Quantifying the Anisotropy and Solar Cycle Dependence of "$1/f$" Solar Wind Fluctuations Observed by Ace

Abstract

The power spectrum of the evolving solar wind shows evidence of a spectral break between an inertial range of turbulent fluctuations at higher frequencies and a "$1/f$" like region at lower frequencies. In the ecliptic plane at $\sim 1$ AU, this break occurs approximately at timescales of a few hours, and is observed in the power spectra of components of velocity and magnetic field. The "$1/f$" energy range is of more direct coronal origin than the inertial range, and carries signatures of the complex magnetic field structure of the solar corona, and of footpoint stirring in the solar photosphere. To quantify the scaling properties we use generic statistical methods such as generalised structure functions and PDFs, focusing on solar cycle dependence and on anisotropy with respect to the background magnetic field. We present structure function analysis of magnetic and velocity field fluctuations, using a novel technique to decompose the fluctuations into directions parallel and perpendicular to the mean local background magnetic field. Whilst the magnetic field is close to "$1/f$", we show that the velocity field is "$1/f^α$" with $α\neq1$. For the velocity, the value of $α$ varies between parallel and perpendicular fluctuations and with the solar cycle. There is also variation in $α$ with solar wind speed. We have examined the PDFs in the fast, quiet solar wind and intriguingly, whilst parallel and perpendicular are distinct, both the ${\boldmath$B$}$ field and velocity show the same PDF of their perpendicular flucutations, which is close to gamma or inverse Gumbel. These results point to distinct physical processes in the corona, and to their mapping out into the solar wind. The scaling exponents obtained constrain the models for these processes.