Reconstructing the spatial field-perpendicular energy spectrum of magnetic fluctuations near and below the Alfven critical point

In this work we introduce a new methodology to reconstruct the spatial field-perpendicular energy spectrum of magnetic fluctuations from single-point measurements when Taylor Hypothesis is no longer valid, which is expected to be the case in solar wind streams measured by Parker Solar Probe (PSP) near the Alfven critical point where the Alfven Mach number MA ~1 (the ratio between the solar wind speed and the local Alfven speed). The methodology is based on a recent model of the spacetime correlation of magnetohydrodynamic (MHD) turbulence (Bourouaine and Perez 2019; Perez and Bourouaine 2020). In this model, contrary to the common expectation that the validity of TH requires high values of the Alfven Mach number (MA>>1), the validity of TH is determined instead by a parameter ϵ, which quantifies the ratio between the typical speed of large-scale fluid fluctuations and the local field-perpendicular PSP speed in the solar wind frame of reference. Here, we check the validity of TH using data from PSP during its encounters ten and eleven. Our analysis includes intervals in which MA is in the order of one as well as MA<1 (sub-Alfvenic intervals). The selected intervals are classified according to the parameter ϵ, the Alfven Mach number MA, sampling angle as well as other turbulence properties, and are then used to reconstruct the spatial (field-perpendicular) energy spectrum of magnetic fluctuations versus wavenumber from its measured frequency spectra.