Development of the Reconstruction Procedure of the Fluorescence detector Array of Single-pixel Telescopes for measuring Ultra-High Energy Cosmic Rays

Abstract

The Fluorescence detector Array of Single-pixel Telescopes aims to deploy an array of simplified, autonomous fluorescence telescopes over an area of $\sim60,000$ km$^{2}$ to observe ultra-high energy cosmic rays. The unprecedented size of such an array will enable measurements of cosmic rays with energies above 10$^{20}$ eV with large statistics, providing new insights into UHECR sources. With a single FAST telescope consisting of just four photomultiplier tubes, traditional techniques to reconstruct observed extensive air showers are not applicable. Instead, FAST utilises a top-down approach where simulations are directly compared to data and the best match chosen via a maximum likelihood estimation. This method, known as the "top-down reconstruction (TDR)", requires an accurate "first guess" of the shower parameters to be successful. In this work, improvements to the efficiency and precision of the TDR are made and two different first guess estimation methods are investigated. The combined performance of a machine-learning-based first guess and improved TDR is shown to achieve resolutions in the shower arrival direction, depth of shower maximum and shower energy of $\sim2^\circ$, $\sim30$ g cm$^{-2}$ and $\sim7\%$ respectively for simulated events observed from two or more locations. The improved reconstruction is then applied to data from the current FAST prototype installations at the Pierre Auger Observatory and Telescope Array experiment. Using these results, the first measurements of the UHECR energy spectrum and composition by FAST are presented.