The chaotic solar cycle

II. Analysis of cosmogenic ¹⁰Be data

¹ Inst. für Physik, Geophysik Astrophysik und Meteorologie, Univ.-Platz 5, 8010 Graz, Austria
e-mail: arnold.hanslmeier@uni-graz.at
² Hvar Observatory, Faculty of Geodesy, University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia
e-mail: romanb@geof.hr; jcalogovic@geof.hr; bvrsnak@geof.hr; rdomagoj@geof.hr;
³ Eawag, Swiss Federal Institute of Aquatic Science and Technology, Überlandstrasse 133, 8600 Dübendorf, Switzerland
e-mail: friedhelm.steinhilber@eawag.ch
⁴ Department of Astronomy, University of Washington, PO Box 351580, Seattle, WA 98195, USA
e-mail: cmacleod@astro.washington.edu; ivezic@astro.washington.edu
⁵ Department of Physics, University of Zagreb, Bijenička c. 32, PP 331, 10000 Zagreb, Croatia
⁶ Cybrotech Ltd., Bohinjska 11, 10000 Zagreb, Croatia
e-mail: ivica.skokic@cybrotech.hr

Received: 15 June 2010
Accepted: 14 September 2012

Abstract

Context. The variations of solar activity over long time intervals using a solar activity reconstruction based on the cosmogenic radionuclide ¹⁰Be 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 ¹⁴C data with the results obtained using ¹⁰Be 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 ¹⁰Be 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 ¹⁰Be data with the ¹⁴C 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 ¹⁰Be 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.