Applicability of Taylor’s hypothesis during Parker Solar Probe perihelia

¹ Department of Aerospace, Physics and Space Sciences, Florida Institute of Technology, Melbourne, Florida 32901, USA
e-mail: jcperez@fit.edu
² Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA
e-mail: sofiane.bourouaine@jhuapl.edu;nour.raouafi@jhuapl.edu
³ School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK

Received: 9 November 2020
Accepted: 24 March 2021

Abstract

We investigate the validity of Taylor’s hypothesis (TH) in the analysis of velocity and magnetic field fluctuations in Alfvénic solar wind streams measured by Parker Solar Probe (PSP) during the first four encounters. The analysis is based on a recent model of the spacetime correlation of magnetohydrodynamic (MHD) turbulence, which has been validated in high-resolution numerical simulations of strong reduced MHD turbulence. We use PSP velocity and magnetic field measurements from 24 h intervals selected from each of the first four encounters. The applicability of TH is investigated by measuring the parameter ϵ = δu₀/√2V_⊥, which quantifies the ratio between the typical speed of large-scale fluctuations, δu₀, and the local perpendicular PSP speed in the solar wind frame, V_⊥. TH is expected to be applicable for ϵ ≲ 0.5 when PSP is moving nearly perpendicular to the local magnetic field in the plasma frame, irrespective of the Alfvén Mach number M_A = V_SW∕V_A, where V_SW and V_A are the local solar wind and Alfvén speed, respectively. For the four selected solar wind intervals, we find that between 10 and 60% of the time, the parameter ϵ is below 0.2 and the sampling angle (between the spacecraft velocity in the plasma frame and the local magnetic field) is greater than 30°. For angles above 30°, the sampling direction is sufficiently oblique to allow one to reconstruct the reduced energy spectrum E(k_⊥) of magnetic fluctuations from its measured frequency spectra. The spectral indices determined from power-law fits of the measured frequency spectrum accurately represent the spectral indices associated with the underlying spatial spectrum of turbulent fluctuations in the plasma frame. Aside from a frequency broadening due to large-scale sweeping that requires careful consideration, the spatial spectrum can be recovered to obtain the distribution of fluctuation’s energy across scales in the plasma frame.