Randomly Modulated Periodicities in Relative Sunspot Numbers
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This paper presents a new spectral approach to the study of the periodic variation of relative sunspot cycles and the extent of the randomness in the amplitudes and phases of the harmonic components of the fundamental frequency of the cycles. The new method is called the signal coherence spectrum of a time series that has a randomly modulated periodicity. The data we use is the relative sunspot numbers beginning December 21, 1838 until June 30, 2008 as compiled by the Solar Influences Data Analysis Center (SIDC) at the Royal Observatory of Belgium using the FORTRAN 95 program developed by Hinich (2000). Deterministic sinusoids are often used to model cycles as a mathematical convenience. However, it is time to break away from this simplification in order to model the various periodic signals that are observed in fields ranging from biology, communications, acoustics, astronomy, and the various sciences. We detect a strong coherence at 3966 days (10.86 years) which is consistent with the reported 11-year sunspot cycle. Additionally, we find strongly coherent harmonics at about 20 days (0.8 coherence), 2.75 days (0.87 coherence), and 2.1 days (0.83 coherence). We have no physical explanation for the randomly modulated periodicities in relative sunspot numbers.