Tsallis Distributions and the q-Triplet of the Magnetic Field in the Heliosheath

Abstract:

The Tsallis distribution (which is proportional to the q-exponential function and is related to the κ-distribution) was derived from an entropy function, inspired by multifractals, which gives a generalization of Boltzmann-Gibbs statistical mechanics. A Tsallis distribution describes the distribution of increments of daily averages of the magnetic field strength B observed by Voyager 2 (V2) in the heliosheath during 2010 in association with exceptionally low solar activity. A parameter q derived from this distribution is q_stat = 1.75. The correlation function of B(t) is a power law on scales from 1 to 16 days, and from the exponent one obtains the parameter q_rel = 3.9. The fluctuations of B are described by a multifractal spectrum f(α) on scales from 1 to 8 days, from which one obtains q_sen = 1.75. The “q-triplet” (q_sen, q_rel, q_stat) defines basic observable properties of an open, driven system in a meta-equilibrium state, which strongly constrains physical models of the system. The distribution of B is Gaussian, probably related to the unipolar region in which V2 was located. A 1/f spectrum of B was observed on scales from 1 to 100 days. The Tsallis distribution also describes the “turbulence” observed on very small scales, from 48 sec to several hours, observed by V2 behind the termination shock from day 245 - 301, 2007.