Excerpt from Sunspot Cycle Simulation Using a Narrowband Gaussian Process

Since the discovery of the cyclic behavior of sunspots by Schwabe in 1843, many authors have referred to the sunspot record as an example of naturally occurring periodic behavior not easily explained by the dynamics of rotating systems. Yule [1] characterized the sunspot numbers as a disturbed harmonic function, which he likened to the motion of a pendulum that boys are pelting with peas. Time series analysis texts [2] and statistical works [3] commonly cite the sunspot number series as a function that is more or less periodic. The noisy, but nearly periodic, character of the sunspot record suggests a very simple model of solar activity that simulates the observed Sunspot numbers to a surprising degree. The observed annual mean sunspot numbers [4] and simulated annual mean sunspot numbers (produced using methods described in this paper) are shown in figure 1.

Our model, in its simplest form, is the squared output of a narrowband filter driven by white Gaussian noise. If elaborate filtering schemes are used, it is possible to mimic the stochastic properties of agy existing signal. In other words, given sufficient resources, it is possible to mimic almost any existing signal. Suppose, on the other hand, a white noise signal (perhaps the simplest of signals) is filtered by a simple narrowband filter and the squared output signal resembles a com plicated existing signal in all its gross characteristics does this not compel one to give serious consideration to the physical implications of the stochastic process?

We see no reason to be uncomfortable with the suggestion that some Gaussian-noise process may be at work in the interior of the Sun. White Gaussian-noise is common in the Universe at all levels from the microscopic to the macroscopic; whether we consider the noise produced in thermionic emission in an electron tube or the noise received from some distant radio galaxy. By the same token, it is not discomforting to consider that the Sun might have resonant modes which act as filters. Many of the physical objects in our everyday lives exhibit the properties of filters. That is, they respond to certain modes of excitation and they are to a greater or lesser extent resonators. Is it not natural then to expect that the massive solar body with great mechanical, thermal and gravitational forces at work has its own natural modes of response that cause it to behave as a filter? Indeed, calculations of the solar thermal diffusion constant [5] indicate that where solar luminosity is concerned, the Sun does act like a low pass filter.

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