The <Δ> methodAn estimator for the mass composition of ultra-high-energy cosmic rays

Abstract

ABSTRACT One of the main characteristics of cosmic rays is their vast energy spectrum, extended from few GeV up to tens of EeV. The ultra-high-energy cosmic rays are only those whose energies are larger than 1 EeV. Cosmic rays are continuously bombarding our atmosphere, but their flux is a decreasing function of the energy, so that for the highest energies only one particle per km^2 and per century reaches the Earth. With this extremely low rate at the highest energies the only way to detect a significant number of particles is by deploying detectors covering enormous areas on the ground. When cosmic rays with these extreme energies arrive to the Earth, they collide with the atmospheric nuclei giving rise to huge showers of billions of secondary particles which propagate through the atmosphere until they are absorbed or reach the ground. The study of ultra-high-energy cosmic rays is done exclusively through these secondary particles, customarily known as Extensive Air Showers (EAS). The Pierre Auger Observatory [1], located in the province of Mendoza, Argentina, is the largest and most sensitive apparatus ever built to record and study EASs. Covering an area of 3000 km^2, this observatory was devised to reveal the nature of ultra-high-energy cosmic rays thanks to a hybrid design which allows the combination of two detection techniques: the detection of fluoresce light and the sampling of the particles that reach the ground. Nowadays there is a large number of unanswered questions related to the nature and origin of ultra-high-energy cosmic rays. One of these puzzles is the determination of the mass composition at the highest energies. This is especially difficult due to two reasons. On the one hand, the most adequate observable, Xmax, is based on fluorescence measurements [2]. This means that the observations are restricted to clear moonless nights, with the subsequent reduction of statistics at energies larger than 10^19.5 eV. On the other hand, to interpret the data, one must use the predictions of hadronic interaction models at centre-of-mass energy around 300 TeV, well beyond what is accessible in the LHC (14TeV). This fact is particularly problematic taking into account that recent observations of the Pierre Auger Observatory suggest that these predictions are inadequate to describe the hadronic component of the EASs [3]. One of the possible solutions to increase the statistics is the use of alternative observables to Xmax, based on data collected with arrays of surface detectors, where the duty cycle is nearly 100%. Nevertheless, most of these observables can not be used to make inferences about mass because they are related to the hadronic component of the air showers and thus the comparison with models result in unreliable predictions. All these obstacles make obvious the necessity of new methods for mass composition studies which allow facing the problem from a new perspective. These new methods should be based on measurements of surface detectors to increase the statistics at the highest energies. It would be also desirable that they are not related to the hadronic component of the EASs, to allow a more reliable comparison with models. The subject of this thesis follows exactly this approach. Using an observable obtained from the surface detectors of the Pierre Auger Observatory, the risetime, we develop a method to infer the mass composition of ultra-high-energy cosmic rays that fulfills the previous requirements. This thesis is organized as follows. Chapter 1 gives an overview of cosmic rays. In chapter 2 the main features of the Pierre Auger Observatory are described in detail. Chapter 3 is dedicated exclusively to the experimental determination of the risetime. In chapter 4 we introduce the specific method used in this thesis to study mass composition: the ⟨Δ⟩ method. In chapters 5 and 6 we apply the ⟨Δ⟩ method to data collected with the Pierre Auger Observatory. In chapter 5 we use the data collected with the array of surface detectors whose separation is 1500 m while in chapter 6 we use a smaller array with a separation between detectors amounting to 750 m. The difference between both data sets comes from the different energy ranges. The 1500 m array is fully efficient for above 3 EeV while the 750 m array provides data at lower energies. The chapter 7 shows the combination of the results obtained in chapters 5 and 6. Finally, in chapter 8 we conclude this thesis using the observable ⟨Δ⟩ for an additional purpose: to assess the level of concordance between data and the predictions provided by hadronic interactions models tuned to reproduced LHC data.