Tsallis distributions of magnetic field strength variations in the heliosphere: 5 to 90 AU

Abstract

The Tsallis (q‐exponential) distribution function, derived from the entropy principle of nonextensive statistical mechanics, describes fluctuations in the magnetic field strength on many scales throughout the heliosphere. This paper shows that a one‐dimensional multifluid magnetohydrodynamic (MHD) model, with Advanced Composition Explorer (ACE) observations at 1 AU as input, predicts Tsallis distributions between 5 and 90 AU on scales from 1 to 128 days. At a scale of 1 day, the radial variation of the entropic indexqdecreases fromq≥ 5/3 atR≤ 50 AU toq≤ 5/3 atR≥ 60 AU, corresponding to a change from a divergent to a convergent second moment of the Tsallis distribution, suggesting the possibility of a “phase transition” and/or a relaxation effect at ≈60 AU. The Tsallis distribution derived from the time series of one‐dimensional MHD model is nearly identical to those observed by Voyager 1 at ∼80 AU over the scales from 1 to 64 days during the year 2000. The Tsallis distribution appears over a wide range of scales and distances despite the complex nonlinear dynamical evolution of the heliospheric magnetic field during 1999/2000.