Estimating intermittency significance by means of surrogate data: implications for solar wind turbulence

Abstract

Introduction: Intermittency is a property of turbulent astrophysical plasmas, such as the solar wind, that implies irregularity and fragmentation, leading to non-uniformity in the transfer rate of energy carried by nonlinear structures from large to small scales. We evaluated the intermittency level of the turbulent magnetic field measured by the Parker Solar Probe (PSP) in the slow solar wind in the proximity of the Sun during the probe’s first close encounter.Methods: A quantitative measure of intermittency could be deduced from the normalized fourth-order moment of the probability distribution functions, the flatness parameter. We calculated the flatness of the magnetic field data collected by the PSP between 1 and 9 November 2018. We observed that when dividing the data into contiguous time intervals of various lengths, ranging from 3 to 24 hours, the flatness computed for individual intervals differed significantly, suggesting a variation in intermittency from “quieter” to more intermittent intervals. In order to quantify this variability, we applied an elaborate statistical test tailored to identify nonlinear dynamics in a time series. Our approach is based on evaluating the flatness of a set of surrogate data built from the original PSP data in such a way that all nonlinear correlations contained in the dynamics of the signal are eliminated. Nevertheless, the surrogate data are otherwise consistent with the “underlying” linear process, i.e., the null hypothesis that we want to falsify. If a discriminating statistic for the original signal, such as the flatness parameter, is found to be significantly different from that of the ensemble of surrogates, then the null hypothesis is not valid, and we can conclude that the computed flatness reliably reflects the intermittency level of the underlying nonlinear processes.Results and discussion: We determined that the non-stationarity of the time series strongly influences the flatness of both the data and the surrogates and that the null hypothesis cannot be falsified. A global fit of the structure functions revealed a decrease in flatness at scales smaller than a few seconds: intermittency is reduced in this scale range. This behavior was mirrored by the spectral analysis, which was suggestive of an acceleration of the energy cascade at the high-frequency end of the inertial regime.