Nonlinear dynamics and intermittency of the solar wind magnetic field fluctuations probed with surrogate data

We present a statistical approach to estimate the significance of the intermittency of solar wind magnetic field fluctuations. We analyze nine days of magnetic field data provided by Parker Solar Probe (PSP) at about 0.17 AU from the Sun during the probe’s first perihelion (Encounter 1). Intermittency is estimated based on flatness, the normalized fourth-order moment of the probability distribution functions. When we divide the signal in sub-intervals of 3 to 24 hours length, we find that flatness/intermittency varies from interval to interval. Sub-intervals showing very low levels of intermittency, with flatness values close to three at all scales, alternated with highly intermittent sub-intervals where flatness reaches values close to 60.

In order to understand the observed variability of the intermittency level, we applied a statistical test based on data surrogates (Theiler et al., 1992) tailored to identify nonlinear dynamics in a time series. The aim is to falsify a null hypothesis that is a-priori known to be invalid, i.e. the intermittency observed in PSP data results from a linear Gaussian-like physical process, with the nonlinearity being due to the observation function.

The surrogates are generated such that all nonlinear correlations contained in the dynamics of the signal are eliminated. We find that the flatness computed for the original signal is significantly different from that computed for the ensemble of surrogates, i.e. the null hypothesis is falsified. Thus, the flatness is indeed a descriptor of the intermittency resulting from the inherent nonlinear dynamics of the process captured by the magnetic field observations of the PSP. We also discuss how the non-stationarity of a time series affects the flatness computed for both the PSP data and the surrogates, precluding the null hypothesis is falsified.

Further, a multi-order simultaneous 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.