Hybrid Universality Model Development and Air Shower Reconstruction for the Pierre Auger Observatory

Cosmic rays have been studied for more than 100 years, providing valuable information on the measured spectrum and theories to particle propagation and interaction. Potential sources, which could also serve possible acceleration mechanisms, include active galactic nuclei, gamma-ray bursts and supernova shock fronts. Due to our increased understanding of cosmic ray physics and technological improvements on a detector level, measurements have progressed towards even higher energies than before. To understand their origin, it is pertinent to understand their mass composition, energy spectrum and arrival direction. Laboratory-based particle accelerators and low energy cosmic ray experiments have elucidated our understanding of particle interaction, providing insight on possible acceleration and propagation models. However, ultra-high cosmic rays at $10^{20}$ eV are significantly above the highest energies achievable by the LHC (about two orders of magnitude between the center-of-mass energies). They are also very rare; with an incident flux of 1 particle per $km^{2}$ per century at $10^{20}$ eV. Accelerator-based models can be extrapolated to the highest energies. However, it is pertinent for large-scale detectors to be able to measure unique properties of cosmic rays interacting with the detection medium. The Auger is the largest cosmic ray detector to date, covering an area of more than 3000 ${km^{2}}$. It utilizes surface, underground and fluorescence techniques to measure the macroscopic properties of extensive air showers (initiated by a cosmic ray particle interacting with a nucleus in the atmosphere). Through the fluorescence technique the longitudinal profile can be directly observed. From its maximum, $X_{\text{max}}$, the cosmic ray mass can be inferred. However, due to specific operational conditions it has a duty cycle of $\approx15$%, limiting the statistics of more energetic events. The surface and underground detectors can measure data with a duty cycle of $\approx100$%. Most surface detectors are distributed in a triangular grid with a spacing of 1500 m. A small fraction is distributed in an infilled grid with a spacing of 750 m. Furthermore, each surface detector in the filled grid is paired with an underground detector. Their combined information provides another mass composition sensitive parameter -the muon content. Air shower universality capitalizes on the universal shape of the longitudinal profile, irrespective of primary or hadronic model. It encapsulates the underlying shower physics and allows for a reconstruction based on mass-composition sensitive shower parameters (the shower maximum $X_{\text{max}}$, maximum of muon production depth $X^{\mu}_{\text{max}}$ and relative muon content $R_{\mu}$) seen through unique features in the time and signal distributions. The universality approach allows for a highly modular reconstruction algorithm, set as a function of primary energy, mass and geometry. The major focus of this work was the development of the a new signal and time model for secondary particles at ground seen by the WCD and MD, as well as dedicated efforts to effectively process large quantities of simulated air showers. Reconstructed air shower simulations were studied and compared for contemporary high energy hadronic interaction models. In this work, I show how I could successfully model the signal in the detector corresponding to air showers between $10^{17}$ eV and $10^{20}$ eV with uncertainties below the 5% level. The temporal distribution is also successfully modelled, mostly within the 3% level. A novelty, the maximum muon production depth, $X^{\mu}_{\text{max}}$, has been successfully introduced into the MD universality models. With the newly obtained WCD and MD, I could prove that the muon content, $R_{\mu}$, is a global shower variable. Furthermore, first analysis was performed on hybrid reconstructions for the infilled detector setup. Preliminary resolutions of the shower parameters $X_{\text{max}}$ and $X^{\mu}_{\text{max}}$ are of the order 40 ${g cm^{-2}}$ and 50 ${g cm^{-2}}$ respectively, which can be further enhanced. Also, the quality of $R_{\mu}$ has greatly improved, with an uncertainty of only 10%. This work sets an important basis for future analyses (mass composition and shower physics) with data from the WCD and MD. Results obtained in this work could also be used for new detector systems, such as the SSD (part of the AugerPrime upgrade).