Nonlinear time series analysis of solar and stellar data

Date of Completion

January 2003


Physics, Astronomy and Astrophysics




Nonlinear time series analysis was developed to study chaotic systems. Its utility was investigated for the study of solar and stellar data time series. Sunspot data are the longest astronomical time series, and it reflects the long-term variation of the solar magnetic field. Due to periods of low solar activity, such as the Maunder minimum, and the solar cycle's quasiperiodicity, it has been postulated that the solar dynamo is a chaotic system. We show that, due to the definition of sunspot number, using nonlinear time series methods, it is not possible to test this postulate. To complement the sunspot data analysis, theoretically generated data for the α-Ω solar dynamo with meridional circulation were analyzed. Effects of stochastic fluctuations on the energy of an α-Ω dynamo with meridional circulation were investigated. This proved extremely useful in generating a clearer understanding of the effect of dynamical noise on the unperturbed system. This was useful in the study of the light intensity curve of white dwarf PG 1351+489. Dynamical resetting was identified for PG 1351+489, using phase space methods, and then, using nonlinear noise reduction methods, the white noise tail of the power spectrum was lowered by a factor of 40. This allowed the identification of 10 new lines in the power spectrum. Finally, using Poincare section return times, a periodicity in the light curve of cataclysmic variable SS Cygni was identified. We initially expected that time delay methods would be useful as a qualitative comparison tool. However, they were capable, under the proper set of constraints on the data sets, of providing quantitative information about the signal source. ^