A Nonextensive Entropy Approach to Solar Wind Intermittency

The probability distributions (PDFs) of the differences of any physicalvariable in the intermittent, turbulent interplanetary medium are scaledependent. Strong non-Gaussianity of solar wind fluctuations applies for shorttime-lag spacecraft observations, corresponding to small-scale spatialseparations, whereas for large scales the differences turn into a Gaussiannormal distribution. These characteristics were hitherto described in thecontext of the log-normal, the Castaing distribution or the shell model. On theother hand, a possible explanation for nonlocality in turbulence is offeredwithin the context of nonextensive entropy generalization by a recentlyintroduced bi-kappa distribution, generating through a convolution of anegative-kappa core and positive-kappa halo pronounced non-Gaussian structures.The PDFs of solar wind scalar field differences are computed from WIND and ACEdata for different time lags and compared with the characteristics of thetheoretical bi-kappa functional, well representing the overall scale dependenceof the spatial solar wind intermittency. The observed PDF characteristics forincreased spatial scales are manifest in the theoretical distributionfunctional by enhancing the only tuning parameter $\kappa$, measuring thedegree of nonextensivity where the large-scale Gaussian is approached for$\kappa \to \infty$. The nonextensive approach assures for experimental studiesof solar wind intermittency independence from influence of a priori modelassumptions. It is argued that the intermittency of the turbulent fluctuationsshould be related physically to the nonextensive character of theinterplanetary medium counting for nonlocal interactions via the entropygeneralization.Comment: 17 pages, 7 figures, accepted for publication in Astrophys.