Beyond the maltese cross: Geometry of turbulence between 0.2 and 1 au

The spectral anisotropy of turbulent structures has been measured in the solar wind since 1990, relying on the assumption of axisymmetry about the mean magnetic field, B0. However, several works indicate that this hypothesis might be partially wrong, thus raising two questions: (i) is it correct to interpret measurements at 1 au (the so-called Maltese cross) in term of a sum of slab and two-dimensional (2D) turbulence; and (ii) what information is really contained in the Maltese cross? We solve direct numerical simulations of the magnetohydrodynamic equations including the transverse stretching exerted by the solar wind flow and study the genuine 3D anisotropy of turbulence as well as that one resulting from the assumption of axisymmetry about B0. We show that the evolution of the turbulent spectrum from 0.2 to 1 au depends strongly on its initial anisotropy. An axisymmetric spectrum with respect to B0 keeps its axisymmetry, i.e., resists stretching perpendicular to radial, while an isotropic spectrum becomes essentially axisymmetric with respect to the radial direction. We conclude that close to the Sun, slow-wind turbulence has a spectrum that is axisymmetric around B0 and the measured 2D component at 1 au describes the real shape of turbulent structures. In contrast, fast-wind turbulence has a more isotropic spectrum at the source and becomes radially symmetric at 1au. Such structure is hidden by the symmetrization applied to the data that instead returns a slab geometry.