Applicability of Taylor's Hypothesis during Parker Solar Probe perihelia

TL;DR

This study assesses when Taylor's Hypothesis is valid for analyzing solar wind turbulence using Parker Solar Probe data, finding it applicable under specific conditions related to the sampling angle and fluctuation speeds.

Contribution

It provides a quantitative criterion for the applicability of Taylor's Hypothesis in solar wind measurements near the Sun, based on the parameter epsilon and sampling angles.

Findings

Taylor's Hypothesis is valid for epsilon less than 0.5 when sampling angles exceed 30 degrees.

Between 10% and 60% of the time, epsilon is below 0.2 for certain intervals.

The measured frequency spectra accurately reflect the spatial turbulence spectra under suitable conditions.

Abstract

We investigate the validity of Taylor's Hypothesis (TH) in the analysis of Alfv\'enic fluctuations of velocity and magnetic fields in solar wind streams measured by Parker Solar Probe (PSP)~during the first four encounters. 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 $\epsilon=\delta u_0/\sqrt{2}V_\perp$, which quantifies the ratio between the typical speed of large-scale fluctuations, $\delta u_0$, and the local perpendicular PSP speed in the solar wind frame, $V_\perp$. TH is expected to be applicable for $\epsilon\lesssim0.5$ when PSP is moving nearly perpendicular to the local magnetic field in the plasma frame, irrespective of the Alfv\'en Mach number $M_{\rm A}=V_{\rm SW}/V_{\rm A}$, where $V_{\rm SW}$ and $V_{\rm A}$ are the local solar wind and Alfv\'en speed, respectively. For the four selected solar wind intervals we find that between 10% to 60% of the time the parameter $\epsilon$ is below 0.2 when the sampling angle (between the spacecraft velocity in the plasma frame and the local magnetic field) is greater than $30^\circ$. For angles above $30^\circ$, the sampling direction is sufficiently oblique to allow one to reconstruct the reduced energy spectrum $E(k_\perp)$ 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 among scales in the plasma frame.