Nonparametric and Parametric Methods for Solar Oscillation Spectra
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The study of the systematic oscillations of the Sun has led to better understanding of the Sun’s inner structure and dynamics, and may help to resolve inconsistencies between observations and the standard solar model. Recent studies have concluded that solar modal structure remains coherent past turbulence in the convection zone and imprints its signatures on the solar wind and the interplanetary magnetic field fluctuations, and these structures are coherent with atmospheric pressure variations, terrestrial seismic oscillations, and data from communications systems. Time series containing modal structure can be expected to contain several thousands of resolved and unresolved line components in very short bands in frequency, and the measure- ment of these modes pushes spectrum estimation methods for time series to its limit. This thesis presents two theoretical contributions for modeling solar oscillations in power spectra (i) expressions for the expected number and shape of significant spuri- ous peaks in spectrum estimates are given, in the absence of modal structure, and a permutation test for the identification of spectra containing pathological numbers of modal components. (ii) A model for maximum likelihood estimation of the solar os- cillation parameters in composite spectra is given. The scientific contributions of this thesis are (a) identification of highly significant modal artifacts in solar wind mea- surements as seen by the Advanced Composition Explorer (ACE) on the 2 − 3mHz band and (b) quantification of the presence of modal structure in secondary cosmic rays (specifically neutrons) on Earth.