Inferring the mass composition of ultra-high-energy cosmic rays through the characterisation of the muon production profile

Resumen

Introduction. In the early twentieth century, Victor Hess [1] discovered the extra-terrestrial origin of cosmic rays. For over 100 years, physicists have studied this radiation with increasingly precise techniques. The existence of muons, mesons and even antimatter was discovered by the careful study of cosmic rays. The cosmic ray energy spectrum spans over eleven orders of magnitude, from the GeV cosmic rays of solar origin up the ultra-high-energy cosmic rays (UHECRs) with energies larger than 10 to the 18 eV. Cosmic rays are continuously bombarding the atmosphere isotropically, but their flux is rapidly decreasing with the energy, so at the highest energies only one particle per square kilometre per century reaches the Earth. This extremely low rate has immediate consequences on their detection, which is generally achieved by deploying detectors covering large areas on ground. When cosmic rays collide with atmospheric nuclei, they produce secondary particles which are energetic enough to keep the process going, subsequently giving birth to billions of secondary particles that propagate through the atmosphere and eventually reach ground. These secondary particles, known as Extensive Air Showers (EASs), are registered by the detectors, and from them one extracts information regarding the energy, origin and composition of the primary particle. The properties of the mechanism of generation of secondaries are complex, and depend strongly on the first interaction, which takes place at an energy beyond the ones reached at accelerators. As a consequence, the analysis of UHECRs is subject to large uncertainties and hence, many of their properties, in particular their composition, are still unclear. The Pierre Auger Observatory. The Pierre Auger Observatory [2], located in the province of Mendoza, Argentina, was designed to study the properties of UHECRs. It is the largest hybrid detector ever built, combining a fluorescence detector (FD) and a surface detector (SD). The FD collects the ultraviolet light emitted by the de-excitation of nitrogen nuclei in the atmosphere, and can operate only in clear, moonless nights. The SD samples the density of particles at ground level using more than 1600 Water- Cherenkov tanks deployed over an area of about 3000 km2 and has a nearly 100% duty cycle. Mass composition of UHECRs. The main goal of this thesis is the measurement of the mass composition of UHECRs using data of the SD. The correct determination of the mass composition is key in order to understand the origin of cosmic radiation and the mechanisms of acceleration that can boost particles up to such enormous energies. These questions remain unanswered after more than one century of cosmic ray Physics. The Pierre Auger Observatory has published prominent results regarding mass composition of UHECRs using FD measurements [3]. However, it is of much interest to measure the mass composition of UHECRs using only SD data, as they provide an independent measurement that can either support or disfavour FD results. Moreover, the large duty cycle of the SD yields an event statistics one order of magnitude larger than the FD, which opens the window to a better characterisation of the very largest energies, at which the flux is extremely low. In this thesis, the analysis of mass composition of UHECRs is performed through the characterisation of the longitudinal development of the muonic component of EASs. Chapter 1 gives an overview of cosmic rays, including some of the most relevant experimental results. In chapter 2, the main features of the Pierre Auger Observatory are described in detail, including the reconstruction of the most relevant variables. Chapter 3 concludes the review of previous results with a thorough description of the shower development and the most relevant variables that have been proposed to infer the mass composition of UHECRs. Chapters 4 and 5 introduce the main caveats that were found while aiming to obtain a good reconstruction of the variables of interest, together with the proposed solutions. Chapter 6 explores the possibility of measuring shower-to-shower fluctuations with the SD, as an independent hint of mass composition. All of these measurements are interpreted in chapter 7 in terms of mass composition, where some future potentialities of the method are introduced for further work. Finally, a few additional mathematical details are briefly described in the appendixes. Conclusions. The main topic addressed by this thesis is the measurement of the mass composition of ultra- high-energy cosmic rays (UHECRs) using data from the surface detector (SD) of the Pierre Auger Observatory. The determination of the mass composition of UHECRs is a long-standing problem of great interest to the scientific community, for it can help understanding the origin and mechanisms of acceleration of these highly energetic particles. The starting point of this thesis is the reconstruction of the muon production depth profile (MPD), which was introduced some years ago as a proof-of-concept by the same research group. The main goal of this work is to widen the zenith and energy windows that are suitable of being analysed. This poses different problems that were addressed sequentially. Correction of the radial dependence of MPDs. Using Monte Carlo simulations, we introduced an empirical factor that corrects for the dependence of the MPD with the observation distance r. This factor acts as a transformation on the production distance of muons measured vertically, zv, so that their distribution after the transformation does not depend on r. The analytical expression of this factor is (equation (1)) z'v = zv (zv tan2(theta)-r)/(zv tan2(theta)-r0) where theta is the zenith angle and r0 a free parameter which represent the optimum observation distance at which the observed MPD is identical to the full MPD apart from a scaling factor. It was shown that this correction fulfils all the pre-requisites. In particular, it makes for an unbiased reconstruction of the maximum of the MPD Xµmax regardless of the observation point. Extension of the MPD analysis to a wider zenith and energy range In order to apply equation (1) to shower reconstructions, parameter r0 needs to be parametrised in terms of the primary energy and zenith angle. It was shown that this parametrisation is robust under different primaries and hadronic models. Another caveat of reconstructing MPDs at smaller zenith angle is the increase of the electro- magnetic contamination. This problem was solved using a two-fold strategy, that lays on both rejecting very late signals and choosing an appropriate signal threshold, in such a way that muonic signal is enhanced over electromagnetic signal. Putting everything together, it was shown that it is possible to reconstruct the MPD using stations further than r > 1000 m and closer than r < 4000 m with a total electromagnetic contamination that is always below 26% and a total efficiency selecting muons above 92%. Finally, in order to simultaneously analyse a zenith window of 20º width, it becomes necessary to refer all the values of Xµmax to a common zenith angle. For that purpose, the slope of the dependence of Xµmax versus the cosine of theta was parametrised and used to build Xµmax55 , which represents the equivalent Xµmax referred to a 55º. The most relevant improvements are a reduction of the resolution of about 20 g/cm2 at low energy1 and about 10 g/cm2 at large energy, and an increase in the available statistics by about a factor eight. Measuring shower-to-shower fluctuations with the SD. Being all of the stated above of much interest, the most relevant result presented in this work has to do with the measurement of the shower-to-shower fluctuations. This thesis demonstrates that the resolution of the detector in the determination of Xµmax can be obtained using a data-driven method. This method is based on the splitting of SD station into two equivalent sets in terms of their azimuth angle, taking advantage of the azimuthal symmetry. It was shown that, apart from a statistical factor, the comparison of the two reconstructed values of Xµmax55 yields a good estimate of the detector resolution. Furthermore, it was shown that this resolution has negligible dependence with the hadronic model, and that data are well bracketed by Monte Carlo simulations. The correct determination of the detector resolution allows for a subtraction of the resolution to the observed fluctuations in order to correctly obtain the physical fluctuations. This is an innovative and independent measurement of the mass composition of UHECRs in the context of MPDs. Furthermore, the method developed to determine the resolution of the detector for this particular observable can be used for other observables straightforwardly, and hence constitutes a valuable tool for the future. Interpretation of the first two moments of the MPD distribution. The measured values of <Xµmax> and sigma(Xµmax) can be interpreted within the framework of the superposition model [4]. In particular, the values of <ln A> and sigma2(lnA) , i. e., the first two moments of the lnA distribution, where A represents the mass number of the primary, can be inferred using <lnA>=ln56 (<Xµmax>p - <Xµmax>)/(<Xµmax>p - <Xµmax>Fe) sigma2 = [ln56]2 (sigma2 (Xµmax)p- [1-a<lnA>] )/(<Xµmax>p - <Xµmax>Fe)2 The obtained values of <lnA> agree remarkably well with the previous measurements of the standard MPD analysis at 60º . However, the interpretation of <lnA> is difficult when the hadronic model Epos-LHC is used to interpret data, as they yield a much larger average logarithm mass than the results of the fluorescence detector (FD). In terms of sigma2 , the results agree with the FD in the whole energy range. Nevertheless, for the hadronic model QGSJetII-04 some negative values of sigma2 are found, which makes no physical sense. By analysing the trend of these two observables, we can conclude that no hadronic model correctly describes simultaneously the mean and spread of lnA predicted by the MPD measurement. This technique, hence, can be used to constrain the predictions of hadronic models in the muonic sector. Concerning mass composition, we conclude that the measurements obtained by the Pierre Auger Observatory both by the SD and the FD clearly disfavour a pure light composition at the highest energies. Correlation between Xmax and Xµmax55. The combination of Xµmax55 with measurements of the FD was also explored. This combination was impossible under the standard MPD analysis, as the statistics was too scarce. It was shown that under the new approach to the MPD reconstruction it is possible to establish the correlation between Xµmax55 and Xmax . This analysis has a large potentiality for the future, as the sensitivity of the mass inference significantly improves when adding multiple mass-sensitive variables to the analysis. However, before being able to use these two variables in a multi-dimensional analysis, a full understanding of the influence of the detector resolution, especially in the case of Xµmax,55 given its relatively large value, is required. References. [1] V.F. Hess, Phys.Z., 1084 [2] J. Abraham et al., Nucl.Inst.Meth. A523 (2004), 50. [3] J. Abraham et al., Phys.Rev.Lett. 104 (2010), 091101. [4] P. Abreu et al., JCAP 1302 (2013), 026.