Analytical planar wavefront reconstruction and error estimates for radio detection of extensive air showers

Abstract

When performing radio detection of ultra-high energy astroparticles, the planar wavefront model is often used as a first step to evaluate the arrival direction of primary particles. This model estimates the direction by adjusting the wavefront orientation based on the peak timing of the signal traces from individual antennas. However, despite it's simplicity, the usefulness of this approach is limited by the lack of a good assessment of its robustness and the lack of confidence in its performance. To address these limitations, this study presents two analytical methods to solve for the planar wavefront arrival direction. In addition, we provide the corresponding analytical reconstruction uncertainty, offering a more a more detailed evaluation of the reconstruction's reliability.