The chaotic solar cycle - II. Analysis of cosmogenic 10Be data

Context. The variations of solar activity over long time intervals using a solar activity reconstruction based on the cosmogenic radionuclide 10 Be measured in polar ice cores are studied.Aims. The periodicity of the solar activity cycle is studied. The solar activity cycle is governed by a complex dynamo mechanism. Methods of nonlinear dynamics enable us to learn more about the regular and chaotic behavior of solar activity. In this work we compare our earlier findings based on 14 C data with the results obtained using 10 Be data.Methods. By applying methods of nonlinear dynamics, the solar activity cycle is studied using solar activity proxies that have been reaching into the past for over 9300 years. The complexity of the system is expressed by several parameters of nonlinear dynamics, such as embedding dimension or false nearest neighbors, and the method of delay coordinates is applied to the time series. We also fit a damped random walk model, which accurately describes the variability of quasars, to the solar 10 Be data and investigate the corresponding power spectral distribution. The periods in the data series were searched by the Fourier and wavelet analyses.Results. The solar activity on the long-term scale is found to be on the edge of chaotic behavior. This can explain the observed intermittent period of longer lasting solar activity minima. Filtering the data by eliminating variations below a certain period (the periods of 380 yr and 57 yr were used) yields a far more regular behavior of solar activity. A comparison between the results for the 10 Be data with the 14 C data shows many similarities. Both cosmogenic isotopes are strongly correlated mutually and with solar activity. Finally, we find that a series of damped random walk models provides a good fit to the 10 Be data with a fixed characteristic time scale of 1000 years, which is roughly consistent with the quasi-periods found by the Fourier and wavelet analyses. Conclusions. The time series of solar activity proxies used here clearly shows that solar activity behaves differently from random data. The unfiltered data exhibit a complex dynamics that becomes more regular when filtering the data. The results indicate that solar activity proxies are also influenced by other than solar variations and reflect solar activity only on longer time scales.

[1]  P. R. Wilson.  Solar and stellar activity cycles , 1994 .

[2]  Brandon C. Kelly,et al.  Are the Variations in Quasar Optical Flux Driven by Thermal Fluctuations , 2009 .

[3]  J. Zirker.  The Magnetic Universe , 2009 .

[4]  N. Sheeley,et al.  The rotation of photospheric magnetic fields: A random walk transport model , 1994 .

[5]  Press,et al.  Class of fast methods for processing irregularly sampled or otherwise inhomogeneous one-dimensional data. , 1995, Physical review letters.

[6]  Christophe Letellier,et al.  The Symmetry of Chaos , 2007 .

[7]  T. Schreiber.  Interdisciplinary application of nonlinear time series methods , 1998, chao-dyn/9807001.

[8]  E. Spiegel.  Chaos and Intermittency in the Solar Cycle , 2009 .

[9]  R. Braǰsa,et al.  On the 24-day period observed in solar flare occurrence , 2004 .

[10]  R. Leighton.  Transport of Magnetic Fields on the Sun. , 1964 .

[11]  Usa,et al.  QUANTIFYING QUASAR VARIABILITY AS PART OF A GENERAL APPROACH TO CLASSIFYING CONTINUOUSLY VARYING SOURCES , 2009, 0909.1326.

[12]  C. Fröhlich,et al.  Total solar irradiance during the Holocene , 2009 .

[13]  A. Wolfendale,et al.  Secular solar and geomagnetic variations in the last 10,000 years. Proceedings at the NATO Advanced Research Workshop, held at Durham, England, 6 - 10 April 1987. , 1988 .

[14]  M. Ossendrijver,et al.  The solar dynamo , 2003 .

[15]  W. Press,et al.  Interpolation, realization, and reconstruction of noisy, irregularly sampled data , 1992 .

[16]  J. Beer,et al.  Large variations in Holocene solar activity: Constraints from 10Be in the Greenland Ice Core Project ice core , 2006 .

[17]  P. Hoyng.  Mean Field Dynamo Theory , 1992 .

[18]  Oded Regev,et al.  Chaos and complexity in astrophysics , 2007, 0705.2251.

[19]  L. Ma.  Thousand-Year Cycle Signals in Solar Activity , 2007 .

[20]  M. Schüssler,et al.  Theoretical Models of Solar Magnetic Variability , 2004 .

[21]  S. Solanki,et al.  Unusual activity of the Sun during recent decades compared to the previous 11,000 years , 2004, Nature.

[22]  Manfred Morari,et al.  False-nearest-neighbors algorithm and noise-corrupted time series , 1997 .

[23]  C. Torrence,et al.  A Practical Guide to Wavelet Analysis. , 1998 .

[24]  T. Deeming.  Fourier analysis with unequally-spaced data , 1975 .

[25]  A. Kosovichev,et al.  Application of Data Assimilation Method for Predicting Solar Cycles , 2008 .

[26]  S. Solanki,et al.  On the common solar signal in different cosmogenic isotope data sets , 2009 .

[27]  Stefano Sello,et al.  Solar cycle forecasting: A nonlinear dynamics approach , 2001 .

[28]  D. Sokoloff,et al.  Solar Grand Minima and Random Fluctuations in Dynamo Parameters , 2008, 0806.3331.

[29]  A. Ruzmaikin,et al.  Radiocarbon evidence of the global stochasticity of solar activity , 1990 .

[30]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[31]  K. Mccracken.  Geomagnetic and atmospheric effects upon the cosmogenic 10Be observed in polar ice , 2004 .

[32]  William H. Press,et al.  The Time Delay of Gravitational Lens 0957+561. I. Methodology and Analysis of Optical Photometric Data , 1992 .

[33]  J. Beer,et al.  Interplanetary magnetic field during the past 9300 years inferred from cosmogenic radionuclides , 2010 .

[34]  L. Mestel.  Stellar magnetism , 1999 .

[35]  C. Schrijver,et al.  Dispersal of Magnetic Flux in the Quiet Solar Photosphere , 1999 .

[36]  L. A. Aguirre,et al.  Forecasting the Time Series of Sunspot Numbers , 2008 .

[37]  J. Beer.  Long-term indirect indices of solar variability , 2000 .

[38]  N. Sheeley,et al.  The origin of rigidly rotating magnetic field patterns on the sun , 1987 .

[39]  L. D. Meeker,et al.  Major features and forcing of high‐latitude northern hemisphere atmospheric circulation using a 110,000‐year‐long glaciochemical series , 1997 .

[40]  E. Bullock,et al.  MODELING THE TIME VARIABILITY OF SDSS STRIPE 82 QUASARS AS A DAMPED RANDOM WALK , 2010, 1004.0276.

[41]  J. Schmelz,et al.  The sun : a laboratory for astrophysics , 1992 .

[42]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .