Testing for nonlinearity and low-dimensional dynamics in the slow solar wind

We focus on nonlinearity and possible deterministic behavior of the low-speed solar wind. We analyze time series of velocities of the streams including Alfvénic fluctuations measured by the Helios spacecraft in the inner heliosphere. Because of nonlinear behavior of that flow we use the average-mutual-information and false-nearest-neighbors methods. The fraction of false-nearest-neighbors drops to zero at dimension equal to four for both the radial velocity and Alfvénic velocity, independent of the distance from the Sun. The question of possible colored noise in the solar wind is also discussed. The obtained results clearly indicate that a low-dimensional attractor should exist. One can therefore hope to infer information about some complex nonlinear phenomena from the geometrical properties of the attractor or by solving a set of four nonlinear ordinary differential equations describing the system. One can expect that the attractor should contain information about the dynamic variations of the coronal streamers or it could represent a structure of the time sequence of near-Sun coronal fine-stream tubes.