Turbulent and Chaotic Dynamics Underlying Solar Magnetic Variability

We examine the temporal scaling properties of solar magnetic activity on timescales from days to decades. Because of more than 63,000 usable data points, we concentrate on the daily International Sunspot Number. Some results have been checked with other data sets, primarily the 10.7 cm microwave flux with about 16,000 data points. Such time series provide a measure whose scaling and intermittency properties are analyzed.

By means of correlation analysis and both Fourier and wavelet spectral analysis, we distinguish two regimes of temporal behavior of the magnetic variability. The scaling of the time series is analyzed in terms of multiplicative cascade processes which prove to be invariant over more than two decades of scale from about 2 yr down to about 2 days or less. We interpret this result to indicate generic turbulent structuring of the magnetic fields as they rise through the convection zone. We find that a low-dimensional, chaotic behavior in the sunspot number operates entirely at timescales longer than a transition threshold scale of about 8 yr. Magnetic variability on timescales between 2 yr and 8 yr apparently requires handling by direct simulation.