Determination of fractal dimensions of solar radio bursts

We present a dimension analysis of a set of solar type I storms and type IV events with different kind of fine structures, recorded at the Trieste Astronomical Observatory. The signature of such types of solar radio events is highly structured in time. However, periodicities are rather seldom, and linear mode theory can provide only limited interpretation of the data. Therefore, we performed an analysis based on methods of the nonlinear dynamics theory. Additionally to the commonly used correlation dimension, we also calculated local pointwise dimensions. This alternative approach is motivated by the fact that astrophysical time series represent real-world systems, which cannot be kept in a controlled state and which are highly interconnected with their surroundings. In such systems pure determinism is rather unlikely to be realized, and therefore a characterization by invariants of the dynamics might probably be inadequate. In fact, the outcome of the dimension analysis does not give hints for low-dimensional determinism in the data, but we show that, contrary to the correlation dimension method, local dimension estimations can give physical insight into the events even in cases in which pure determinism cannot be established. In particular, in most of the analyzed radio events nonlinearity in the data is detected, and the local dimension analysis provides a basis for a quantitative description of the time series, which can be used to characterize the complexity of the related physical system in a comparative and non-invariant manner. In this frame, the degree of complexity we inferred for type I storms is on the average lower than that relevant to type IV events. For the type IV events significant differences occur with regard to the various subtypes, where pulsations and sudden reductions can be described by distinctly lower values than spikes and fast pulsations.