$1/f$ Noise in Synthetic and Solar Wind Data: Superposition Principles

TL;DR

This paper investigates how superposition principles can generate the observed 1/f noise in solar wind magnetic field data, combining synthetic models and long-term spacecraft measurements.

Contribution

It demonstrates that superposition of scale-invariant or lognormal correlation times can produce the 1/f spectral regime observed in solar wind data.

Findings

Synthetic time series with superposed correlation times can replicate 1/f noise.

Decade-long ACE spacecraft data shows persistent 1/f spectral characteristics.

Superposition explains the ubiquity of 1/f noise in heliospheric magnetic fields.

Abstract

The interplanetary magnetic field exhibits a distinctive $1/f$ spectral density from frequencies of around $\unit[10^{-6}]{Hz}$ to around $\unit[10^{-4}]{Hz}$, ranging from harmonics of the solar rotation to the reciprocal of the turbulence correlation time in the spacecraft frame. Various theories have been proposed to explain its origin, typically invoking either processes in the lower corona or in the solar interior, or local interplanetary dynamics. Here, we investigate the {\it superposition principle} that underlies explanations of the solar/coronal types, which in principle can generate the full observed range of $1/f$ noise. Using synthetic time series with scale-invariant or lognormal distributions of correlation times, we examine the efficacy of several superposition approaches in generating a $1/f$ regime. The persistence of $1/f$ spectrum is further illustrated with decade-long {\it in situ} magnetic field measurements from the ACE spacecraft. Together, these results help explain the ubiquity of $1/f$ noise under the unavoidable superposition inherent in long-duration heliospheric data.