Dependence of solar wind power spectra on the direction of the local mean magnetic field

(Abridged) Wavelet analysis can be used to measure the power spectrum of solar wind fluctuations along a line in any direction with respect to the local mean magnetic field. This technique is applied to study solar wind turbulence in high-speed streams in the ecliptic plane near solar minimum using magnetic field measurements with a cadence of eight vectors per second. The analysis of nine high-speed streams shows that the reduced spectrum of magnetic field fluctuations (trace power) is approximately azimuthally symmetric about B_0 in both the inertial range and dissipation range; in the inertial range the spectra are characterized by a power-law exponent that changes continuously from 1.6 \pm 0.1 in the direction perpendicular to the mean field to 2.0 \pm 0.1 in the direction parallel to the mean field. The large uncertainties suggest that the perpendicular power-law indices 3/2 and 5/3 are both consistent with the data. The results are similar to those found by Horbury et al. (2008) at high heliographic latitudes.

💡 Research Summary

The paper presents a detailed investigation of the directional dependence of solar‑wind magnetic‑field power spectra using a wavelet‑based technique that allows the reduced spectrum to be measured along any line relative to the local mean magnetic field B₀. High‑resolution magnetic‑field data (8 vectors s⁻¹) from nine high‑speed streams observed near the ecliptic plane during solar minimum were analyzed. For each time point the authors compute a local mean field, determine its polar angle θ with respect to the fluctuation vector, and construct a trace‑power spectrum conditioned on θ. This approach circumvents the isotropizing effect of traditional Fourier methods and directly captures anisotropic features of the turbulence.

The results show two robust properties. First, both the inertial range (≈0.1–1 Hz) and the dissipation range (≈10 Hz and above) exhibit approximate azimuthal symmetry about B₀; the spectra are essentially independent of the azimuthal angle φ, indicating that the dominant anisotropy is a function of the polar angle only. Second, the spectral exponent α varies continuously with θ: for fluctuations perpendicular to B₀ (θ≈90°) the exponent is α = 1.6 ± 0.1, while for fluctuations parallel to B₀ (θ≈0°) it steepens to α = 2.0 ± 0.1. The uncertainties are large enough that both the Kolmogorov‑type 5/3 (α≈1.67) and the Iroshnikov‑Kraichnan‑type 3/2 (α≈1.5) predictions lie within the error bars, so the data do not discriminate between these classic turbulence models.

The continuous change of α with θ is consistent with the “critical balance” picture of anisotropic Alfvénic turbulence, where the cascade proceeds more efficiently across the field than along it. Perpendicular fluctuations retain a relatively shallow spectrum, reflecting strong Alfvénic wave propagation, whereas parallel fluctuations display a steeper spectrum, suggesting that non‑linear interactions are suppressed in that direction. Importantly, the findings mirror those reported by Horbury et al. (2008) for high‑latitude solar wind, indicating that the observed anisotropy is a universal feature of the solar wind, not confined to a specific heliographic latitude.

Methodologically, the study demonstrates that wavelet analysis combined with a locally defined mean field provides a powerful tool for probing directional spectra in space plasmas. It validates the assumption that azimuthal symmetry can be imposed in turbulence models, simplifying the description of the cascade to a dependence on θ alone.

Future work suggested by the authors includes extending the analysis to a broader frequency range, incorporating plasma β and temperature‑anisotropy effects, and applying the technique to multi‑spacecraft data (e.g., MMS, Parker Solar Probe) to resolve three‑dimensional spatial structures. Such extensions will enable more stringent tests of competing turbulence theories (Goldreich‑Sridhar, Boldyrev, etc.) and improve our ability to model solar‑wind–magnetosphere coupling and space‑weather forecasting.