Probability density functions for the variable solar wind near the solar cycle minimum

TL;DR

This study analyzes magnetic field fluctuations in the solar wind near solar minimum, demonstrating that a limited set of probability distribution functions can effectively model the data's statistical properties across different scales and conditions.

Contribution

It introduces a comprehensive statistical analysis of solar wind magnetic fluctuations using various PDFs, highlighting the effectiveness of skewed log-kappa distributions for turbulent cascade modeling.

Findings

Skewed log-kappa PDFs better fit small-scale turbulent fluctuations.

Minimum data lengths for reliable parameter estimation depend on scale and process.

Conditional and unconditional statistics reveal different fluctuation characteristics.

Abstract

Unconditional and conditional statistics is used for studying the histograms of magnetic field multi-scale fluctuations in the solar wind near the solar cycle minimum in 2008. The unconditional statistics involves the magnetic data during the whole year 2008. The conditional statistics involves the magnetic field time series splitted into concatenated subsets of data according to a threshold in dynamic pressure. The threshold separates fast stream leading edge compressional and trailing edge uncompressional fluctuations. The histograms obtained from these data sets are associated with both large-scale (B) and small-scale ({\delta}B) magnetic fluctuations, the latter corresponding to time-delayed differences. It is shown here that, by keeping flexibility but avoiding the unnecessary redundancy in modeling, the histograms can be effectively described by a limited set of theoretical probability distribution functions (PDFs), such as the normal, log-normal, kappa and logkappa functions. In a statistical sense the model PDFs correspond to additive and multiplicative processes exhibiting correlations. It is demonstrated here that the skewed small-scale histograms inherent in turbulent cascades are better described by the skewed log-kappa than by the symmetric kappa model. Nevertheless, the observed skewness is rather small, resulting in potential difficulties of estimation of the third-order moments. This paper also investigates the dependence of the statistical convergence of PDF model parameters, goodness of fit and skewness on the data sample size. It is shown that the minimum lengths of data intervals required for the robust estimation of parameters is scale, process and model dependent.