the observed series, which adequately describe the shape of the peaks and the oscillations of the system. The system of equations obtained from this fitting procedure is shown to be equivalent to a truncation of the dynamo equations. A linear transformation maps the phase space of these equations into the phase space reconstructed from the observations. The irregularities of the solar cycle were modeled through the introduction of a stochastic parameter in the equations to simulate the randomness arising in the process of eruption of magnetic flow to the solar surface. The mean values and deviations obtained for the periods, rise times and peak values, are in good agreement with the values obtained from the sunspot time series.