Towards event-by-event studies of the ultrahigh-energy cosmic-ray composition

Abstract

We suggest a method which improves the precision of studies of the primary composition of ultra-high-energy cosmic rays. Two principal ingredients of the method are: (1) comparison of the observed and simulated parameters for individual showers, without averaging over arrival directions and (2) event-by-event selection of simulated showers by the physical observables and not by the reconstructed primary parameters. A detailed description of the algorithm is presented and illustrated by several examples.

Introduction

The determination of the primary composition of cosmic rays with energies higher than ∼10¹⁷ eV is a real challenge. The lack of knowledge of the types of primary ultra-high-energy particles which induce extensive air showers makes it difficult to study their origin and in some cases even to determine their energy spectrum. More precise and less model-dependent determination of the cosmic-ray primary composition, especially in the highest-energy domain, is one of the most important tasks in contemporary astroparticle physics (for a review and discussions see e.g. Ref. [1]).

Ultra-high-energy cosmic rays are observed through air showers, and to extract information about the primary particle, selected observables of real air showers are compared to those of simulated ones for different primaries. Because of large shower-to-shower fluctuations, one cannot determine the primary-particle type of an individual air shower. That is why traditional approaches to the composition studies are based on the determination of average characteristics of a large sample of cosmic-ray events. This approach has obvious advantages: for a homogeneous composition, averaging smoothens out the fluctuations, and large statistics results in higher precision. Furthermore, the computational time required to perform reliable simulations of an observable averaged over a large sample is much smaller than that necessary for detailed simulations of all events in the data set. However, for mixed composition, averaging might become a problem because fluctuations of the discriminating observables over their central values are larger when air showers from different arrival directions are combined in one sample. Different zenith angles correspond to different atmospheric depths, and air showers detected by surface arrays have different stages of development and hence may have quite different observable parameters even for the same energies and primaries. Moreover, the geomagnetic field introduces the azimuthal dependence for photon [2] and very inclined hadron [3] showers. Even fluorescent detectors, which observe the shower development on its way through the atmosphere, respond to showers from different arrival directions in different ways, notably with different accuracies. For γ-ray primaries at $E\gtrsim 5\times {10}^{19}\text{eV}$, the entire shower development is direction-dependent.

We suggest to improve considerably the precision of the composition studies by performing individual simulations for each observed high-energy event. In the case of a large number of events in a data sample, averaging in bins of arrival directions may be used. If one is not interested in the study of possible γ-ray primaries with $E\gtrsim 5\times {10}^{19}\text{eV}$, binning in zenith angle only is often sufficient.

This method, in its simplest form with one observable, has been successfully implemented to obtain a limit on the γ-ray fraction in the primary flux at $E>{10}^{20}\text{eV}$ using the data of the AGASA and Yakutsk experiments [4]. Event-by-event simulations (without selection by reconstructed parameters) were previously used for the composition studies in Refs. [5], [6], [7].

The rest of the paper is organized as follows. In Section 2, we present the sketch of the event-by-event approach to the composition studies, discuss the choice of the air-shower observables (Section 2.1), give a general idea of how to constrain the probable primary-particle type of an individual air shower (Section 2.2) and how to use these shower-by-shower constraints to gain information about the chemical composition of the primary cosmic-ray flux using a sample of events (Section 2.3). Section 3 contains the detailed description of the procedure outlined in Section 2 and ready-to-use formulae implementing this procedure. Section 4 presents several examples which illustrate the method by the analysis of small (and hence statistically insignificant) samples of events. There, we consider only one composition-related observable, the muon density, and use samples of highest-energy AGASA and Yakutsk events as examples. In Section 4.1, we analyse in detail a single event (the highest energy air shower reported by AGASA). The procedure for estimating the limit on the fraction of particular primaries in a given energy range is illustrated in Section 4.2 with the sample of six AGASA showers with reported energies higher than 10²⁰ eV and known muon content, while the algorithm to determine the best-fit composition assuming two possible primaries is illustrated in Section 4.3 with a sample of four events with reported energies above $1.5\times {10}^{20}\text{eV}$ detected by the AGASA and Yakutsk experiments. Both samples are small and the analysis of Section 4 serves for illustrative purposes only. We briefly summarize and discuss novelties of our method in Section 5. Some of our notations are summarized in Appendix A. Appendix B Observed and simulated events used in examples, Appendix C Reconstruction of energy and muon density contain technical information related to the examples presented in Section 4.