Multi-spacecraft Analysis of the Properties of Magnetohydrodynamic Fluctuations in Sub-Alfv\'enic Solar Wind Turbulence at 1 AU

Abstract

We present three-dimensional magnetic power spectra in wavevector space to investigate anisotropy and scalings of sub-Alfv\'enic solar wind turbulence at magnetohydrodynamic (MHD) scale using the Magnetospheric Multiscale spacecraft. The magnetic power distributions are organized in a new coordinate determined by wavevectors (k) and background magnetic field ($b_0$) in Fourier space. This study utilizes two approaches to determine wavevectors: singular value decomposition method and timing analysis. The combination of the two methods allows an examination of magnetic field properties in terms of mode compositions without any spatiotemporal hypothesis. Observations show that fluctuations ($\delta B_{\perp1}$) in the direction perpendicular to k and $b_0$ prominently cascade perpendicular to $b_0$, and such anisotropy increases with wavenumber. The reduced power spectra of $\delta B_{\perp1}$ follow Goldreich-Sridhar scalings: $P(k_\perp)\sim k_\perp^{-5/3}$ and $P(k_{||}) \sim k_{||}^{-2}$. In contrast, fluctuations within $kb_0$ plane show isotropic behaviors: perpendicular power distributions are approximately the same as parallel distributions. The reduced power spectra of fluctuations within $kb_0$ plane follow the scalings: $P(k_\perp)\sim k_\perp^{-3/2}$ and $P(k_{||})\sim k_{||}^{-3/2}$. Comparing frequency-wavevector spectra with theoretical dispersion relations of MHD modes, we find that $\delta B_{\perp1}$ are probably associated with Alfven modes. Moreover, for the Alfv\'enic component, the ratio of cascading time to the wave period is found to be a factor of a few, consistent with critical balance in the strong turbulence regime. The magnetic field fluctuations within $kb_0$ plane more likely originate from fast modes based on isotropic behaviors.