Abstract
We present a new technique suitable for a detailed comparison between solar dynamo models and observations. The method is based on the technique of dynamo spectroscopy proposed by Hoyng & Schutgens (1995) and bi-orthogonal decomposition of solar data. This decomposition provides a representation of the mean and fluctuating components of the flows, yielding relevant information for the comparison. To illustrate the method, we use a simple kinematic dynamo model of the solar cycle. Irregularities are introduced in the evolution of the magnetic fields modeling the turbulent behavior of the solar convective region with a random perturbation on the external source for the poloidal field. After fine tuning the parameters of the model we obtain solar like solutions displaying a magnetic cycle of 22 years, with fluctuations in its period and amplitude. In addition, the model generates Maunder-like events with a time span of 60−100 years.
Highlights
Since the pioneering papers by Parker (1955), Babcock (1961) and Leighton (1969), our understanding of the solar dynamo has increased considerably (Dikpati & Charbonneau 1999; Nandy & Choudhuri 2002)
A bi-orthogonal decomposition (BOD) of the temporal and latitudinal distribution of solar magnetic fields inferred from sunspots since 1874 showed that the butterfly diagram can be interpreted as the result of two oscillations with approximately constant amplitudes and phase shift (Fig. 5c), both with periods close to 22 years (Mininni et al 2002b)
When we apply the BOD to the toroidal magnetic field given by our unperturbed model, 100% of the energy goes into the asymmetric modes, and the first two modes comprise more than 96% of the total energy
Summary
Since the pioneering papers by Parker (1955) (proposing the first theoretical mechanism for sunspot formation), Babcock (1961) (a qualitative model of the solar cycle) and Leighton (1969) (the first numerical simulation based on Babcock’s scenario), our understanding of the solar dynamo has increased considerably (Dikpati & Charbonneau 1999; Nandy & Choudhuri 2002). The sunspot data contain a large amount of information concerning the shape and dynamics of the spatial distribution of magnetic activity, which is not considered for the validation of the models This problem turns out to be quite relevant, since many of the observed features of the solar cycle can be reproduced either with chaotic or stochastic paradigms. We want to point out that we are not proposing this simplified model as a physical description of the solar dynamo, but rather as a paradigmatic example in which the power of spectral comparison can be appreciated In this context, a study of the effect of stochastic force in 2D models in one hemisphere with moderately long runs was carried out recently by Charbonneau & Dikpati (2000).
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