Mass Composition Studies with the Pierre Auger Observatory Surface Detector

The origin and nature of Ultra-High-Energy Cosmic Rays (UHECRs) are still open questions. UHECRs are extreme astrophysical phenomena, single particles with macroscopic energies exceeding $10^{18}\,$eV. Their study is complicated by their extremely minute flux at the highest energies (less than 1 particle per square kilometer per century), where recent results hint at interesting new physics. The cheif architect of these advances is the Pierre Auger Observatory, a cosmic ray detector in Argentina that covers 3000\,km$^2$ with both a surface array of 1660 water-Cherenkov detectors (with 100\% uptime) and a set of 27 fluorescence telescopes (with 15\% uptime). Its hybrid design uses the smaller, robust data sample collected by the fluorescence telescopes to calibrate the energy of surface array's larger dataset. UHECRs cannot be studied directly; instead, their properties must be inferred from the statistical properties of the enormous air showers they produce upon entering the upper atmosphere. UHECR mass composition is studied through the shower depth of maximum development $X_\text{max}$, which is measured directly by the fluorescence detector. In recent years, Auger has extended its hybrid paradigm to mass composition measurements, using the fluorescence detector data to calibrate composition measurements with the surface array. One such technique is the $\Delta$ method, which exploits the composition sensitivity of signal risetimes in the water-Cherenkov tanks. This work presents an update and extension of the $\Delta$ technique to higher zenith angles and updates several data-driven parameterizations and studies of systematic uncertainties essential for the technique. The Fluorescence detector Array of Single-pixel Telescopes (FAST) is a design concept for a next-generation UHECR observatory, aimed at extending current exposures by an order of magnitude with inexpensive fluorescence detectors targeting the highest energy cosmic rays. This work outlines the design, installation, and results of four prototype telescopes running at the two largest UHECR observatories.