A&A Supplement series, Vol. 127, January II 1998, 309-318
Received October 28, 1996; accepted May 13, 1997
U. Schwarz 
- J. Kurths -
B. Kliem 
- A. Krüger -
S. Urpo 
Send offprint request: U. Schwarz, USchwarz@agnld.uni-potsdam.de
Institut für Theoretische Physik und Astrophysik, Universität
Potsdam,
Am Neuen Palais, D-14469 Potsdam, Germany
Astrophysical Institute Potsdam, An der Sternwarte 16,
D-14482 Potsdam, Germany
Helsinki University of Technology, Otakaari 5a, SF-02150 Espoo,
Finland
Two methods of multi-scale time series analysis are applied to solar mm-wavelength flux time profiles in order to assess the diagnostic power of these tools for the exploration of nonlinear energy release processes. Both the multiresolution analysis (MRA), a method based on the wavelet transform, and the structure function analysis (SFA) permit the treatment of non-stationary time series. In addition, the MRA offers a local decomposition of the scaling behavior of the flux variations. Our main emphasis is directed at a decomposition of the contributions of the different time scales to the overall flux profile. The methods yield consistent values of the "spectral index" which describes the scalings contained in the time series.
We find that time profiles of bursts are qualitatively analogous to fractional Brownian motion (fBm), possessing long-range temporal correlations. Such correlations are not found in quiet Sun observations.
The MRA of six solar mm-wave bursts shows that the radio flux is always composed of contributions from a broad range of time scales. Also during the main phase of bursts, which appears to be structurally analogous to the pre- and post-burst phases at a resolution limit of 1 s, flux fluctuations are enhanced in a broad range of time scales. This suggests that the mm-wave bursts are composed of unresolved elements, just as the pre- and post-burst time profiles. The underlying energy release thus appears to be fragmentary. These results are discussed in terms of the avalanche model and plasma physical models for solar energy release events.
keywords: Sun: radio radiation -- Sun: flares -- methods: data analysis