Multi-spacecraft Analysis of the Properties of Magnetohydrodynamic
  Fluctuations in Sub-Alfv\'enic Solar Wind Turbulence at 1 AU
  We present observations of three-dimensional magnetic power spectra in
wavevector space to investigate the anisotropy and scalings of sub-Alfv\'enic
solar wind turbulence in low$-\beta_p$ plasma 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: the singular value decomposition method
and multi-spacecraft timing analysis. The combination of both methods allows an
examination of magnetic field fluctuation properties in terms of mode
compositions without 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 Alfv\'en modes. On the other hand, magnetic field
fluctuations within $kb_0$ plane more likely originate from fast modes in
low-$\beta_p$ plasma based on their isotropic behaviors. The observations of
anisotropy and scalings of different magnetic field components are consistent
with the predictions of current compressible MHD theory.
