Markovian Features of the Solar Wind at Sub-Proton Scales

TL;DR

This study investigates magnetic field fluctuations in the solar wind at sub-proton scales, demonstrating they follow a Markov process and exhibit scale-invariant probability distributions, shedding light on turbulence at small scales.

Contribution

It introduces a Markovian framework for analyzing sub-proton scale fluctuations and models their PDFs with a Fokker-Planck equation, revealing scale invariance.

Findings

Fluctuations are well described as a Markov process.

PDFs are scale-invariant and match Fokker-Planck stationary solutions.

Results connect small-scale turbulence properties with Markovian dynamics.

Abstract

The interplanetary magnetic field carried out from the Sun by the solar wind displays fluctuations on a wide range of scales. While at large scales, say at frequencies lower than 0.1-1 Hz, fluctuations display clear universal characteristics of fully developed turbulence with a well defined Kolmogorov's like inertial range, the physical and dynamical properties of the small-scale regime as well as their connection with the large-scale ones are still a debated topic. In this work we investigate the near-Sun magnetic field fluctuations at sub-proton scales by analyzing the Markov property of fluctuations and recovering basic information about the nature of the energy transfer across different scales. By evaluating the Kramers-Moyal coefficients we find that fluctuations in the sub-proton range are well described as a Markovian process with Probability Density Functions (PDFs) modeled via a Fokker-Planck (FP) equation. Furthermore, we show that the shape of the PDFs is globally scale-invariant and similar to the one recovered for the stationary solution of the FP equation at different scales. The relevance of our results on the Markovian character of sub-proton scale fluctuations is also discussed in connection with the occurrence of turbulence in this domain.