A Nonextensive Entropy Approach to Solar Wind Intermittency

The probability distribution functions (PDFs) of the differences of any physical variable in the intermittent, turbulent interplanetary medium are scale dependent. Strong non-Gaussianity of solar wind fluctuations applies for short time lag spacecraft observations, corresponding to small-scale spatial separations, whereas for large scales the differences turn into a Gaussian normal distribution. These characteristics were hitherto described in the context of the lognormal, the Castaing distribution, or the shell model. On the other hand, a possible explanation for nonlocality in turbulence is offered within the context of nonextensive entropy generalization by a recently introduced bi-kappa distribution, generating through a convolution of a negative-kappa core and positive-kappa halo pronounced non-Gaussian structures. The PDFs of solar wind scalar field differences are computed from Wind and ACE data for different time lags and compared with the characteristics of the theoretical bi-kappa functional, well representing the overall scale dependence of the spatial solar wind intermittency. The observed PDF characteristics for increased spatial scales are manifest in the theoretical distribution functional by enhancing the only tuning parameter κ, measuring the degree of nonextensivity where the large-scale Gaussian is approached for κ → ∞. The nonextensive approach assures for experimental studies of solar wind intermittency independence from influence of a priori model assumptions. It is argued that the intermittency of the turbulent fluctuations should be related physically to the nonextensive character of the interplanetary medium counting for nonlocal interactions via the entropy generalization.