Solar wind data analysis aided by synthetic modeling: a better understanding of plasma-frame variations from temporal data

In-situ measurements of the solar wind, a turbulent and anisotropic plasma flow originating at the Sun, are mostly carried out by single spacecraft, resulting in one-dimensional time series. The conversion of these measurements to the spatial frame of the plasma is a great challenge, but required for direct comparison of the measurements with MHD turbulence theories. Here we present a toolkit, based on the synthetic modeling of solar wind fluctuations as two-dimensional noise maps with adjustable spectral and power anisotropy, that can help with the temporal-spatial conversion of real data. Specifically, by following the spacecraft trajectory through a noise map (relative velocity and angle relative to some mean magnetic field) with properties tuned to mimic those of the solar wind, the likelihood that the temporal data fluctuations represent parallel or perpendicular fluctuations in the plasma frame can be quantified by correlating structure functions of the noise map. Synthetic temporal data can also be generated, which can provide a testing ground for analysis applied to the solar wind data. We demonstrate this tool by investigating Parker Solar Probe's E7 trajectory and data, and showcase several possible ways in which it can be used. We find that whether temporal variations in the spacecraft frame come from parallel or perpendicular variations in the plasma frame strongly depends on the spectral and power anisotropy of the measured wind. Data analysis assisted by such underlying synthetic models as presented here could open up new ways to interpret measurements in the future, specifically in the more reliable determination of plasma frame quantities from temporal measurements.