Solar radio bursts are typical examples of superpositions of transient phenomena, i.e. the underlying physical processes are non-stationary (Isliker & Kurths 1993). To study the energization and emission processes that cause bursts, data analysis methods are required which can be applied to such non-stationary time series. Promising methods of this kind are the structure function analysis (SFA) and the multiresolution analysis (MRA), whose potential in the investigation of such bursts is discussed here. In particular, the wavelet transform of the MRA permits a local decomposition of the scaling behavior in a time series - in contrast to methods designed to detect global properties, such as the Fourier analysis and the SFA.
Using these methods we look for structural differences between time series of the flux of different sources (bursts, quiet Sun, and sky background) as well as between different phases of the bursts at mm-wavelengths.
Statistical studies of solar energy release events, e.g. the distribution of event number versus energy content as observed at hard X-rays, have led to a description in terms of avalanches in a corona which has stored energy and is in a state of self-organized criticality (Lu & Hamilton 1991). The observed power-law distribution naturally follows from that model. One basic property of this model is that the system under consideration has no characteristic spatial scale above an elementary scale of the smallest avalanche (the smallest energy release event), up to the system size, the size of active regions. This elementary scale, which is a characteristic of the involved plasmaphysical process, is below the current resolution limit, since the power-law distribution extends down to the resolution limit. The success of this approach suggests that the energy release is basically fragmentary, the events being composed of elementary building blocks.
Many attempts have been made to resolve the elementary building blocks of the energy release and possibly also larger characteristic scales from the time profile of the solar flux, particularly in the radio and the hard X-ray ranges. Most of these studies have concentrated on the shortest time scales detectable. For example, Kiplinger et al. (1983) have found fast hard X-ray spikes with duration down to 45 msec and Güdel & Benz (1990) have found similar durations in decimeter radio wavelength spike burst observations. Here we follow a different approach by attempting to resolve a broad range of time scales above 0.5 s present in a flux record of the emission at millimeter wavelengths. Thus, we quantify the general structure of the emission and study its evolution in time, and we are able to investigate whether a hierarchy of dominant time scales is present in the flux profile, as has been discussed previously (Krüger et al. 1987, 1994), or whether the distribution of contributing time scales is more or less structureless, as predicted by the avalanche model. In comparison to hard X-ray data, the choice of this wavelength range has the advantage that the flux profile before and after bursts can also be analyzed and compared with the burst data (since detector or sky noise contributions remain small), and in comparison to the decimetric range the mm-wavelength flux profile is supposed to reflect the energy release process in a more direct manner, less influenced by nonlinear plasma processes which may modulate the radio wave intensity.
The organization of this paper is as follows: In the following section we present the data. In Sect. 3 (click here) we introduce the tools of data analysis: SFA and MRA. The diagnostic capabilities of these tools in the application to the radio burst time profiles are discussed in Sect. 4 (click here). In Sect. 5 (click here), we discuss the physical interpretation of some features of the obtained results, and Sect. 6 (click here) presents the conclusions.